The probability of two loci, separated by a certain genome length, being in contact can be inferred using the chromosome conformation capture (3C) method and related Hi-C experiments. How to go from the contact map, a matrix listing the mean contact probabilities between a large number of pairs of loci, to an ensemble of three-dimensional structures is an open problem. A solution to this problem, without assuming an assumed energy function, would be the first step in understanding the way nature has solved the packaging of chromosomes in tight cellular spaces. We created a theory, based on polymer physics characteristics of chromosomes and the maximum entropy principles, referred to as HIPPS (Hi-C-polymer-physics-structures) method, that allows us to calculate the 3D structures solely from Hi-C contact maps. The first step in the HIPPS method is to relate the mean contact probability ($⟨p_{ij}⟩$) between loci $i$ and $j$ and the average spatial distance $⟨{\overline{r}}_{ij}⟩$. This is a difficult problem to solve because the cell population is heterogeneous, which means that a given contact exists only in a small unknown fraction of cells. Despite the population heterogeneity, we first prove that there is a theoretical lower bound connecting $⟨p_{ij}⟩$ and $⟨{\overline{r}}_{ij}⟩$ via a power-law relation. We show, using simulations of a precisely solvable model, that the overall organization is accurately captured by constructing the distance map from the contact map even if the cell population is highly heterogeneous, thus justifying the use of the lower bound. In the second step, the mean distance matrix, with elements $⟨{\overline{r}}_{ij}⟩\prime \mathrm{s}$, is used as a constraint in the maximum entropy principle to obtain the joint distribution of spatial positions of the loci. Using the two steps, we created an ensemble of 3D structures for the 23 chromosomes from lymphoblastoid cells using the measured contact maps as inputs. The HIPPS method shows that conformations of chromosomes are heterogeneous even in a single cell type. The differences in the conformational heterogeneity of the same chromosome in different cell types (normal as well as cancerous cells) can also be quantitatively discerned using our theory. We validate the method by showing that the calculated volumes of the 23 chromosomes from the predicted 3D structures are in good agreement with experimental estimates. Because the method is general, the 3D structures for any species may be calculated directly from the contact map without the need to assume a specific polymer model, as is customarily done.

Competition and collaboration are at the heart of multiagent probabilistic spreading processes. The battle for public opinion and competitive marketing campaigns are typical examples of the former, while the joint spread of multiple diseases such as HIV and tuberculosis demonstrates the latter. These spreads are influenced by the underlying network topology, the infection rates between network constituents, recovery rates, and, equally important, the interactions between the spreading processes themselves. Here, for the first time, we derive dynamic message-passing equations that provide an exact description of the dynamics of two, interacting, unidirectional spreading processes on tree graphs, and we develop systematic low-complexity models that predict the spread on general graphs. We also develop a theoretical framework for the optimal control of interacting spreading processes through optimized resource allocation under budget constraints and within a finite time window. Derived algorithms can be used to maximize the desired spread in the presence of a rival competitive process and to limit the spread through vaccination in the case of coupled infectious diseases. We demonstrate the efficacy of the framework and optimization method on both synthetic and real-world networks.

Opinion polarization is on the rise, causing concerns for the openness of public debates. Additionally, extreme opinions on different topics often show significant correlations. The dynamics leading to these polarized ideological opinions pose a challenge: How can such correlations emerge, without assuming them a priori in individual preferences or in a preexisting social structure? Here, we propose a simple model that qualitatively reproduces ideological opinion states found in survey data, even between rather unrelated, but sufficiently controversial, topics. Inspired by skew coordinate systems recently proposed in natural language processing models, we solidify these intuitions in a formalism of opinions unfolding in a multidimensional space where topics form a nonorthogonal basis. Opinions evolve according to the social interactions among the agents, which are ruled by homophily: Two agents sharing similar opinions are more likely to interact. The model features phase transitions between a global consensus, opinion polarization, and ideological states. Interestingly, the ideological phase emerges by relaxing the assumption of an orthogonal basis of the topic space, i.e., if topics thematically overlap. Furthermore, we analytically and numerically show that these transitions are driven by the controversialness of the topics discussed; the more controversial the topics, the more likely are opinions to be correlated. Our findings shed light upon the mechanisms driving the emergence of ideology in the formation of opinions.

