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Diffusion MRI is a powerful tool that serves as a bridge between brain microstructure and cognition. Recent advancements in cognitive neuroscience have highlighted the persistent challenge of understanding how individual differences in brain structure influence behavior, especially in healthy people. While traditional linear models like Canonical Correlation Analysis (CCA) and Partial Least Squares (PLS) have been fundamental in this analysis, they face limitations, particularly with high-dimensional data analysis outside the training sample. To address these issues, we introduce a novel approach using deep learninga multivariate autoencoder model-to explore the complex non-linear relationships between brain microstructure and cognitive functions. The model's architecture involves separate encoder modules for brain structure and cognitive data, with a shared decoder, facilitating the analysis of multivariate patterns across these domains. Both encoders were trained simultaneously, before the decoder, to ensure a good latent representation that captures the phenomenon. Using data from the Human Connectome Project, our study centres on the insula's role in cognitive processes. Through rigorous validation, including 5 sample analyses for out-of-sample analysis, our results demonstrate that the multivariate autoencoder model outperforms traditional methods in capturing and generalizing correlations between brain and behavior beyond the training sample. These findings underscore the potential of deep learning models to enhance our understanding of brain-behavior relationships in cognitive neuroscience, offering more accurate and comprehensive insights despite the complexities inherent in neuroimaging studies.

The estimation of directed couplings between the nodes of a network from indirect measurements is a central methodological challenge in scientific fields such as neuroscience, systems biology and economics. Unfortunately, the problem is generally ill-posed due to the possible presence of unknown delays in the measurements. In this paper, we offer a solution of this problem by using a variational Bayes framework, where the uncertainty over the delays is marginalized in order to obtain conservative coupling estimates. To overcome the well-known overconfidence of classical variational methods, we use a hybrid-VI scheme where the (possibly flat or multimodal) posterior over the measurement parameters is estimated using a forward KL loss while the (nearly convex) conditional posterior over the couplings is estimated using the highly scalable gradient-based VI. In our ground-truth experiments, we show that the network provides reliable and conservative estimates of the couplings, greatly outperforming similar methods such as regression DCM.

In 1982, Cameron and Liebler investigated certain "special sets of lines" in PG(3,q), and gave several equivalent characterizations. Due to their interesting geometric and algebraic properties, these "Cameron-Liebler line classes" got a lot of attention. Several generalizations and variants have been considered in the literature, the main directions being a variation of the dimensions of the involved spaces, and studying the analogous situation in the subset lattice. An important tool is the interpretation of the objects as Boolean functions in the "Johnson" and "q-Johnson schemes". In this article, we develop a unified theory covering all these variations. Generalized versions of algebraic and geometric properties will be investigated, having a parallel in the notion of "designs" and "antidesigns" in association schemes, which is connected to Delsarte's concept of "design-orthogonality". This leads to a natural definition of the "degree" and the "weights" of functions in the ambient scheme, refining the existing definitions. We will study the effect of dualization and of elementary modifications of the ambient space on the degree and the weights. Moreover, a divisibility property of the sizes of Boolean functions of degree t will be proven.

Combinatorial designs have been studied for nearly 200 years. 50 years ago, Cameron, Delsarte, and Ray-Chaudhury started investigating their $q$-analogs, also known as subspace designs or designs over finite fields. Designs can be defined analogously in finite classical polar spaces, too. The definition includes the $m$-regular systems from projective geometry as the special case where the blocks are generators of the polar space. The first nontrivial such designs for $t > 1$ were found by De Bruyn and Vanhove in 2012, and some more designs appeared recently in the PhD thesis of Lansdown. In this article, we investigate the theory of classical and subspace designs for applicability to designs in polar spaces, explicitly allowing arbitrary block dimensions. In this way, we obtain divisibility conditions on the parameters, derived and residual designs, intersection numbers and an analog of Fisher's inequality. We classify the parameters of symmetric designs. Furthermore, we conduct a computer search to construct designs of strength $t=2$, resulting in designs for more than 140 previously unknown parameter sets in various classical polar spaces over $\mathbb{F}_2$ and $\mathbb{F}_3$.

Previous work on additively-manufactured oxide dispersion strengthened alloys focused on experimental approaches, resulting in larger dispersoid sizes and lower number densities than can be achieved with conventional powder metallurgy. To improve the as-fabricated microstructure, this work integrates experiments with a thermodynamic and kinetic modeling framework to probe the limits of the dispersoid sizes and number densities that can be achieved with powder bed fusion-laser beam. Bulk samples of a Ni-20Cr $+$ 1 wt.% Y$_2$O$_3$ alloy are fabricated using a range of laser power and scanning velocity combinations. Scanning transmission electron microscopy characterization is performed to quantify the dispersoid size distributions across the processing space. The smallest mean dispersoid diameter (29 nm) is observed at 300 W and 1200 mm/s, with a number density of 1.0$\times$10$^{20}$ m$^{-3}$. The largest mean diameter (72 nm) is observed at 200 W and 200 mm/s, with a number density of 1.5$\times$10$^{19}$ m$^{-3}$. Scanning electron microscopy suggests that a considerable fraction of the oxide added to the feedstock is lost during processing, due to oxide agglomeration and the ejection of oxide-rich spatter from the melt pool. After accounting for these losses, the model predictions for the dispersoid diameter and number density align with the experimental trends. The results suggest that the mechanism that limits the final number density is collision coarsening of dispersoids in the melt pool. The modeling framework is leveraged to propose processing strategies to limit dispersoid size and increase number density., Comment: Main text: 37 pages, 20 figures

In today's digital world, cybercrime is responsible for significant damage to organizations, including financial losses, operational disruptions, or intellectual property theft. Cyberattacks often start with an email, the major means of corporate communication. Some rare, severely damaging email threats - known as spear phishing or Business Email Compromise - have emerged. However, the literature disagrees on their definition, impeding security vendors and researchers from mitigating targeted attacks. Therefore, we introduce targeted attacks. We describe targeted-attack-detection techniques as well as social-engineering methods used by fraudsters. Additionally, we present text-based attacks - with textual content as malicious payload - and compare non-targeted and targeted variants.

