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The notion of Fr\'echet mean (also known as "barycenter") network is the workhorse of most machine learning algorithms that require the estimation of a "location" parameter to analyse network-valued data. In this context, it is critical that the network barycenter inherits the topological structure of the networks in the training dataset. The metric - which measures the proximity between networks - controls the structural properties of the barycenter. This work is significant because it provides for the first time analytical estimates of the sample Fr\'echet mean for the stochastic blockmodel, which is at the cutting edge of rigorous probabilistic analysis of random networks. We show that the mean network computed with the Hamming distance is unable to capture the topology of the networks in the training sample, whereas the mean network computed using the effective resistance distance recovers the correct partitions and associated edge density. From a practical standpoint, our work informs the choice of metrics in the context where the sample Fr\'echet mean network is used to characterise the topology of networks for network-valued machine learning, Comment: 23 pages

Proteomics is the large scale study of protein structure and function from biological systems through protein identification and quantification. "Shotgun proteomics" or "bottom-up proteomics" is the prevailing strategy, in which proteins are hydrolyzed into peptides that are analyzed by mass spectrometry. Proteomics studies can be applied to diverse studies ranging from simple protein identification to studies of proteoforms, protein-protein interactions, protein structural alterations, absolute and relative protein quantification, post-translational modifications, and protein stability. To enable this range of different experiments, there are diverse strategies for proteome analysis. The nuances of how proteomic workflows differ may be challenging to understand for new practitioners. Here, we provide a comprehensive overview of different proteomics methods to aid the novice and experienced researcher. We cover from biochemistry basics and protein extraction to biological interpretation and orthogonal validation. We expect this work to serve as a basic resource for new practitioners in the field of shotgun or bottom-up proteomics.

How predictable is the next move of an animal? Specifically, which factors govern the short- and long-term motion patterns and the overall dynamics of landbound, plant-eating animals and ruminants in particular? To answer this question, we here study the movement dynamics of springbok antelopes Antidorcas marsupialis. We propose complementary statistical analysis techniques combined with machine learning approaches to analyze, across multiple time scales, the springbok motion recorded in long-term GPS-tracking of collared springboks at a private wildlife reserve in Namibia. As a new result, we are able to predict the springbok movement within the next hour with a certainty of about 20\%. The remaining 80\% are stochastic in nature and are induced by unaccounted factors in the modeling algorithm and by individual behavioral features of springboks. We find that directedness of motion contributes approximately 17\% to this predicted fraction. We find that the measure for directedeness is strongly dependent on the daily cycle. The previously known daily affinity of springboks to their water points, as predicted from our machine learning algorithm, overall accounts for only 3\% of this predicted deterministic component of springbok motion. Moreover, the resting points are found to affect the motion of springboks at least as much as the formally studied effects of water points. The generality of these statements for the motion patterns and their underlying behavioral reasons for other ruminants can be examined on the basis of our statistical analysis tools., Comment: 17 pages, 9 figures, RevTeX

This work addresses the rising demand for novel tools in statistical and machine learning for "graph-valued random variables" by proposing a fast algorithm to compute the sample Frechet mean, which replaces the concept of sample mean for graphs (or networks). We use convolutional neural networks to learn the morphology of the graphs in a set of graphs. Our experiments on several ensembles of random graphs demonstrate that our method can reliably recover the sample Frechet mean.

For graph-valued data sampled iid from a distribution $\mu$, the sample moments are computed with respect to a choice of metric. In this work, we equip the set of graphs with the pseudo-metric defined by the $\ell_2$ norm between the eigenvalues of the respective adjacency matrices. We use this pseudo metric and the respective sample moments of a graph valued data set to infer the parameters of a distribution $\hat{\mu}$ and interpret this distribution as an approximation of $\mu$. We verify experimentally that complex distributions $\mu$ can be approximated well taking this approach.