We determine for the first time the magnetic dipole moment of a short-lived nucleus with part-per-million (ppm) accuracy. To achieve this 2-orders-of-magnitude improvement over previous studies, we implement a number of innovations into our $\beta$-detected nuclear magnetic resonance ($\beta$-NMR) setup at ISOLDE at CERN. Using liquid samples as hosts, we obtain narrow, subkilohertz-linewidth, resonances, while a simultaneous in situ ${}^1\mathrm{H}$ NMR measurement allows us to calibrate and stabilize the magnetic field to ppm precision, thus eliminating the need for additional $\beta$-NMR reference measurements. Furthermore, we use ab initio calculations of NMR shielding constants to improve the accuracy of the reference magnetic moment, thus removing a large systematic error. We demonstrate the potential of this combined approach with the 1.1 s half-life radioactive nucleus ${}^{26}\mathrm{Na}$, which is relevant for biochemical studies. Our technique can be readily extended to other isotopic chains, providing accurate magnetic moments for many short-lived nuclei. Furthermore, we discuss how our approach can open the path toward a wide range of applications of the ultrasensitive $\beta$-NMR in physics, chemistry, and biology.

On 31 December, 2019, an outbreak of a novel coronavirus, SARS-CoV-2, that causes the COVID-19 disease, was first reported in Hubei, mainland China. This epidemics’ health threat is probably one of the biggest challenges faced by our interconnected modern societies. According to the epidemiological reports, the large basic reproduction number $R_0\sim 3.0$, together with a huge fraction of asymptomatic infections, paved the way for a major crisis of the national health capacity systems. Here, we develop an age-stratified mobility-based metapopulation model that encapsulates the main particularities of the spreading of COVID-19 regarding (i) its transmission among individuals, (ii) the specificities of certain demographic groups with respect to the impact of COVID-19, and (iii) the human mobility patterns inside and among regions. The full dynamics of the epidemic is formalized in terms of a microscopic Markov chain approach that incorporates the former elements and the possibility of implementing containment measures based on social distancing and confinement. With this model, we study the evolution of the effective reproduction number $\mathcal{R}(t)$, the key epidemiological parameter to track the evolution of the transmissibility and the effects of containment measures, as it quantifies the number of secondary infections generated by an infected individual. The suppression of the epidemic is directly related to this value and is attained when $\mathcal{R}<1$. We find an analytical expression connecting $\mathcal{R}$ with nonpharmacological interventions, and its phase diagram is presented. We apply this model at the municipality level in Spain, successfully forecasting the observed incidence and the number of fatalities in the country at each of its regions. The expression for $\mathcal{R}$ should assist policymakers to evaluate the epidemics’ response to actions, such as enforcing or relaxing confinement and social distancing.

In recent years, social media has become an important platform for political discourse, being a site of both political conversations between voters and political advertisements from campaigns. While their individual influences on public discourse are well documented, the interplay between individual-level cognitive biases, social influence processes, dueling campaign efforts, and social media platforms remains unexamined. We introduce an agent-based model that integrates these dynamics and illustrates how their combination can lead to the formation of echo chambers. We find that the range of political viewpoints that individuals are willing to consider is a key determinant in the formation of polarized networks and the emergence of echo chambers and show that aggressive political campaigns can have counterproductive outcomes by radicalizing supporters and alienating moderates. Our model results demonstrate how certain elements of public discourse and political polarization can be understood as the result of an interactive process of shifting individual opinions, evolving social networks, and political campaigns. We also introduce a dynamic empirical case, retweet networks from the final stage of the 2016 U.S. presidential election, to show how our proposed model can be calibrated with real-world behavior.

We present modeling of the COVID-19 epidemic in Illinois, USA, capturing the implementation of a stay-at-home order and scenarios for its eventual release. We use a non-Markovian age-of-infection model that is capable of handling long and variable time delays without changing its model topology. Bayesian estimation of model parameters is carried out using Markov chain Monte Carlo methods. This framework allows us to treat all available input information, including both the previously published parameters of the epidemic and available local data, in a uniform manner. To accurately model deaths as well as demand on the healthcare system, we calibrate our predictions to total and in-hospital deaths as well as hospital and ICU bed occupancy by COVID-19 patients. We apply this model not only to the state as a whole but also its subregions in order to account for the wide disparities in population size and density. Without prior information on nonpharmaceutical interventions, the model independently reproduces a mitigation trend closely matching mobility data reported by Google and Unacast. Forward predictions of the model provide robust estimates of the peak position and severity and also enable forecasting the regional-dependent results of releasing stay-at-home orders. The resulting highly constrained narrative of the epidemic is able to provide estimates of its unseen progression and inform scenarios for sustainable monitoring and control of the epidemic.

Cell signaling is essential for cell fate determination and tissue patterning. As signaling ligands are presented to the receiving cell, they are recruited and recognized by the cell membrane so as to elicit a biological response and to pattern multicellular tissues. Cells can accumulate and transport these ligands, which results in an emergent organization of the ligands’ spatial distribution. To study this organization, we make use of a simplified experimental setup, in which single mouse embryonic stem cells (mESCs) can interact with immobilized ligands. We introduce a two-species age-dependent correlation function that allows the description and quantification of the spatiotemporal dynamics of single cell-ligand interactions. Through the analysis of mESC data and numerical simulations, we show that cells act as effective force-field generators, perturbing and organizing their environment. This organization, captured in the form of an aging effective potential, is an emergent property of the population of single cells interacting with randomly distributed localized ligands.