Given observed data and a probabilistic generative model, Bayesian inference searches for the distribution of the model's parameters that could have yielded the data. Inference is challenging for large population studies where millions of measurements are performed over a cohort of hundreds of subjects, resulting in a massive parameter space. This large cardinality renders off-the-shelf Variational Inference (VI) computationally impractical. In this work, we design structured VI families that efficiently tackle large population studies. Our main idea is to share the parameterization and learning across the different i.i.d. variables in a generative model, symbolized by the model's \textit{plates}. We name this concept \textit{plate amortization}. Contrary to off-the-shelf stochastic VI, which slows down inference, plate amortization results in orders of magnitude faster to train variational distributions. Applied to large-scale hierarchical problems, PAVI yields expressive, parsimoniously parameterized VI with an affordable training time. This faster convergence effectively unlocks inference in those large regimes. We illustrate the practical utility of PAVI through a challenging Neuroimaging example featuring 400 million latent parameters, demonstrating a significant step towards scalable and expressive Variational Inference.

In 1985, Janko and Tran Van Trung published an algorithm for constructing symmetric designs with prescribed automorphisms. This algorithm is based on the equations by Dembowski (1958) for tactical decompositions of point-block incidence matrices. In the sequel, the algorithm has been generalized and improved in many articles. In parallel, higher incidence matrices have been introduced by Wilson in 1982. They have proven useful for obtaining several restrictions on the existence of designs. For example, a short proof of the generalized Fisher's inequality makes use of these incidence matrices. In this paper, we introduce a unified approach to tactical decompositions and incidence matrices. It works for both combinatorial and subspace designs alike. As a result, we obtain a generalized Fisher's inequality for tactical decompositions of combinatorial and subspace designs. Moreover, our approach is explored for the construction of combinatorial and subspace designs of arbitrary strength.

Given some observed data and a probabilistic generative model, Bayesian inference aims at obtaining the distribution of a model's latent parameters that could have yielded the data. This task is challenging for large population studies where thousands of measurements are performed over a cohort of hundreds of subjects, resulting in a massive latent parameter space. This large cardinality renders off-the-shelf Variational Inference (VI) computationally impractical. In this work, we design structured VI families that can efficiently tackle large population studies. To this end, our main idea is to share the parameterization and learning across the different i.i.d. variables in a generative model -symbolized by the model's plates. We name this concept plate amortization, and illustrate the powerful synergies it entitles, resulting in expressive, parsimoniously parameterized and orders of magnitude faster to train large scale hierarchical variational distributions. We illustrate the practical utility of PAVI through a challenging Neuroimaging example featuring a million latent parameters, demonstrating a significant step towards scalable and expressive Variational Inference.

The silicification of DNA origami structures increases their mechanical and thermal stability and provides chemical protection. So far, it is unclear how silicification affects the internal structure of the DNA origami and whether the whole DNA framework is embedded or if silica just forms an outer shell. By using in situ small-angle X-ray scattering (SAXS), we show that the net-cationic silica precursor TMAPS induces substantial condensation of the DNA origami, which is further enhanced by the addition of TEOS at early reaction times to an almost 10 % size reduction. We identify the SAXS Porod invariant as a reliable, model-free parameter for the evaluation of the amount of silica formation at a given time. Contrast matching of the DNA double helix Lorentzian peak reveals that silica growth also occurs on the inner surfaces of the origami. The less polar silica forming within the origami structure, replacing more than 40 % of the internal hydration water causes a hydrophobic effect: origami condensation. In the maximally condensed state, thermal stabilization of the origami up to 60 {\deg}C could be observed. If the reaction is driven beyond this point, the overall size of the silicified origami increases again due to more and more silica deposition on the DNA origami. DNA origami objects with flat surfaces show a strong tendency towards aggregation during silicification, presumably driven by the very same entropic forces causing condensation. Our studies provide novel insights into the silicification reaction and hints for the formulation of optimized reaction protocols.

Researchers in neuroscience have a growing number of datasets available to study the brain, which is made possible by recent technological advances. Given the extent to which the brain has been studied, there is also available ontological knowledge encoding the current state of the art regarding its different areas, activation patterns, key words associated with studies, etc. Furthermore, there is an inherent uncertainty associated with brain scans arising from the mapping between voxels -- 3D pixels -- and actual points in different individual brains. Unfortunately, there is currently no unifying framework for accessing such collections of rich heterogeneous data under uncertainty, making it necessary for researchers to rely on ad hoc tools. In particular, one major weakness of current tools that attempt to address this kind of task is that only very limited propositional query languages have been developed. In this paper, we present NeuroLang, an ontology language with existential rules, probabilistic uncertainty, and built-in mechanisms to guarantee tractable query answering over very large datasets. After presenting the language and its general query answering architecture, we discuss real-world use cases showing how NeuroLang can be applied to practical scenarios for which current tools are inadequate.

