Mouse neural tube organoids self-organize floorplate through BMP-mediated cluster competition - Krammer, Teresa; Stuart, Hannah T.; Gromberg, Elena; Ishihara, Keisuke; Cislo, Dillon; Melchionda, Manuela; Becerril Perez, Fernando; Wang, Jingkui; Costantini, Elena; Rus, Stefanie; Arbanas, Laura; Hörmann, Alexandra; et al. (Developmental Cell)
During neural tube (NT) development, the notochord induces an organizer, the floorplate, which secretes Sonic Hedgehog (SHH) to pattern neural progenitors. Conversely, NT organoids (NTOs) from embryonic stem cells (ESCs) spontaneously form floorplates without the notochord, demonstrating that stem cells can self-organize without embryonic inducers. Here, we investigated floorplate self-organization in clonal mouse NTOs. Expression of the floorplate marker FOXA2 was initially spatially scattered before resolving into multiple clusters, which underwent competition and sorting, resulting in a stable “winning” floorplate. We identified that BMP signaling governed long-range cluster competition. FOXA2+ clusters expressed BMP4, suppressing FOXA2 in receiving cells while simultaneously expressing the BMP-inhibitor NOGGIN, promoting cluster persistence. Noggin mutation perturbed floorplate formation in NTOs and in the NT in vivo at mid/hindbrain regions, demonstrating how the floorplate can form autonomously without the notochord. Identifying the pathways governing organizer self-organization is critical for harnessing the developmental plasticity of stem cells in tissue engineering.

Adaptive hierarchical representations in the hippocampus - Chiossi, Heloisa
The hippocampus is central to memory formation, storage and retrieval over many timescales. Neurons in this brain area are highly selective to spatial position as well as to many other variables of the environment. It is believed that the selectivity patterns of hippocampal neurons reflect the structure of tasks an animal performs. However, especially at timescales longer than a few minutes or hours it is not fully known how these representations evolve, nor how they map to behaviour in the process. In this thesis, I monitored the evolution of hippocampal representations in a novel spatial-associative memory task for rats. Reward locations were associated with global sensory cues (i.e. context); animals had to remember the associations and dig for food in those locations only. I used in vivo electrophysiology to record the activity of the hippocampus dorsal CA1 neurons during the learning period of a few days. I report here a novel and simple method to classify behaviour performance to account for individual variability in learning speed and spurious performance unrelated to true task rule learning. Using this classification I was then able to investigate neural responses on different stages of learning matched across animals. On the first day of learning, I observed a fast formation of single-cell selectivity to task variables which remained stable over days. I also observed that reward tuning was not a single process but dependent on task-related cognitive load. At the population level, a linear decoding approach revealed a hierarchy in the representation of task variables that changed with learning. In the high-dimensional space of population activity, the representation of contexts was specific to each position in the maze, and could thus be better decoded if the position was known. The decoding of position did not improve with knowledge of other variables. As learning progressed, the hippocampal code underwent a reorganisation of high-variance directions in population activity, identified by principal component analysis. I found that dominant dimensions started carrying increasing amounts of information about task context specifically at those positions where it mattered for task performance. When I contrasted this with variables less relevant to task performance (e.g. movement direction), I did not observe differences in decoding quality over positions nor a reduction of dimensionality with learning. Overall, the largest changes in CA1 neural response with task learning happened in a matter of a few trials; over days, changes undetectable in single-cell statistics were responsible for re-structuring the hierarchy of neural representations at the population level; these changes were task-specific and reflected different stages of learning. This indicates that complex task learning may involve different magnitudes of response modulation in CA1, which happen at specific time scales linked to behaviour.