The COVID-19 pandemic has presented many challenges that have spurred biotechnological research to address specific problems. Diagnostics is one area where biotechnology has been critical. Diagnostic tests play a vital role in managing a viral threat by facilitating the detection of infected and/or recovered individuals. From the perspective of what information is provided, these tests fall into two major categories, molecular and serological. Molecular diagnostic techniques assay whether a virus is present in a biological sample, thus making it possible to identify individuals who are currently infected. Additionally, when the immune system is exposed to a virus, it responds by producing antibodies specific to the virus. Serological tests make it possible to identify individuals who have mounted an immune response to a virus of interest and therefore facilitate the identification of individuals who have previously encountered the virus. These two categories of tests provide different perspectives valuable to understanding the spread of SARS-CoV-2. Within these categories, different biotechnological approaches offer specific advantages and disadvantages. Here we review the categories of tests developed for the detection of the SARS-CoV-2 virus or antibodies against SARS-CoV-2 and discuss the role of diagnostics in the COVID-19 pandemic.

Wordle is an online word puzzle game that gained viral popularity in January 2022. The goal is to guess a hidden five letter word. After each guess, the player gains information about whether the letters they guessed are present in the word, and whether they are in the correct position. Numerous blogs have suggested guessing strategies and starting word lists that improve the chance of winning. Optimized algorithms can win 100% of games within five of the six allowed trials. However, it is infeasible for human players to use these algorithms due to an inability to perfectly recall all known 5-letter words and perform complex calculations that optimize information gain. Here, we present two different methods for choosing starting words along with a framework for discovering the optimal human strategy based on reinforcement learning. Human Wordle players can use the rules we discover to optimize their chance of winning.

We address the following foundational question: what is the population, and sample, Frechet mean (or median) graph of an ensemble of inhomogeneous Erdos-Renyi random graphs? We prove that if we use the Hamming distance to compute distances between graphs, then the Frechet mean (or median) graph of an ensemble of inhomogeneous random graphs is obtained by thresholding the expected adjacency matrix of the ensemble. We show that the result also holds for the sample mean (or median) when the population expected adjacency matrix is replaced with the sample mean adjacency matrix. Consequently, the Frechet mean (or median) graph of inhomogeneous Erdos-Renyi random graphs exhibits a sharp threshold: it is either the empty graph, or the complete graph. This novel theoretical result has some significant practical consequences; for instance, the Frechet mean of an ensemble of sparse inhomogeneous random graphs is always the empty graph.

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Frechet mean. In this work, we equip a set of graphs with the pseudometric defined by the norm between the eigenvalues of their respective adjacency matrix. Unlike the edit distance, this pseudometric reveals structural changes at multiple scales, and is well adapted to studying various statistical problems for graph-valued data. We describe an algorithm to compute an approximation to the sample Frechet mean of a set of undirected unweighted graphs with a fixed size using this pseudometric., Comment: arXiv admin note: text overlap with arXiv:2105.04062

The availability of large datasets composed of graphs creates an unprecedented need to invent novel tools in statistical learning for graph-valued random variables. To characterize the average of a sample of graphs, one can compute the sample Frechet mean and median graphs. In this paper, we address the following foundational question: does a mean or median graph inherit the structural properties of the graphs in the sample? An important graph property is the edge density; we establish that edge density is an hereditary property, which can be transmitted from a graph sample to its sample Frechet mean or median graphs, irrespective of the method used to estimate the mean or the median. Because of the prominence of the Frechet mean in graph-valued machine learning, this novel theoretical result has some significant practical consequences., Comment: 14 pages

Deviations from Brownian motion leading to anomalous diffusion are ubiquitously found in transport dynamics, playing a crucial role in phenomena from quantum physics to life sciences. The detection and characterization of anomalous diffusion from the measurement of an individual trajectory are challenging tasks, which traditionally rely on calculating the mean squared displacement of the trajectory. However, this approach breaks down for cases of important practical interest, e.g., short or noisy trajectories, ensembles of heterogeneous trajectories, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. Aiming to perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams independently applied their own algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, the results revealed clear differences between the various approaches, providing practical advice for users and a benchmark for developers., Comment: 63 pages, 5 main figures, 1 table, 28 supplementary figures. Website: http://www.andi-challenge.org

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Fr\'echet mean. In this work, we equip a set of graph with the pseudometric defined by the $\ell_2$ norm between the eigenvalues of their respective adjacency matrix . Unlike the edit distance, this pseudometric reveals structural changes at multiple scales, and is well adapted to studying various statistical problems on sets of graphs. We describe an algorithm to compute an approximation to the Fr\'echet mean of a set of undirected unweighted graphs with a fixed size., Comment: 28 pages