Multivariate anomaly detection can be used to identify outages within large volumes of telemetry data for computing systems. However, developing an efficient anomaly detector that can provide users with relevant information is a challenging problem. We introduce our approach to hierarchical multivariate anomaly detection called DeCorus, a statistical multivariate anomaly detector which achieves linear complexity. It extends standard statistical techniques to improve their ability to find relevant anomalies within noisy signals and makes use of types of domain knowledge that system operators commonly possess to compute system-level anomaly scores. We describe the implementation of DeCorus an online log anomaly detection tool for network device syslog messages deployed at a cloud service provider. We use real-world data sets that consist of $1.5$ billion network device syslog messages and hundreds of incident tickets to characterize the performance of DeCorus and compare its ability to detect incidents with five alternative anomaly detectors. While DeCorus outperforms the other anomaly detectors, all of them are challenged by our data set. We share how DeCorus provides value in the field and how we plan to improve its incident detection accuracy., Comment: 11 pages, 4 figures, draft

Effective characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in diffusion MRI (dMRI). Solving the problem of relating the dMRI signal with cytoarchitectural characteristics calls for the definition of a mathematical model that describes brain tissue via a handful of physiologically-relevant parameters and an algorithm for inverting the model. To address this issue, we propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model. As opposed to other approaches from the literature, our algorithm yields not only an estimation of the parameter vector $\theta$ that best describes a given observed data point $x_0$, but also a full posterior distribution $p(\theta|x_0)$ over the parameter space. This enables a richer description of the model inversion, providing indicators such as credible intervals for the estimated parameters and a complete characterization of the parameter regions where the model may present indeterminacies. We approximate the posterior distribution using deep neural density estimators, known as normalizing flows, and fit them using a set of repeated simulations from the forward model. We validate our approach on simulations using dmipy and then apply the whole pipeline on two publicly available datasets.

Inferring which pathways are affected by a brain lesion is key for both pre and post-treatment planning. However, many disruptive lesions cause changes in the tissue that interrupt tractography algorithms. In such cases, aggregating information from healthy subjects can provide a solution to inferring the affected pathways. In this paper, we introduce a novel label fusion technique that leverages diffusion information to locate brain pathways. Through simulations and experiments in publicly available data we show that our method is able to correctly reconstruct brain pathways, even if they are affected by a focal lesion.

Frequently, population studies feature pyramidally-organized data represented using Hierarchical Bayesian Models (HBM) enriched with plates. These models can become prohibitively large in settings such as neuroimaging, where a sample is composed of a functional MRI signal measured on 300 brain locations, across 4 measurement sessions, and 30 subjects, resulting in around 1 million latent parameters.Such high dimensionality hampers the usage of modern, expressive flow-based techniques.To infer parameter posterior distributions in this challenging class of problems, we designed a novel methodology that automatically produces a variational family dual to a target HBM. This variational family, represented as a neural network, consists in the combination of an attention-based hierarchical encoder feeding summary statistics to a set of normalizing flows. Our automatically-derived neural network exploits exchangeability in the plate-enriched HBM and factorizes its parameter space. The resulting architecture reduces by orders of magnitude its parameterization with respect to that of a typical flow-based representation, while maintaining expressivity.Our method performs inference on the specified HBM in an amortized setup: once trained, it can readily be applied to a new data sample to compute the parameters' full posterior.We demonstrate the capability and scalability of our method on simulated data, as well as a challenging high-dimensional brain parcellation experiment. We also open up several questions that lie at the intersection between normalizing flows, SBI, structured Variational Inference, and inference amortization.

Strongly walk regular graphs (SWRGs or $s$-SWRGs) form a natural generalization of strongly regular graphs (SRGs) where paths of length~2 are replaced by paths of length~$s$. They can be constructed as coset graphs of the duals of projective three-weight codes whose weights satisfy a certain equation. We provide classifications of the feasible parameters of these codes in the binary and ternary case for medium size code lengths. For the binary case, the divisibility of the weights of these codes is investigated and several general results are shown. It is known that an $s$-SWRG has at most 4 distinct eigenvalues $k > \theta_1 > \theta_2 > \theta_3$, and that the triple $(\theta_1, \theta_2, \theta_3)$ satisfies a certain homogeneous polynomial equation of degree $s - 2$ (Van Dam, Omidi, 2013). This equation defines a plane algebraic curve; we use methods from algorithmic arithmetic geometry to show that for $s = 5$ and $s = 7$, there are only the obvious solutions, and we conjecture this to remain true for all (odd) $s \ge 9$., Comment: 42 pages

With the growing number of published functional magnetic resonance imaging (fMRI) studies, meta-analysis databases and models have become an integral part of brain mapping research. Coordinate-based meta-analysis (CBMA) databases are built by automatically extracting both coordinates of reported peak activations and term associations using natural language processing (NLP) techniques. Solving term-based queries on these databases make it possible to obtain statistical maps of the brain related to specific cognitive processes. However, with tools like Neurosynth, only singleterm queries lead to statistically reliable results. When solving richer queries, too few studies from the database contribute to the statistical estimations. We design a probabilistic domain-specific language (DSL) standing on Datalog and one of its probabilistic extensions, CP-Logic, for expressing and solving rich logic-based queries. We encode a CBMA database into a probabilistic program. Using the joint distribution of its Bayesian network translation, we show that solutions of queries on this program compute the right probability distributions of voxel activations. We explain how recent lifted query processing algorithms make it possible to scale to the size of large neuroimaging data, where state of the art knowledge compilation (KC) techniques fail to solve queries fast enough for practical applications. Finally, we introduce a method for relating studies to terms probabilistically, leading to better solutions for conjunctive queries on smaller databases. We demonstrate results for two-term conjunctive queries, both on simulated meta-analysis databases and on the widely-used Neurosynth database.