Developmental transformation of nanodomain coupling between Ca2+ channels and release sensors at a central GABAergic synapse - Chen, JingJing
The coupling between presynaptic Ca2+ channels and release sensors is a key factor that determines speed and efficacy of synapse transmission. At some excitatory synapses, channel–sensor coupling becomes tighter during development, and tightening is often associated with a switch in the reliance on different Ca2+ channel subtypes. However, the coupling topography at many synapses remains unknown, and it is unclear how it changes during development. To address this question, we analyzed the coupling configuration at the cerebellar basket cell (BC) to Purkinje cell (PC) synapse at different developmental stages, combining biophysical analysis, structural analysis, and modeling. Quantal analysis of BC–PC indicated that release probability decreased, while the number of functional sites increased during development. Although transmitter release persistently relied on P/Q-type Ca2+ channels in the time period postnatal day 7–23, effects of the Ca2+ chelator EGTA and BAPTA applied by intracellular pipette perfusion decreased during development, indicative of tightening of source-sensor coupling. Furthermore, presynaptic action potentials became shorter during development, suggesting reduced efficacy of Ca2+ channel activation. Structural analysis by freeze-fracture replica labeling (FRL) and transmission electron microscopy (EM) indicated that presynaptic P/Q-type Ca2+ channels formed nanoclusters throughout development, whereas docked vesicles were only clustered at later developmental stages. The number of functional release sites correlated better with the AZ number early in development, but match better with the Ca2+ channel cluster number at later stages. Modeling suggested a developmental transformation from a more random to a more clustered coupling nanotopography. Thus, presynaptic signaling developmentally approaches a point-to-point configuration, optimizing speed, reliability, and energy efficiency of synaptic transmission.

SCAF1 drives the compositional diversity of mammalian respirasomes - Vercellino, Irene; Sazanov, Leonid A (Nature Structural and Molecular Biology)
Supercomplexes of the respiratory chain are established constituents of the oxidative phosphorylation system, but their role in mammalian metabolism has been hotly debated. Although recent studies have shown that different tissues/organs are equipped with specific sets of supercomplexes, depending on their metabolic needs, the notion that supercomplexes have a role in the regulation of metabolism has been challenged. However, irrespective of the mechanistic conclusions, the composition of various high molecular weight supercomplexes remains uncertain. Here, using cryogenic electron microscopy, we demonstrate that mammalian (mouse) tissues contain three defined types of ‘respirasome’, supercomplexes made of CI, CIII2 and CIV. The stoichiometry and position of CIV differs in the three respirasomes, of which only one contains the supercomplex-associated factor SCAF1, whose involvement in respirasome formation has long been contended. Our structures confirm that the ‘canonical’ respirasome (the C-respirasome, CICIII2CIV) does not contain SCAF1, which is instead associated to a different respirasome (the CS-respirasome), containing a second copy of CIV. We also identify an alternative respirasome (A-respirasome), with CIV bound to the ‘back’ of CI, instead of the ‘toe’. This structural characterization of mouse mitochondrial supercomplexes allows us to hypothesize a mechanistic basis for their specific role in different metabolic conditions.

Protocol for fabricating elastomeric stencils for patterned stem cell differentiation - Rus, Stefanie; Merrin, Jack; Kulig, Monika Aleksandra; Minchington, Thomas; Kicheva, Anna (STAR Protocols)
Geometrically controlled stem cell differentiation promotes reproducible pattern formation. Here, we present a protocol to fabricate elastomeric stencils for patterned stem cell differentiation. We describe procedures for using photolithography to produce molds, followed by molding polydimethylsiloxane (PDMS) to obtain stencils with through holes. We then provide instructions for culturing cells on stencils and, finally, removing stencils to allow colony growth and cell migration. This approach yields reproducible two-dimensional organoids tailored for quantitative studies of growth and pattern formation. For complete details on the use and execution of this protocol, please refer to Lehr et al.1