False-positive results and bias may be common features of the biomedical literature today, including risk factor-chronic disease research. A study was undertaken to assess the reliability of base studies used in a meta-analysis examining whether carbon monoxide, particulate matter 10 and 2.5 micro molar, sulfur dioxide, nitrogen dioxide and ozone are risk factors for asthma exacerbation (hospital admission and emergency room visits for asthma attack). The number of statistical tests and models were counted in 17 randomly selected base papers from 87 used in the meta-analysis. P-value plots for each air component were constructed to evaluate the effect heterogeneity of p-values used from all 87 base papers The number of statistical tests possible in the 17 selected base papers was large, median=15,360 (interquartile range=1,536 to 40,960), in comparison to results presented. Each p-value plot showed a two-component mixture with small p-values less than .001 while other p-values appeared random (p-values greater than .05). Given potentially large numbers of statistical tests conducted in the 17 selected base papers, p-hacking cannot be ruled out as explanations for small p-values. Our interpretation of the meta-analysis is that the random p-values indicating null associations are more plausible and that the meta-analysis will not likely replicate in the absence of bias. We conclude the meta-analysis and base papers used are unreliable and do not offer evidence of value to inform public health practitioners about air quality as a risk factor for asthma exacerbation. The following areas are crucial for enabling improvements in risk factor chronic disease observational studies at the funding agency and journal level: preregistration, changes in funding agency and journal editor (and reviewer) practices, open sharing of data and facilitation of reproducibility research., Comment: Paper with supplemental material

We study a method for detecting the origins of anomalous diffusion, when it is observed in an ensemble of times-series, generated experimentally or numerically, without having knowledge about the exact underlying dynamics. The reasons for anomalous diffusive scaling of the mean-squared displacement are decomposed into three root causes: increment correlations are expressed by the "Joseph effect" [Mandelbrot 1968], fat-tails of the increment probability density lead to a "Noah effect" [Mandelbrot 1968], and non-stationarity, to the "Moses effect" [Chen et al. 2017]. After appropriate rescaling, based on the quantification of these effects, the increment distribution converges at increasing times to a time-invariant asymptotic shape. For different processes, this asymptotic limit can be an equilibrium state, an infinite-invariant, or an infinite-covariant density. We use numerical methods of time-series analysis to quantify the three effects in a model of a non-linearly coupled L\'evy walk, compare our results to theoretical predictions, and discuss the generality of the method., Comment: Main text is 13 pages, 3 pages of appendixes

We analyze European temperature variability from station data with the method of detrended fluctuation analysis. This method is known to give a scaling exponent indicating long range correlations in time for temperature anomalies. However, by a more careful look at the fluctuation function we are able to explain the emergent scaling behaviour by short time relaxation, the yearly cycle and one additional process. It turns out that for many stations this interannual variability is an oscillatory mode with a period length of approximately 7-8 years, which is consistent with results of other methods. We discuss the spatial patterns in all parameters and validate the finding of the 7-8 year period by comparing stations with and without this mode.

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees in data in these fields yields insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances (also known as $\lambda$ distances) and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies and different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and empirical datasets. We put forward a multi-scale picture of graph structure, in which the effect of global and local structure upon the distance measures is considered. We make recommendations on the applicability of different distance measures to empirical graph data problem based on this multi-scale view. Finally, we introduce the Python library NetComp which implements the graph distances used in this work.

Identification of nearly all proteins in a system using data-dependent acquisition (DDA) mass spectrometry has become routine for simple organisms, such as bacteria and yeast. Still, quantification of the identified proteins may be a complex process and require multiple different software packages. This protocol describes identification and label-free quantification of proteins from bottom-up proteomics experiments. This method can be used to quantify all the detectable proteins in any DDA dataset collected with high-resolution precursor scans. This protocol may be used to quantify proteome remodeling in response to a drug treatment or a gene knockout. Notably, the method uses the latest and fastest freely-available software, and the entire protocol can be completed in a few hours with data from organisms with relatively small genomes, such as yeast or bacteria.