We prove equality of analytic and topological $L^2$-torsion associated with an odd-dimensional finite volume hyperbolic manifold and a representation of the fundamental group which extends to the ambient Lie group. This generalizes a previous result due to L\"uck and Schick. Alternatively, this result can be regarded as the $L^2$-analogue of recent work by M\"uller and Rochon., Comment: 35 pages, 3 figures

Ensembling is now recognized as an effective approach for increasing the predictive performance and calibration of deep networks. We introduce a new approach, Parameter Ensembling by Perturbation (PEP), that constructs an ensemble of parameter values as random perturbations of the optimal parameter set from training by a Gaussian with a single variance parameter. The variance is chosen to maximize the log-likelihood of the ensemble average ($\mathbb{L}$) on the validation data set. Empirically, and perhaps surprisingly, $\mathbb{L}$ has a well-defined maximum as the variance grows from zero (which corresponds to the baseline model). Conveniently, calibration level of predictions also tends to grow favorably until the peak of $\mathbb{L}$ is reached. In most experiments, PEP provides a small improvement in performance, and, in some cases, a substantial improvement in empirical calibration. We show that this "PEP effect" (the gain in log-likelihood) is related to the mean curvature of the likelihood function and the empirical Fisher information. Experiments on ImageNet pre-trained networks including ResNet, DenseNet, and Inception showed improved calibration and likelihood. We further observed a mild improvement in classification accuracy on these networks. Experiments on classification benchmarks such as MNIST and CIFAR-10 showed improved calibration and likelihood, as well as the relationship between the PEP effect and overfitting; this demonstrates that PEP can be used to probe the level of overfitting that occurred during training. In general, no special training procedure or network architecture is needed, and in the case of pre-trained networks, no additional training is needed., Comment: NeurIPS 2020

This paper proposes an extension of the finite cell method (FCM) to V-rep models, a novel geometric framework for volumetric representations. This combination of an embedded domain approach (FCM) and a new modeling framework (V-rep) forms the basis for an efficient and accurate simulation of mechanical artifacts, which are not only characterized by complex shapes but also by their non-standard interior structure. These objects gain more and more interest in the context of the new design opportunities opened by additive manufacturing, mainly when graded or micro-structured material is applied. Two different types of functionally graded materials (FGM) are considered: The first one, multi-material FGM, is described using the V-rep models' inherent property to assign different properties throughout the interior of a domain. The second, single-material FGM -- which is heterogeneously micro-structured -- characterizes the effective material behavior of representative volume elements by homogenization and performs large-scale simulations using the embedded domain approach., Comment: Preprint submitted to Advanced Modeling and Simulation in Engineering Sciences

We generalize a Cheeger-M\"uller type theorem for flat, unitary bundles on infinite covering spaces over manifolds-with-boundary, proven by Burghelea, Friedlander and Kappeller arXiv:dg-ga/9510010 [math.DG]. Employing recent anomaly results by Br\"uning, Ma and Zhang, we prove an analogous statement for a general flat bundle that is only required to have a unimodular restriction to the boundary., Comment: 34 pages

The fundamental changes in power supply and increasing decentralization require more active grid operation and an increased integration of ICT at all power system actors. This trend raises complexity and increasingly leads to interactions between primary grid operation and ICT as well as different power system actors. For example, virtual power plants control various assets in the distribution grid via ICT to jointly market existing flexibilities. Failures of ICT or targeted attacks can thus have serious effects on security of supply and system stability. This paper presents a holistic approach to providing methods specifically for actors in the power system for prevention, detection, and reaction to ICT attacks and failures. The focus of our measures are solutions for ICT monitoring, systems for the detection of ICT attacks and intrusions in the process network, and the provision of actionable guidelines as well as a practice environment for the response to potential ICT security incidents., Comment: 6 pages, 4 figures, to be published in Proceedings of the 2020 6th IEEE International Energy Conference (ENERGYCon)

Population imaging markedly increased the size of functional-imaging datasets, shedding new light on the neural basis of inter-individual differences. Analyzing these large data entails new scalability challenges, computational and statistical. For this reason, brain images are typically summarized in a few signals, for instance reducing voxel-level measures with brain atlases or functional modes. A good choice of the corresponding brain networks is important, as most data analyses start from these reduced signals. We contribute finely-resolved atlases of functional modes, comprising from 64 to 1024 networks. These dictionaries of functional modes (DiFuMo) are trained on millions of fMRI functional brain volumes of total size 2.4TB, spanned over 27 studies and many research groups. We demonstrate the benefits of extracting reduced signals on our fine-grain atlases for many classic functional data analysis pipelines: stimuli decoding from 12,334 brain responses, standard GLM analysis of fMRI across sessions and individuals, extraction of resting-state functional-connectomes biomarkers for 2,500 individuals, data compression and meta-analysis over more than 15,000 statistical maps. In each of these analysis scenarii, we compare the performance of our functional atlases with that of other popular references, and to a simple voxel-level analysis. Results highlight the importance of using high-dimensional "soft" functional atlases, to represent and analyse brain activity while capturing its functional gradients. Analyses on high-dimensional modes achieve similar statistical performance as at the voxel level, but with much reduced computational cost and higher interpretability. In addition to making them available, we provide meaningful names for these modes, based on their anatomical location. It will facilitate reporting of results.