Investigating acute microglia response to seizure activity in vivo: Combining 2-Photon imaging and EEG recording - Murmann, Julie Stefanie
Epilepsy affects about 50 to 65 million people globally. It summarizes a spectrum of neurological disorders that have in common a hyperactivity of the neuronal network resulting in seizures. A common assumption is that an imbalance between neuronal excitation and inhibition is a key mechanism in seizure generation and epileptogeneisis. In at least one-third of the patients, current therapies have proven unsuccessful in treating seizure progression. One potential reason could be that the therapies only focus on neurons. Recent studies suggest that neuronal hyperactivity causes a microglial response, which reinstates brain homeostasis. Additionally, interactions between microglia and neurons have been shown to inhibit neuronal firing and dampen seizure activity. However, the exact relationship between microglia and seizure progression in epilepsy is yet to be elucidated. A main bottleneck is that several studies investigate microglia dynamics in ex vivo slice models, which can severely affect the microglia dynamics due to their rapid response to environmental changes. On the other hand, in vivo studies focus mostly on behavior characterization of the epileptic seizure phenotype and their long-term consequences on microglia activity leaving out the direct consequences of acute seizure activity on microglia dynamics. Here, we perform a pilot study to combine electroencephalography (EEG) and in vivo live imaging to directly monitor and correlate the onset of seizure activity with microglia response. To induce seizures, we take advantage of the kainic acid (KA) model, which represents similar neuropathological and electroencephalographic features seen in human patients with temporal lobe epilepsy (TLE). After confirmation of induction of the seizure and microglia activity in the hippocampus as a focal point, we investigated whether these changes also reached the primary visual cortex (V1) as a secondary generalized seizure activity. Indeed, we found that microglia changed their morphology at high doses of KA in the V1. Next, we optimized each of the two methodological components: for the EEG recording, our initial attempts under the microscope suffered from extensive electrical noise, which overlaid the actual signal. Thus, we built a customized Faraday-cage and confirmed that the signal-to-noise ratio was sufficiently reduced to be able to record brain oscillatory activity. For the in vivo live imaging of microglia, we had to optimize the imaging parameters, so that we would be able to detect microglial processes in a sufficient resolution to track their process changes. Finally, we combined both methodologies with the KA model. We confirmed that KA induced seizure activity and found first indication that those correlate with microglia volume changes. Overall, we have developed a first methodological approach, which allows the analysis of the acute effects of seizure onset on microglia. Future studies will have to continue to optimize the drift during imaging recording and the post-image analysis.

Novel approaches to studying alternative splicing in Drosophila Melanogaster : Insights into sex-specific gene expression and the evolution of sex determination - Raices, Julia
Males and females exhibit numerous differences, from the initial stages of sex determination to the development of secondary sexual characteristics. In Drosophila, these differences have been thoroughly studied. Extensive research has been performed to understand the role and molecular mode of action of central sex in determining switch genes, such as transformer (tra) and Sex-lethal (Sxl). Furthermore, studies have highlighted differential gene expression as an essential mechanism to create sexual dimorphism. An alternative path to sexual dimorphism that has been less explored is alternative splicing, the mechanism through which genes can produce multiple transcripts with distinct properties and functions. The primary switch sex-determining gene Sxl is a good example of the role of alternative splicing for sex-specific functions: the inclusion of a specific exon determines the male or female form of the protein, which in turn switches on either the male or female developmental pathway. The genes that act upstream of Sxl and determine which form is expressed - the counter genes - have received less attention. This thesis addresses two critical questions about the molecular encoding of sexes in the Drosophila melanogaster genome: First, the use of splice forms in male and female tissues in D. melanogaster is examined, inferring the molecular and evolutionary parameters shaping the diversity of the splicing landscape. Second, the behaviour of counter genes in Drosophila-related species is investigated, shedding light on potential changes leading to their incorporation into the sex-determination pathway. For the alternative splicing analyses, long-read RNA sequencing of testes, ovaries, female and male midguts, heads, and whole bodies was performed. A novel pipeline was developed to assign unique transcript identifiers for each sequence of exons and introns in the read, enabling detailed comparisons of splicing variants in each tissue/sex. Alternative splicing was found to be more pervasive in females than males (22,201 exclusive splice forms in females versus 12,631 in males), especially when comparing ovaries to other tissues. The ovaries alone displayed 15,299 exclusive splice forms, suggesting most female exclusive splice forms originate there. Genome location and gene age were also correlated with the number of splice forms per gene. In particular, the X and 4th chromosomes (Muller elements A and F) showed more splice forms per gene than other chromosomes. Additionally, genes older than 63 million years exhibited more splice forms per gene than younger genes. Our results suggest that alternative splicing is more prevalent than previously believed, with numerous female-exclusive forms, age, and location playing significant roles in shaping its prevalence. For the counter genes analyses, we combined published gene expression, genomic, and gene interaction data from various clades (Bactrocera jarvisi, B. oleae, Ceratitis capitata, Mus musculus, Caenorhabditis elegans, Homo sapiens, and D. melanogaster). The counter genes scute (sc), extra macrochaetae (emc), groucho (gro), deadpan (dpn), daughterless (da), runt (run), Sxl, hermaphrodite (her), and tra maintain conserved Muller element locations between C. capitata and D. melanogaster, which are most of the counter genes identified in the C. capitata genome. Their expression patterns during early embryogenesis in B. jarvisi and D. melanogaster are also similar for counter genes dpn, gro, da, and emc. However, Sxl and sc are also found to have more extreme expression ratios between the species. Lastly, gene interactions within the counter genes are conserved, with da-sc and gro-dpn interactions occurring in Drosophila, worms, humans, and mice. Interactions such as dpn-sc, dpn-da, da-emc, and gro-run are present in Drosophila, mice, and humans, suggesting these genes were recruited by ancestral characteristics, primarily during embryogenesis. The conserved expression, location, and interactions of counter genes suggest serendipitous recruitment of such genes instead of a change in those characteristics as they were recruited for this function.