We decompose the anomalous diffusive behavior found in a model of aging into its fundamental constitutive causes. The model process is a sum of increments that are iterates of a chaotic dynamical system, the Pomeau-Manneville map. The increments can have long-time correlations, fat-tailed distributions and be non-stationary. Each of these properties can cause anomalous diffusion through what is known as the Joseph, Noah and Moses effects, respectively. The model can have either sub- or super-diffusive behavior, which we find is generally due to a combination of the three effects. Scaling exponents quantifying each of the three constitutive effects are calculated using analytic methods and confirmed with numerical simulations. They are then related to the scaling of the distribution of the process through a scaling relation. Finally, the importance of the Moses effect in the anomalous diffusion of experimental systems is discussed., Comment: This is an author-created, un-copyedited version of an article accepted for publication in the New Journal of Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1367-2630/aaeea2

The study of time-varying (dynamic) networks (graphs) is of fundamental importance for computer network analytics. Several methods have been proposed to detect the effect of significant structural changes in a time series of graphs. The main contribution of this work is a detailed analysis of a dynamic community graph model. This model is formed by adding new vertices, and randomly attaching them to the existing nodes. It is a dynamic extension of the well-known stochastic blockmodel. The goal of the work is to detect the time at which the graph dynamics switches from a normal evolution -- where balanced communities grow at the same rate -- to an abnormal behavior -- where communities start merging. In order to circumvent the problem of decomposing each graph into communities, we use a metric to quantify changes in the graph topology as a function of time. The detection of anomalies becomes one of testing the hypothesis that the graph is undergoing a significant structural change. In addition the the theoretical analysis of the test statistic, we perform Monte Carlo simulations of our dynamic graph model to demonstrate that our test can detect changes in graph topology.

We report on the development of a new family of SQUID current sensors based on sub-micron cross-type Josephson tunnel junctions. Their low total junction capacitance permit high usable voltage swings of more than 100 {\mu}V and exceptional low noise of the SQUIDs at 4.2 K. Integrated rf-filter as well as high tolerable background fields during cool-down of up to 9.6 mT enable their highly reliable and easy use. With input coil inductances ranging from 10 nH to 2.8 {\mu}H and current sensitivities and coupled energy resolution down to 65 fA/Hz^{1/2} and below 10 h, respectively, they are a versatile tool for numerous applications., Comment: 6 pages, 4 figures

We report on the development of nearly quantum limited SQUIDs with miniature pickup loop dimensions. The implemented high quality and low capacitance cross-type Nb/AlOx/Nb Josephson junctions offer large $I_CR_N$-products and therefore enable an exceptional low noise level of the SQUIDs. Devices with loop dimensions of 1 {\mu}m exhibit white flux noise levels as low as $45 n{\Phi}_0/Hz^{1/2}$ corresponding to an energy resolution {\epsilon} of about 1 h at 4.2 K, with h being Plancks constant. Moreover, the large usable voltage swings of the devices of about 300 {\mu}V allow highly sensitive and easy single-stage operation while exploring nearly the intrinsic noise of the SQUIDs, beneficial e.g. for sensor arrays in SQUID microscopy.

We report on the development of an ultralow noise thin-film based SQUID magnetometer. A niobium thin-film pickup coil is connected to the input coil of a SQUID current sensor. The low capacitance of the used sub-micrometer cross-type Josephson junctions enable superior noise performance of the device. Application scenarios e.g. in geophysics and ultra-low field magnetic resonance imaging are discussed., Comment: 3 pages, 2 figures

We describe here the recent results of a multidisciplinary effort to design a biomarker that can actively and continuously decode the progressive changes in neuronal organization leading to epilepsy, a process known as epileptogenesis. Using an animal model of acquired epilepsy, wechronically record hippocampal evoked potentials elicited by an auditory stimulus. Using a set of reduced coordinates, our algorithm can identify universal smooth low-dimensional configurations of the auditory evoked potentials that correspond to distinct stages of epileptogenesis. We use a hidden Markov model to learn the dynamics of the evoked potential, as it evolves along these smooth low-dimensional subsets. We provide experimental evidence that the biomarker is able to exploit subtle changes in the evoked potential to reliably decode the stage of epileptogenesis and predict whether an animal will eventually recover from the injury, or develop spontaneous seizures.