Covariance mapping [L. J. Frasinski, K. Codling, and P. A. Hatherly, Science 246, 1029 (1989)] is a well-established technique used for the study of mechanisms of laser-induced molecular ionization and decomposition. It measures statistical correlations between fluctuating signals of pairs of detected species (ions, fragments, electrons). A positive correlation identifies pairs of products originating from the same dissociation or ionization event. A major challenge for covariance-mapping spectroscopy is accessing decompositions of large polyatomic molecules, where true physical correlations are overwhelmed by spurious signals of no physical significance induced by fluctuations in experimental parameters. As a result, successful applications of covariance mapping have so far been restricted to low-mass systems, e.g., organic molecules of around 50 daltons (Da). Partial-covariance mapping was suggested to tackle the problem of spurious correlations by taking into account the independently measured fluctuations in the experimental conditions. However, its potential has never been realized for the decomposition of large molecules, because in these complex situations, determining and continuously monitoring multiple experimental parameters affecting all the measured signals simultaneously becomes unfeasible. We introduce, through deriving theoretically and confirming experimentally, a conceptually new type of partial-covariance mapping—self-correcting partial-covariance spectroscopy—based on a parameter extracted from the measured spectrum itself. We use the readily available total ion count as the self-correcting partial-covariance parameter, thus eliminating the challenge of determining experimental parameter fluctuations in covariance measurements of large complex systems. The introduced self-correcting partial covariance enables us to successfully resolve correlations of molecules as large as ${10}^3–{10}^4\mathrm{Da}$, 2 orders of magnitude above the state of the art. This opens new opportunities for mechanistic studies of large molecule decompositions through revealing their fragment-fragment correlations. Moreover, we demonstrate that self-correcting partial covariance is applicable to solving the inverse problem: reconstruction of a molecular structure from its fragment spectrum, within two-dimensional partial-covariance mass spectrometry.

Experimental data are often affected by uncontrolled variables that make analysis and interpretation difficult. For spatiotemporal systems, this problem is further exacerbated by their intricate dynamics. Modern machine learning methods are particularly well suited for analyzing and modeling complex datasets, but to be effective in science, the result needs to be interpretable. We demonstrate an unsupervised learning technique for extracting interpretable physical parameters from noisy spatiotemporal data and for building a transferable model of the system. In particular, we implement a physics-informed architecture based on variational autoencoders that is designed for analyzing systems governed by partial differential equations. The architecture is trained end to end and extracts latent parameters that parametrize the dynamics of a learned predictive model for the system. To test our method, we train our model on simulated data from a variety of partial differential equations with varying dynamical parameters that act as uncontrolled variables. Numerical experiments show that our method can accurately identify relevant parameters and extract them from raw and even noisy spatiotemporal data (tested with roughly 10% added noise). These extracted parameters correlate well (linearly with $R^2>0.95$) with the ground truth physical parameters used to generate the datasets. We then apply this method to nonlinear fiber propagation data, generated by an ab initio simulation, to demonstrate its capabilities on a more realistic dataset. Our method for discovering interpretable latent parameters in spatiotemporal systems will allow us to better analyze and understand real-world phenomena and datasets, which often have unknown and uncontrolled variables that alter the system dynamics and cause varying behaviors that are difficult to disentangle.

Multilayer networks preserve full information about the different interactions among the constituents of a complex system, and have recently proven quite useful in modeling transportation networks, social circles, and the human brain. A fundamental and still open problem is to assess if and when the multilayer representation of a system provides a qualitatively better model than the classical single-layer aggregated network. Here we tackle this problem from an algorithmic information theory perspective. We propose an intuitive way to encode a multilayer network into a bit string, and we define the complexity of a multilayer network as the ratio of the Kolmogorov complexity of the bit strings associated to the multilayer and to the corresponding aggregated graph. We find that there exists a maximum amount of additional information that a multilayer model can encode with respect to the equivalent single-layer graph. We show how our complexity measure can be used to obtain low-dimensional representations of multidimensional systems, to cluster multilayer networks into a small set of meaningful superfamilies, and to detect tipping points in the evolution of different time-varying multilayer graphs. Interestingly, the low-dimensional multiplex networks obtained with the proposed method also retain most of the dynamical properties of the original systems, as demonstrated for instance by the preservation of the epidemic threshold in the multiplex susceptible-infected-susceptible model. These results suggest that information-theoretic approaches can be effectively employed for a more systematic analysis of static and time-varying multidimensional complex systems.