Characterizing the sequence and expression evolution of the t-haplotype, a model meiotic driver - Kelemen, Réka K
Genomes are shaped by natural selection at the level of the organism, as genomic variants that have a beneficial effect on the viability or fecundity of their carriers are on average expected to be passed on to more offspring than less beneficial alleles. However, selection also favors genomic variants that drive their own transmission to the next generation above the mendelian expectation of 50 percent in heterozygotes, even if these self-promoting variants are less beneficial to the organism than other variants at the same locus. Such variants, called meiotic drivers, are found in diverse taxa, and often impose fitness costs on their host organisms. As meiotic drivers often require multiple genes and sequences for transmission ratio distortion, they are often found in regions of low recombination, such as inversions, which prevent their recombination with the non-driving homologous regions. Reduced recombination rates are expected to lead to the accumulation of deleterious mutations, which may affect hundreds of genes trapped in the inversions of meiotic drivers. Although the observed fitness costs of self-promoting haplotypes are thought to possibly reflect sequence degeneration, no study has systematically investigated the level of degeneration on a meiotic driver. Further, the low rates of recombination between driving and non-driving haplotypes have limited the power of traditional genetic studies in uncovering the gene content of meiotic drivers, and made the the identification of the genes causing transmission ratio distortion difficult. After an introduction to meiotic drivers in Chapter 1, this thesis presents three studies that make use of next generation sequencing data to characterize the sequence and expression evolution of genes on the t-haplotype, a large and ancient meiotic driver in house mice that is transmitted to up to 100% of the offspring in males heterozygous for it. Chapter 2 presents a comprehensive assessment of the t-haplotype’s sequence evolution, which shows signs of sequence degeneration counteracted by occasional recombination with the non-driving homolog over large parts of the meiotic driver, proposing an explanation for its long-term survival. Chapter 3 investigates the sequence and expression evolution of genes on the t-haplotype, and finds widespread expression and copy number changes and signs of less efficient purifying selection compared to the genes on the non-driving homolog. Further, this chapter finds candidates for involvment in drive: two positively selected genes on the t-haplotype, and the discovery of a t-specific gene duplicate, which was gained from another chromosome, and which acquired novel sequence and testis-specific expression on the t-haplotype. Finally, Chapter 4 provides unprecedented insights into the gene expression landscape in testes of t-carrier mice, using single nucleus sequencing. Cell-resolved RNA-sequencing allows the comparison of expression in spermatids carrying or not carrying the t-haplotype as well as the timing of t-haplotype-induced expression changes along spermatogenesis. This study shows the timing of previously found drive-associated genes, and uncovers novel candidate genes and biological processes that may underlie the complex biology of transmission ratio distortion of the t-haplotype. Chapter 5 synthesizes the findings of the three studies, and discusses them in the context of the current state of meiotic drive research.
Keywords: meiotic driver; neofunctionalization; single nucleus sequencing