Covariance matrices are fundamental to the analysis and forecast of economic, physical and biological systems. Although the eigenvalues $\{\lambda_i\}$ and eigenvectors $\{{\bf u}_i\}$ of a covariance matrix are central to such endeavors, in practice one must inevitably approximate the covariance matrix based on data with finite sample size $n$ to obtain empirical eigenvalues $\{\tilde{\lambda}_i\}$ and eigenvectors $\{\tilde{{\bf u}}_i\}$, and therefore understanding the error so introduced is of central importance. We analyze eigenvector error $\|{\bf u}_i - \tilde{{\bf u}}_i \|^2$ while leveraging the assumption that the true covariance matrix having size $p$ is drawn from a matrix ensemble with known spectral properties---particularly, we assume the distribution of population eigenvalues weakly converges as $p\to\infty$ to a spectral density $\rho(\lambda)$ and that the spacing between population eigenvalues is similar to that for the Gaussian orthogonal ensemble. Our approach complements previous analyses of eigenvector error that require the full set of eigenvalues to be known, which can be computationally infeasible when $p$ is large. To provide a scalable approach for uncertainty quantification of eigenvector error, we consider a fixed eigenvalue $\lambda$ and approximate the distribution of the expected square error $r= \mathbb{E}\left[\| {\bf u}_i - \tilde{{\bf u}}_i \|^2\right]$ across the matrix ensemble for all ${\bf u}_i$ associated with $\lambda_i=\lambda$. We find, for example, that for sufficiently large matrix size $p$ and sample size $n>p$, the probability density of $r$ scales as $1/nr^2$. This power-law scaling implies that eigenvector error is extremely heterogeneous---even if $r$ is very small for most eigenvectors, it can be large for others with non-negligible probability. We support this and further results with numerical experiments., Comment: 24 pages, 8 figures

To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we propose a family of distances that can be tuned to quantify structural changes occurring on a graph at different scales: from the local scale formed by the neighbors of each vertex, to the largest scale that quantifies the connections between clusters, or communities. Our approach results in the definition of a true distance, and not merely a notion of similarity. We propose fast (linear in the number of edges) randomized algorithms that can quickly compute an approximation to the graph metric. The third contribution involves a fast algorithm to increase the robustness of a network by optimally decreasing the Kirchhoff index. Finally, we conduct several experiments on synthetic graphs and real networks, and we demonstrate that we can detect configurational changes that are directly related to the hidden variables governing the evolution of dynamic networks.

In this work we address the problem of detecting overlapping communities in social networks. Because the word "community" is an ambiguous term, it is necessary to quantify what it means to be a community within the context of a particular type of problem. Our interpretation is that this quantification must be done at a minimum of three scales. These scales are at the level of: individual nodes, individual communities, and the network as a whole. Each of these scales involves quantitative features of community structure that are not accurately represented at the other scales, but are important for defining a particular notion of community. Our work focuses on providing sensible ways to quantify what is desired at each of these scales for a notion of community applicable to social networks, and using these models to develop a community detection algorithm. Appealing features of our approach is that it naturally allows for nodes to belong to multiple communities, and is computationally efficient for large networks with low overall edge density. The scaling of the algorithm is $O(N~\overline{k^2} + \overline{N_{com}^2})$, where $N$ is the number of nodes in the network, $\overline{N_{com}^2}$ is the average squared community size, and $\overline{k^2}$ is the expected value of a node's degree squared. Although our work focuses on developing a computationally efficient algorithm for overlapping community detection in the context of social networks, our primary contribution is developing a methodology that is highly modular and can easily be adapted to target specific notions of community.

We report on the development of highly sensitive SQUIDs featuring sub-micrometer loop dimensions. The integration of high quality and low capacitance SIS Nb/AlOx/Nb cross-type Josephson tunnel junctions results in white flux noise levels as low as 66 n$\Phi_0$/Hz$^{ 1/2} $, well below state-of-the-art values of their Nb-based counterparts based on constriction type junctions. Estimation of the spin sensitivity of the best SQUIDs yield $S_\mu^{ 1/2} < 7 \mu_B$/Hz$^{ 1/2} $ in the white noise region, suitable for the investigation of small spin systems. We discuss fabrication challenges, show results on the electrical characterization of devices with various pickup loops, and describe options for further improvement, which may push the sensitivity of such devices even to single spin resolution., Comment: 8 pages, 3 figures