A projective linear code over $\mathbb{F}_q$ is called $\Delta$-divisible if all weights of its codewords are divisible by $\Delta$. Especially, $q^r$-divisible projective linear codes, where $r$ is some integer, arise in many applications of collections of subspaces in $\mathbb{F}_q^v$. One example are upper bounds on the cardinality of partial spreads. Here we survey the known results on the possible lengths of projective $q^r$-divisible linear codes., Comment: 38 pages

We study the minimum number of minimal codewords in linear codes from the point of view of projective geometry. We derive bounds and in some cases determine the exact values. We also present an extension to minimal subcode supports., Comment: 8 pages, 1 table

In this paper we derive the geodesic equation for massive particles and light for the black spindle spacetime. The solution for light can be formulated in terms of the Weierstra{\ss} {\wp}-, {\sigma}- and {\zeta}-function, whereas a part of the solutions for massive particles is given in terms of derivatives of the Kleinian {\sigma}-function. We analyze the possible orbit types using parametric diagrams and effective potentials. Furthermore we visualize the orbits in a coordinate system, where the spindle-like topology of the horizon is visible., Comment: 11 pages, 5 figures

In this paper we present the Neuron Module that we implemented within the Matlab-based diffusion MRI simulation toolbox SpinDoctor. SpinDoctor uses finite element discretization and adaptive time integration to solve the Bloch-Torrey partial differential equation for general diffusion-encoding sequences, at multiple b-values and in multiple diffusion directions. In order to facilitate the diffusion MRI simulation of realistic neurons by the research community, we constructed finite element meshes for a group of 36 pyramidal neurons and a group of 29 spindle neurons whose morphological descriptions were found in the publicly available neuron repository NeuroMorpho. We also broke the neurons into the soma and dendrite branches and created finite elements meshes for these cell components. Through the Neuron Module, these neuron and cell components finite element meshes can be seamlessly coupled with the functionalities of SpinDoctor. To illustrate some potential uses of the Neuron Module, we show numerical examples of the simulated diffusion MRI signals in multiple diffusion directions from whole neurons as well as from the soma and dendrite branches, and include a comparison of the high b-value behavior between dendrite branches and whole neurons. In addition, we demonstrate that the neuron meshes can be used to perform Monte-Carlo diffusion MRI simulations as well. We show that at equivalent accuracy, if only one gradient direction needs to be simulated, SpinDoctor is faster than a GPU implementation of Monte-Carlo. Finally, we numerically compute the eigenfunctions and the eigenvalues of the Bloch-Torrey and the Laplace operators on the neuron geometries using a finite elements discretization, in order to give guidance in the choice of the space and time discretization parameters for both finite elements and Monte-Carlo approaches., Comment: 42 pages, 17 figures. arXiv admin note: text overlap with arXiv:1902.01025

The numerical simulation of the diffusion MRI signal arising from complex tissue micro-structures is helpful for understanding and interpreting imaging data as well as for designing and optimizing MRI sequences. The discretization of the Bloch-Torrey equation by finite elements is a more recently developed approach for this purpose, in contrast to random walk simulations, which has a longer history. While finite elements discretization is more difficult to implement than random walk simulations, the approach benefits from a long history of theoretical and numerical developments by the mathematical and engineering communities. In particular, software packages for the automated solutions of partial differential equations using finite elements discretization, such as FEniCS, are undergoing active support and development. However, because diffusion MRI simulation is a relatively new application area, there is still a gap between the simulation needs of the MRI community and the available tools provided by finite elements software packages. In this paper, we address two potential difficulties in using FEniCS for diffusion MRI simulation. First, we simplified software installation by the use of FEniCS containers that are completely portable across multiple platforms. Second, we provide a portable simulation framework based on Python and whose code is open source. This simulation framework can be seamlessly integrated with cloud computing resources such as Google Colaboratory notebooks working on a web browser or with Google Cloud Platform with MPI parallelization. We show examples illustrating the accuracy, the computational times, and parallel computing capabilities. The framework contributes to reproducible science and open-source software in computational diffusion MRI with the hope that it will help to speed up method developments and stimulate research collaborations.

Rudolph (1967) introduced one-step majority logic decoding for linear codes derived from combinatorial designs. The decoder is easily realizable in hardware and requires that the dual code has to contain the blocks of so called geometric designs as codewords. Peterson and Weldon (1972) extended Rudolphs algorithm to a two-step majority logic decoder correcting the same number of errors than Reed's celebrated multi-step majority logic decoder. Here, we study the codes from subspace designs. It turns out that these codes have the same majority logic decoding capability as the codes from geometric designs, but their majority logic decoding complexity is sometimes drastically improved.