Membrane proteins in plant physiology and bioenergetics : Investigating auxin efflux transporter PIN8 and ATP synthase inhibition by the novel inhibitor Yaku'amide B - Lukic, Kristina
This thesis comprises two distinct projects, each offering unique insights into fundamental cellular processes. While distinct in their focus, these different perspectives have a common theme: chemiosmotic theory and utilisation of the proton gradient for driving the essential processes like auxin efflux and ATP synthesis, effectively bridging the membrane protein structure and function from the realms of plant biology and cellular bioenergetics. The first project of this thesis centres on the characterisation of PIN proteins, a class of transmembrane transporters pivotal in the regulation of auxin transport and distribution in plants. PINs form a conserved and phylogenetically abundant group of transporters present in land plants and certain algae. Despite their great importance, they were one of the few elusive proteins essential for plant development not to be structurally and mechanistically characterised since their discovery almost 30 years ago. This work aimed to uncover the structural and functional dynamics of the PIN protein-mediated auxin transport using an array of experimental techniques, including protein purification, biochemical assays and structural analysis. Through an exhaustive screening process that took several years and included testing different PIN homologues, expression systems, constructs, and purification conditions, we developed a robust protocol for isolating the pure, stable, and monodisperse PIN8 protein. Moreover, utilising biophysical methods and buffer screening, we demonstrated that PIN8 exhibits detergent and pH-dependent stability, with mild detergents and lower pH (5.0 and 6.0) being optimal for the stability of the protein. Using SEC-MALS and crosslinking, we determined that PIN8 forms dimers, which was confirmed by our structural studies. We obtained a cryo-EM map of PIN8 at pH 6.0, and, compared to recently published structures, our map implies major pH-dependent conformational changes and possibly utilisation of the proton gradient in the transport mechanism. The subject of the second project was F1Fo-ATP synthase, an enzyme complex fundamental to cellular energy metabolism. Through an approach integrating biochemical assays and structural analysis, this research aimed to unveil the molecular mechanism of inhibition of ATP synthase by yaku´amide, a bioactive compound with potential therapeutic implications. Using submitochondrial particles and purified F1Fo-ATP synthase, we demonstrated that, contrary to published data, yaku´amide inhibits both ATP hydrolysis and ATP synthesis reactions. Moreover, we found that yaku´amide inhibitory activity is proton motive force (pmf) dependent, with lower inhibition in a more coupled system. Utilising cryo-EM, we obtained maps and models for the three main rotational states of murine ATP synthase (State 1 at 3.0 Å, 8 State 2 at 3.1 Å, and State 3 at 3.2 Å, overall). We observed several new features in our maps; however, we cannot definitively determine the exact mechanism of yaku amide’s inhibition on the protein due to either resolution limits or suboptimal binding of the inhibitor.

Stability and change in the memory system during rest - Bollmann, Lars
Acquiring, retaining, and retrieving information over a wide range of timescales are crucial functions of the brain. The successful processing of memories affects many aspects of our lives and enables us and many other organisms to operate in a complex environment and to interact with it. In this context, the hippocampus and functionally connected brain areas, such as the prefrontal cortex, are central and have been subject to intensive research in the past decades. Storage of memories is believed to rely on distributed neural activity within these neural circuits. Additionally, neural memory traces of recent experience are reinstated during periods of rest or sleep. These reactivations are thought to play an outstanding role in the consolidation of memories and potentially facilitate the transfer of information from the hippocampus to cortical areas for long-term storage and integration into existing knowledge. However, there is growing evidence that memory-related neural representations in the hippocampus are not as stable as initially thought and that they change even in the absence of learning. It has been suggested that these changes reflect the accumulation of experience, but the influence of interspersed consolidation periods has not been considered. Previous studies have analyzed consolidation periods by detecting activity that strongly resembled neural activity during the acquisition of memory. Besides being often limited to only non-rapid eye movement (NREM) sleep, the used approaches were not capable of tracking changes in neural representations over extended temporal periods. More fluid representations do not only challenge our understanding of how information is stored, but they also affect the transfer of information between brain areas during the consolidation process. For this thesis, I investigated the evolution of memory-related activity during sleep periods expected to be involved in consolidation in the hippocampus and between the hippocampus and prefrontal cortex. I found that reactivated activity in the hippocampus gradually transformed during prolonged periods of sleep and inactivity. In the beginning, neural activity strongly resembled acquisition activity, whereas, with the progression of time, it became more similar to the subsequent recall activity. NREM periods drove this process, while rapid-eye movement (REM) periods showed a resetting effect. This reactivation drift was due to firing rate changes of a subset of cells and mirrored the representational changes from the acquisition to the recall. A stable subset of cells withstood the drift and maintained their activity. Therefore, my results indicate that memory-related representations undergo spontaneous modifications during consolidation periods and that these changes are predictive of representational drift. Furthermore, I found that the amount of change in the neural activity during subsequent sleep periods was biased by prior behavioral performance. Observed changes in the hippocampus and the prefrontal cortex were synchronized and increased after poor performance, highlighting a potential role in the exchange of information. Low-variance vii periods with distinct, more stable activity from a subset of cells significantly contributed to the heightened synchrony between both areas. Hence, interleaved phases of more stable neural activity could facilitate the information transfer between brain areas. In conclusion, my investigations underline the fluidity of memory-related representations and assign a prominent role to sleep reactivation periods in their evolution. In addition, I identified a potential mechanism of stable activity phases that might facilitate the synchronization across hippocampal-prefrontal activity despite ongoing changes. Reconciling and integrating findings from both spontaneous and behaviorally-related representational changes in functionally related brain areas will help to broaden our understanding of how knowledge is stored, maintained, updated, and transferred between brain areas.
Keywords: Memory; Hippocampus; Consolidation

Bayesian linear regression for analyzing general omics data with time-to-event phenotypes - Villanueva Marijuan, Ariadna
Recent advancements in molecular diagnostic techniques have enabled the collection of multiple types of omics data from patients, including genomics, epigenomics, proteomics, and transcriptomics. However, we lack effective methods for integrating all these different data types and combining them with clinical outcomes to study the molecular mechanisms that govern pathological phenotypes. We present multi-omics BayesW, a penalized Bayesian regression method that can handle general omics data for survival analysis of time-to-event phenotypes. Our method can: (1) accommodate incomplete data by allowing censored individuals, (2) use continuous time-to-event data to test associations of markers with a phenotype and (3) estimate effects jointly while allowing for independent groups of biological markers. Extensive simulations using planted signals on real data demonstrate that our model accurately retrieves the true parameters of the model while controlling for false discoveries and maintaining the expected prediction accuracy. We address data correlations by estimating the effects jointly, even between omic groups, while also estimating the individual variance explained by each group. We apply our model to two datasets. Using 18,000 individuals from the Generation Scotland study we model the association of time at onset of Type 2 Diabetes, Stroke, Ischemic Disease, and Osteoarthritis from baseline study entry, with 831,724 CpG methylation probes. We find that large proportions of variation in disease onset times can be attributed to methylation as measured in whole blood at baseline in individuals without disease symptoms. We then apply our model to The Cancer Genome Atlas (TCGA) pan-cancer dataset, in which we use 5 types of omics: copy number variation, epigenetics, somatic mutations, miRNA, and gene expression. For cancer survival age-at-onset we find that, when fitting the 5 groups together, almost all variation attributable to "omics" data is explained by DNA methylation. When considering progression times, both methylation and gene expression explain a large part of the variance. We found 2 genes that are significantly associated (95% posterior inclusion probability) with cancer survival time, conditional on all other genome-wide omics data variation. Owing to the vast variability of mechanisms characterizing different cancers, there are likely few specific genes with a strong signal in a pan-cancer setting. Taken together, we showed the applicability of our multi-omics BayesW model to a wide-range of biological questions in multi-omics data.
Keywords: Epigenetics; Multi-omics; Bayesian regression

High-dimensional limits in artificial neural networks - Shevchenko, Aleksandr
In the modern age of machine learning, artificial neural networks have become an integral part of many practical systems. One of the key ingredients of the success of the deep learning approach is recent computational advances which allowed the training of models with billions of parameters on large-scale data. Such over-parameterized and data-hungry regimes pose a challenge for the theoretical analysis of modern models since “classical” statistical wisdom is no longer applicable. In this view, it is paramount to extend or develop new machinery that will allow tackling the neural network analysis under new challenging asymptotic regimes, which is the focus of this thesis. Large neural network systems are usually optimized via “local” search algorithms, such as stochastic gradient descent (SGD). However, given the high-dimensional nature of the parameter space, it is a priori not clear why such a crude “local” approach works so remarkably well in practice. We take a step towards demystifying this phenomenon by showing that the landscape of the SGD training dynamics exhibits a few beneficial properties for the optimization. First, we show that along the SGD trajectory an over-parameterized network is dropout stable. The emergence of dropout stability allows to conclude that the minima found by SGD are connected via a continuous path of small loss. This in turn means that the high-dimensional landscape of the neural network optimization problem is provably not so unfavourable to gradient-based training, due to mode connectivity. Next, we show that SGD for an over-parameterized network tends to find solutions that are functionally more “simple”. This in turn means that the SGD minima are more robust, since a less complicated solution will less likely overfit the data. More formally, for a prototypical example of a wide two-layer ReLU network on a 1d regression task we show that the SGD algorithm is implicitly selective in its choice of an interpolating solution. Namely, at convergence the neural network implements a piece-wise linear function with the number of linear regions depending only on the amount of training data. This is in contrast to a “smooth”-like behaviour which one would expect given such a severe over-parameterization of the model. Diverging from the generic supervised setting of classification and regression problems, we analyze an auto-encoder model that is commonly used for representation learning and data compression. Despite the wide applicability of the auto-encoding paradigm, the theoretical understanding of their behaviour is limited even in the simplistic shallow case. The related work is restricted to extreme asymptotic regimes in which the auto-encoder is either severely over-parameterized or under-parameterized. In contrast, we provide a tight characterization for the 1-bit compression of Gaussian signals in the challenging proportional regime, i.e., the input dimension and the size of the compressed representation obey the same asymptotics. We also show that gradient-based methods are able to find a globally optimal solution and that the predictions made for Gaussian data extrapolate beyond - to the case of compression of natural images. Next, we relax the Gaussian assumption and study more structured input sources. We show that the shallow model is sometimes agnostic to the structure of the data vii which results in a Gaussian-like behaviour. We prove that making the decoding component slightly less shallow is already enough to escape the “curse” of Gaussian performance.