Let PG$(\mathbb{F}_q^v)$ be the $(v-1)$-dimensional projective space over $\mathbb{F}_q$ and let $\Gamma$ be a simple graph of order ${q^k-1\over q-1}$ for some $k$. A 2$-(v,\Gamma,\lambda)$ design over $\mathbb{F}_q$ is a collection $\cal B$ of graphs (\textit{blocks}) isomorphic to $\Gamma$ with the following properties: the vertex set of every block is a subspace of PG$(\mathbb{F}_q^v)$; every two distinct points of PG$(\mathbb{F}_q^v)$ are adjacent in exactly $\lambda$ blocks. This new definition covers, in particular, the well known concept of a 2$-(v,k,\lambda)$ design over $\mathbb{F}_q$ corresponding to the case that $\Gamma$ is complete. In this work of a foundational nature we illustrate how difference methods allow us to get concrete non-trivial examples of $\Gamma$-decompositions over $\mathbb{F}_2$ or $\mathbb{F}_3$ for which $\Gamma$ is a cycle, a path, a prism, a generalized Petersen graph, or a Moebius ladder. In particular, we will discuss in detail the special and very hard case that $\Gamma$ is complete and $\lambda=1$, i.e., the Steiner 2-designs over a finite field. Also, we briefly touch the new topic of near resolvable 2-$(v,2,1)$ designs over $\mathbb{F}_q$. This study has led us to some (probably new) collateral problems concerning difference sets. Supported by multiple examples, we conjecture the existence of infinite families of $\Gamma$-decompositions over a finite field that can be obtained by suitably labeling the vertices of $\Gamma$ with the elements of a Singer difference set.

The intra-axonal water exchange time {\tau}i, a parameter associated with axonal permeability, could be an important biomarker for understanding demyelinating pathologies such as Multiple Sclerosis. Diffusion-Weighted MRI is sensitive to changes in permeability, however, the parameter has remained elusive due to the intractability of the mathematical models that incorporate it. Machine learning based computational models can potentially be used to estimate such parameters, and recently, a theoretical framework using a random forest (RF) suggests this is a promising approach. In this study, we adopt such an RF approach and experimentally investigate its suitability as a biomarker for demyelinating pathologies through direct comparison with histology. For this, we use an in-vivo cuprizone (CPZ) mouse model of demyelination with available ex-vivo electron microscopy (EM) data. We test our model on noise-free simulations and find very strong correlations between the predicted and ground truth parameters. For realistic noise levels as in our in-vivo data, the performance is affected, however, the parameters are still well estimated. We apply our RF model on in-vivo data from 8 CPZ and 8 wild-type (WT) mice and validate the RF estimates using histology. We find a strong correlation between the in-vivo RF estimates of {\tau}i and the EM measurements of myelin thickness ({\rho_\tau}i = 0.82), and between RF estimates and EM measurements of intra-axonal volume fraction ({\rho_f} = 0.98). When comparing {\tau}i in CPZ and WT mice we find a statistically significant decrease in the corpus callosum of the CPZ compared to the WT mice, in line with our expectations that {\tau}i is lower in regions where the myelin sheath is damaged. Overall, these results demonstrate the suitability of machine learning compartment models with permeability as a potential biomarker for demyelinating pathologies.

It is shown that there does not exist a binary projective triply-even code of length $59$. This settles the last open length for projective triply-even binary codes. Therefore, projective triply-even binary codes exist precisely for lengths $15$, $16$, $30$, $31$, $32$, $45$--$51$, and $\ge 60$., Comment: 12 pages, 4 tables

This paper proposes a computational methodology for the integration of Computer Aided Design (CAD) and the Finite Cell Method (FCM) for models with "dirty geometries". FCM, being a fictitious domain approach based on higher order finite elements, embeds the physical model into a fictitious domain, which can be discretized without having to take into account the boundary of the physical domain. The true geometry is captured by a precise numerical integration of elements cut by the boundary. Thus, an effective Point Membership Classification algorithm that determines the inside-outside state of an integration point with respect to the physical domain is a core operation in FCM. To treat also "dirty geometries", i.e. imprecise or flawed geometric models, a combination of a segment-triangle intersection algorithm and a flood fill algorithm being insensitive to most CAD model flaws is proposed to identify the affiliation of the integration points. The present method thus allows direct computations on geometrically and topologically flawed models. The potential and merit for practical applications of the proposed method is demonstrated by several numerical examples., Comment: Accepted Manuscript

During the last ten years, increasing efforts were made to improve and simplify the process from Computer Aided Design (CAD) modeling to a numerical simulation. It has been shown that the transition from one model to another, i.e. the meshing, is a bottle-neck. Several approaches have been developed to overcome this time-consuming step, e.g. Isogeometric Analysis (IGA), which applies the shape functions used for the geometry description (typically B-Splines and NURBS) directly to the numerical analysis. In contrast to IGA, which deals with boundary represented models (B-Rep), our approach focuses on parametric volumetric models such as Constructive Solid Geometries (CSG). These models have several advantages, as their geometry description is inherently watertight and they provide a description of the model's interior. To be able to use the explicit mathematical description of these models, we employ the Finite Cell Method (FCM). Herein, the only necessary input is a reliable statement whether an (integration-) point lies inside or outside of the geometric model. This paper mainly discusses such point-in-membership tests on various geometric objects like sweeps and lofts, as well as several geometric operations such as filleting or chamfering. We demonstrate that, based on the information of the construction method of these objects, the point-in-membership-test can be carried out efficiently and robustly

Modern 3D Computer-Aided-Design (CAD) systems use mainly two types of geometric models. Classically, objects are defined by a Boundary Representation (B-Rep), where only the objects' surfaces with their corresponding edges and nodes are stored. One disadvantage concerning a numerical simulation is that B-Rep models are not necessarily watertight. These 'dirty geometries' cause major difficulties in computational analysis because even basic geometric operations such as point-in-membership tests fail, not to mention meshing as required by classical boundary conforming finite element methods. Alternatively, objects may be represented by Constructive Solid Geometry (CSG), which is strongly related to Procedural Modeling (PM). In this context, the model is created using Boolean operations on primitives. The modeling process is then either stored as a sequence (PM), or as a construction tree (CSG). In contrast to B-Rep models, CSG models are intrinsically water-tight. To run a finite element simulation on a water-tight CSG model, two alternatives are possible: (i) it can either be converted to a B-Rep-model to obtain a finite element mesh or (ii) its implicit description can be used directly by applying an embedded domain approach, like the Finite Cell Method (FCM). In this contribution, we present a design-through analysis methodology using CSG and FCM. A crucial point in FCM is a fast and reliable point-in-membership test which can be directly derived from the CSG model. We present the outline of the modeling approach, the realization of the point-in-membership test as a sequence of CSG-operations, and discuss advantages and limitations on complex models of relevance in mechanical engineering., Comment: ECCOMAS Congress 2016, Crete, Greece

Despite the digital nature of magnetic resonance imaging, the resulting observations are most frequently reported and stored in text documents. There is a trove of information untapped in medical health records, case reports, and medical publications. In this paper, we propose to mine brain medical publications to learn the spatial distribution associated with anatomical terms. The problem is formulated in terms of minimization of a risk on distributions which leads to a least-deviation cost function. An efficient algorithm in the dual then learns the mapping from documents to brain structures. Empirical results using coordinates extracted from the brain-imaging literature show that i) models must adapt to semantic variation in the terms used to describe a given anatomical structure, ii) voxel-wise parameterization leads to higher likelihood of locations reported in unseen documents, iii) least-deviation cost outperforms least-square. As a proof of concept for our method, we use our model of spatial distributions to predict the distribution of specific neurological conditions from text-only reports.

A well known class of objects in combinatorial design theory are {group divisible designs}. Here, we introduce the $q$-analogs of group divisible designs. It turns out that there are interesting connections to scattered subspaces, $q$-Steiner systems, design packings and $q^r$-divisible projective sets. We give necessary conditions for the existence of $q$-analogs of group divsible designs, construct an infinite series of examples, and provide further existence results with the help of a computer search. One example is a $(6,3,2,2)_2$ group divisible design over $\operatorname{GF}(2)$ which is a design packing consisting of $180$ blocks that such every $2$-dimensional subspace in $\operatorname{GF}(2)^6$ is covered at most twice., Comment: 18 pages, 3 tables, typos corrected

The maximum size $A_2(8,6;4)$ of a binary subspace code of packet length $v=8$, minimum subspace distance $d=6$, and constant dimension $k=4$ is $257$, where the $2$ isomorphism types are extended lifted maximum rank distance codes. In finite geometry terms the maximum number of solids in $\operatorname{PG}(7,2)$, mutually intersecting in at most a point, is $257$. The result was obtained by combining the classification of substructures with integer linear programming techniques. This implies that the maximum size $A_2(8,6)$ of a binary mixed-dimension code of packet length $8$ and minimum subspace distance $6$ is $257$ as well., Comment: 17 pages, 3 tables

We show that there is a binary subspace code of constant dimension 3 in ambient dimension 7, having minimum distance 4 and cardinality 333, i.e., $333 \le A_2(7,4;3)$, which improves the previous best known lower bound of 329. Moreover, if a code with these parameters has at least 333 elements, its automorphism group is in one of $31$ conjugacy classes. This is achieved by a more general technique for an exhaustive search in a finite group that does not depend on the enumeration of all subgroups., Comment: 18 pages; typos corrected

For which positive integers $n,k,r$ does there exist a linear $[n,k]$ code $C$ over $\mathbb{F}_q$ with all codeword weights divisible by $q^r$ and such that the columns of a generating matrix of $C$ are projectively distinct? The motivation for studying this problem comes from the theory of partial spreads, or subspace codes with the highest possible minimum distance, since the set of holes of a partial spread of $r$-flats in $\operatorname{PG}(v-1,\mathbb{F}_q)$ corresponds to a $q^r$-divisible code with $k\leq v$. In this paper we provide an introduction to this problem and report on new results for $q=2$., Comment: 10 pages, 3 tables

This paper presents a novel mathematical framework for representing uncertainty in large deformation diffeomorphic image registration. The Bayesian posterior distribution over the deformations aligning a moving and a fixed image is approximated via a variational formulation. A stochastic differential equation (SDE) modeling the deformations as the evolution of a time-varying velocity field leads to a prior density over deformations in the form of a Gaussian process. This permits estimating the full posterior distribution in order to represent uncertainty, in contrast to methods in which the posterior is approximated via Monte Carlo sampling or maximized in maximum a-posteriori (MAP) estimation. The frame-work is demonstrated in the case of landmark-based image registration, including simulated data and annotated pre and intra-operative 3D images.