Compression of structured data with autoencoders: Provable benefit of nonlinearities and depth - Kögler, Kevin; Shevchenko, Aleksandr; Hassani, Hamed; Mondelli, Marco (Proceedings of the 41st International Conference on Machine Learning)
Autoencoders are a prominent model in many empirical branches of machine learning and lossy data compression. However, basic theoretical questions remain unanswered even in a shallow two-layer setting. In particular, to what degree does a shallow autoencoder capture the structure of the underlying data distribution? For the prototypical case of the 1-bit compression of sparse Gaussian data, we prove that gradient descent converges to a solution that completely disregards the sparse structure of the input. Namely, the performance of the algorithm is the same as if it was compressing a Gaussian source - with no sparsity. For general data distributions, we give evidence of a phase transition phenomenon in the shape of the gradient descent minimizer, as a function of the data sparsity: below the critical sparsity level, the minimizer is a rotation taken uniformly at random (just like in the compression of non-sparse data); above the critical sparsity, the minimizer is the identity (up to a permutation). Finally, by exploiting a connection with approximate message passing algorithms, we show how to improve upon Gaussian performance for the compression of sparse data: adding a denoising function to a shallow architecture already reduces the loss provably, and a suitable multi-layer decoder leads to a further improvement. We validate our findings on image datasets, such as CIFAR-10 and MNIST.

Chromosome-level assembly of Artemia franciscana sheds light on sex chromosome differentiation - Bett, Vincent K; Macon, Ariana; Vicoso, Beatriz; Elkrewi, Marwan N (Genome Biology and Evolution)
Since the commercialization of brine shrimp (genus Artemia) in the 1950s, this lineage, and in particular the model species Artemia franciscana, has been the subject of extensive research. However, our understanding of the genetic mechanisms underlying various aspects of their reproductive biology, including sex determination, is still lacking. This is partly due to the scarcity of genomic resources for Artemia species and crustaceans in general. Here, we present a chromosome-level genome assembly of A. franciscana (Kellogg 1906), from the Great Salt Lake, United States. The genome is 1 GB, and the majority of the genome (81%) is scaffolded into 21 linkage groups using a previously published high-density linkage map. We performed coverage and FST analyses using male and female genomic and transcriptomic reads to quantify the extent of differentiation between the Z and W chromosomes. Additionally, we quantified the expression levels in male and female heads and gonads and found further evidence for dosage compensation in this species.

Single-nucleus atlas of the Artemia female reproductive system suggests germline repression of the Z chromosome - Elkrewi, Marwan N; Vicoso, Beatriz (PLoS Genetics)
Our understanding of the molecular pathways that regulate oogenesis and define cellular identity in the Arthropod female reproductive system and the extent of their conservation is currently very limited. This is due to the focus on model systems, including Drosophila and Daphnia, which do not reflect the observed diversity of morphologies, reproductive modes, and sex chromosome systems. We use single-nucleus RNA and ATAC sequencing to produce a comprehensive single nucleus atlas of the adult Artemia franciscana female reproductive system. We map our data to the Fly Cell Atlas single-nucleus dataset of the Drosophila melanogaster ovary, shedding light on the conserved regulatory programs between the two distantly related Arthropod species. We identify the major cell types known to be present in the Artemia ovary, including germ cells, follicle cells, and ovarian muscle cells. Additionally, we use the germ cells to explore gene regulation and expression of the Z chromosome during meiosis, highlighting its unique regulatory dynamics and allowing us to explore the presence of meiotic sex chromosome silencing in this group.