Current theories hold that brain function is highly related to long-range physical connections through axonal bundles, namely extrinsic connectiv-ity. However, obtaining a groupwise cortical parcellation based on extrinsic connectivity remains challenging. Current parcellation methods are compu-tationally expensive; need tuning of several parameters or rely on ad-hoc constraints. Furthermore, none of these methods present a model for the cortical extrinsic connectivity of the cortex. To tackle these problems, we propose a parsimonious model for the extrinsic connectivity and an efficient parceling technique based on clustering of tractograms. Our technique allows the creation of single subject and groupwise parcellations of the whole cortex. The parcellations obtained with our technique are in agreement with structural and functional parcellations in the literature. In particular, the motor and sensory cortex are subdivided in agreement with the human ho-munculus of Penfield. We illustrate this by comparing our resulting parcels with the motor strip mapping included in the Human Connectome Project data.

Finding the common structural brain connectivity network for a given population is an open problem, crucial for current neuro-science. Recent evidence suggests there's a tightly connected network shared between humans. Obtaining this network will, among many advantages , allow us to focus cognitive and clinical analyses on common connections, thus increasing their statistical power. In turn, knowledge about the common network will facilitate novel analyses to understand the structure-function relationship in the brain. In this work, we present a new algorithm for computing the core structural connectivity network of a subject sample combining graph theory and statistics. Our algorithm works in accordance with novel evidence on brain topology. We analyze the problem theoretically and prove its complexity. Using 309 subjects, we show its advantages when used as a feature selection for connectivity analysis on populations, outperforming the current approaches.

It is shown that the automorphism group of a binary $q$-analog of the Fano plane is either trivial or of order $2$., Comment: 10 pages

In this article, we show the existence of large sets $\operatorname{LS}_2[3](2,k,v)$ for infinitely many values of $k$ and $v$. The exact condition is $v \geq 8$ and $0 \leq k \leq v$ such that for the remainders $\bar{v}$ and $\bar{k}$ of $v$ and $k$ modulo $6$ we have $2 \leq \bar{v} < \bar{k} \leq 5$. The proof is constructive and consists of two parts. First, we give a computer construction for an $\operatorname{LS}_2[3](2,4,8)$, which is a partition of the set of all $4$-dimensional subspaces of an $8$-dimensional vector space over the binary field into three disjoint $2$-$(8, 4, 217)_2$ subspace designs. Together with the already known $\operatorname{LS}_2[3](2,3,8)$, the application of a recursion method based on a decomposition of the Gra{\ss}mannian into joins yields a construction for the claimed large sets.

One of the main problems of subspace coding asks for the maximum possible cardinality of a subspace code with minimum distance at least $d$ over $\mathbb{F}_q^n$, where the dimensions of the codewords, which are vector spaces, are contained in $K\subseteq\{0,1,\dots,n\}$. In the special case of $K=\{k\}$ one speaks of constant dimension codes. Since this (still) emerging field is very prosperous on the one hand side and there are a lot of connections to classical objects from Galois geometry it is a bit difficult to keep or to obtain an overview about the current state of knowledge. To this end we have implemented an on-line database of the (at least to us) known results at \url{subspacecodes.uni-bayreuth.de}. The aim of this recurrently updated technical report is to provide a user guide how this technical tool can be used in research projects and to describe the so far implemented theoretic and algorithmic knowledge., Comment: 44 pages, 6 tables, 7 screenshots

We have developed a novel method to describe human white matter anatomy using an approach that is both intuitive and simple to use, and which automatically extracts white matter tracts from diffusion MRI volumes. Further, our method simplifies the quantification and statistical analysis of white matter tracts on large diffusion MRI databases. This work reflects the careful syntactical definition of major white matter fiber tracts in the human brain based on a neuroanatomist's expert knowledge. The framework is based on a novel query language with a near-to-English textual syntax. This query language makes it possible to construct a dictionary of anatomical definitions that describe white matter tracts. The definitions include adjacent gray and white matter regions, and rules for spatial relations. This novel method makes it possible to automatically label white matter anatomy across subjects. After describing this method, we provide an example of its implementation where we encode anatomical knowledge in human white matter for 10 association and 15 projection tracts per hemisphere, along with 7 commissural tracts. Importantly, this novel method is comparable in accuracy to manual labeling. Finally, we present results applying this method to create a white matter atlas from 77 healthy subjects, and we use this atlas in a small proof-of-concept study to detect changes in association tracts that characterize schizophrenia., Comment: Brain Structure and Function, Springer Verlag, 2016

In this paper we investigate codes over finite commutative rings R, whose generator matrices are built from \$\alpha\$-circulant matrices. For a non-trivial ideal I

Using integer linear programming and table-lookups we prove that there is no binary linear $[1988, 12, 992]$ code. As a by-product, the non-existence of binary linear codes with the parameters $[324, 10, 160]$, $[356, 10, 176]$, $[772,11,384]$, and $[836,11,416]$ is shown. Our work is motivated by the recent construction of the extended dualized Kerdock code $\hat{\mathcal{K}}^*_{6}$, which is a $\mathbb{Z}_4$-linear code having a non-linear binary Gray image with the parameters $(1988,2^{12},992)$. By our result, the code $\hat{\mathcal{K}}^*_{6}$ can be added to the small list of $\mathbb{Z}_4$-codes for which it is known that the Gray image is better than any binary linear code.