Ten years of demographic modelling of divergence and speciation in the sea - De Jode, Aurélien; Le Moan, Alan; Johannesson, Kerstin; Faria, Rui; Stankowski, Sean; Westram, Anja M; Butlin, Roger K.; Rafajlović, Marina; Fraisse, Christelle (Evolutionary Applications)
Understanding population divergence that eventually leads to speciation is essential for evolutionary biology. High species diversity in the sea was regarded as a paradox when strict allopatry was considered necessary for most speciation events because geographical barriers seemed largely absent in the sea, and many marine species have high dispersal capacities. Combining genome-wide data with demographic modelling to infer the demographic history of divergence has introduced new ways to address this classical issue. These models assume an ancestral population that splits into two subpopulations diverging according to different scenarios that allow tests for periods of gene flow. Models can also test for heterogeneities in population sizes and migration rates along the genome to account, respectively, for background selection and selection against introgressed ancestry. To investigate how barriers to gene flow arise in the sea, we compiled studies modelling the demographic history of divergence in marine organisms and extracted preferred demographic scenarios together with estimates of demographic parameters. These studies show that geographical barriers to gene flow do exist in the sea but that divergence can also occur without strict isolation. Heterogeneity of gene flow was detected in most population pairs suggesting the predominance of semipermeable barriers during divergence. We found a weak positive relationship between the fraction of the genome experiencing reduced gene flow and levels of genome-wide differentiation. Furthermore, we found that the upper bound of the ‘grey zone of speciation’ for our dataset extended beyond that found before, implying that gene flow between diverging taxa is possible at higher levels of divergence than previously thought. Finally, we list recommendations for further strengthening the use of demographic modelling in speciation research. These include a more balanced representation of taxa, more consistent and comprehensive modelling, clear reporting of results and simulation studies to rule out nonbiological explanations for general results.

Asymmetric Ramsey properties of random graphs involving cliques and cycles - Liebenau, Anita; Mattos, Letícia; Mendonca Dos Santos, Walner; Skokan, Jozef (Random Structures and Algorithms)
We say that (Formula presented.) if, in every edge coloring (Formula presented.), we can find either a 1-colored copy of (Formula presented.) or a 2-colored copy of (Formula presented.). The well-known states that the threshold for the property (Formula presented.) is equal to (Formula presented.), where (Formula presented.) is given by (Formula presented.) for any pair of graphs (Formula presented.) and (Formula presented.) with (Formula presented.). In this article, we show the 0-statement of the Kohayakawa–Kreuter conjecture for every pair of cycles and cliques.

Quenched universality for deformed Wigner matrices - Cipolloni, Giorgio; Erdös, László; Schröder, Dominik J (Probability Theory and Related Fields)
Following E. Wigner’s original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices H+xA with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just using the randomness of a single scalar real random variable x. Both results constitute quenched versions of bulk universality that has so far only been proven in annealed sense with respect to the probability space of the matrix ensemble.

Inserting one edge into a simple drawing is hard - Arroyo Guevara, Alan M; Klute, Fabian; Parada, Irene; Vogtenhuber, Birgit; Seidel, Raimund; Wiedera, Tilo (Discrete and Computational Geometry)
A simple drawing D(G) of a graph G is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge e in the complement of G can be inserted into D(G) if there exists a simple drawing of G+e extending D(G). As a result of Levi’s Enlargement Lemma, if a drawing is rectilinear (pseudolinear), that is, the edges can be extended into an arrangement of lines (pseudolines), then any edge in the complement of G can be inserted. In contrast, we show that it is NP-complete to decide whether one edge can be inserted into a simple drawing. This remains true even if we assume that the drawing is pseudocircular, that is, the edges can be extended to an arrangement of pseudocircles. On the positive side, we show that, given an arrangement of pseudocircles A and a pseudosegment σ, it can be decided in polynomial time whether there exists a pseudocircle Φσ extending σ for which A∪Φσ is again an arrangement of pseudocircles.

A simple algorithm for higher-order Delaunay mosaics and alpha shapes - Edelsbrunner, Herbert; Osang, Georg F (Algorithmica)
We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-k mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order-k mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation. We extend this algorithm to compute higher-order α-shapes and provide open-source implementations. We present experimental results for properties of higher-order Delaunay mosaics of random point sets.