Unraveling bacterial strategies for spatial exploration is crucial for understanding the complexity in the organization of life. Bacterial motility determines the spatiotemporal structure of microbial and controls infection spreading and the microbiota organization in guts or in soils. Most theoretical approaches for modeling bacterial transport rely on their run-and-tumble motion. For Escherichia coli, the run-time distribution is reported to follow a Poisson process with a single characteristic time related to the rotational switching of the flagellar motors. However, direct measurements on flagellar motors show heavy-tailed distributions of rotation times stemming from the intrinsic noise in the chemotactic mechanism. Currently, there is no direct experimental evidence that the stochasticity in the chemotactic machinery affects the macroscopic motility of bacteria. In stark contrast with the accepted vision of run and tumble, here we report a large behavioral variability of wild-type E. coli, revealed in their three-dimensional trajectories. At short observation times, a large distribution of run times is measured on a population and attributed to the slow fluctuations of a signaling protein triggering the flagellar motor reversal. Over long times, individual bacteria undergo significant changes in motility. We demonstrate that such a large distribution of run times introduces measurement biases in most practical situations. Our results reconcile the notorious conundrum between run-time observations and motor-switching statistics. We finally propose that statistical modeling of transport properties, currently undertaken in the emerging framework of active matter studies, should be reconsidered under the scope of this large variability of motility features.

In filtering, each output is produced by a certain number of different inputs. We explore the statistics of this degeneracy in an explicitly treatable filtering problem in which filtering performs the maximal compression of relevant information contained in inputs (arrays of zeros and ones). This problem serves as a reference model for the statistics of filtering and related sampling problems. The filter patterns in this problem conveniently allow a microscopic, combinatorial consideration. This allows us to find the statistics of outputs, namely the exact distribution of output degeneracies, for arbitrary input sizes. We observe that the resulting degeneracy distribution of outputs decays as $e^{-c{\log }^{\alpha }d}$ with degeneracy $d$, where $c$ is a constant and exponent $\alpha >1$, i.e., faster than a power law. Importantly, its form essentially depends on the size of the input dataset, appearing to be closer to a power-law dependence for small dataset sizes than for large ones. We demonstrate that for sufficiently small input dataset sizes typical for empirical studies, this distribution could be easily perceived as a power law. We extend our results to filter patterns of various sizes and demonstrate that the shortest filter pattern provides the maximum informative representations of the inputs.

Cellular mechanics drives epithelial morphogenesis, the process wherein cells collectively rearrange to produce tissue-scale deformations that determine organismal shape. However, quantitative understanding of tissue mechanics is impaired by the difficulty of direct measurement of stress in vivo. This difficulty has spurred the development of image-based inference algorithms that estimate stress from snapshots of epithelial geometry. Such methods are challenged by sensitivity to measurement error and thus require accurate geometric segmentation for practical use. We overcome this difficulty by introducing a novel approach—the variational method of stress inference (VMSI)—which exploits the fundamental duality between stress and geometry at equilibrium of discrete mechanical networks that model confluent cellular layers. We approximate the apical geometry of an epithelial tissue by a 2D tiling with circular arc polygons in which arcs represent intercellular interfaces defined by the balance of local line tension and pressure differentials between adjacent cells. The mechanical equilibrium of such networks imposes extensive local constraints on circular arc polygon geometry. These constraints provide the foundation of VMSI which, starting with images of epithelial monolayers, simultaneously approximates both tissue geometry and internal forces, subject to the constraint of equilibrium. We find VMSI to be more robust than previous methods. Specifically, the VMSI performance is validated by the comparison of the predicted cellular and mesoscopic scale stress with the measured myosin II patterns during early Drosophila embryogenesis. VMSI prediction of a mesoscopic stress tensor correlates at the 80% level with the measured myosin distribution and reveals that most of the myosin activity in that case is involved in a static internal force balance within the epithelial layer. In addition to insight into cell mechanics, this study provides a practical method for nondestructive estimation of stress in live epithelial tissue.

We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which represents a generalization of degree-ordered percolation, we derive a scaling solution on uncorrelated complex networks, unveiling the existence of diverse mechanisms leading to the formation of a percolating cluster. The scaling solution accurately reproduces universal properties of the transition. This finding is used to infer the critical properties of the susceptible-infected-susceptible model for epidemics in infinite and finite power-law distributed networks. Here, discrepancies between analytical approaches and numerical results regarding the finite-size scaling of the epidemic threshold are a crucial open issue in the literature. We find that the scaling exponent assumes a nontrivial value during a long preasymptotic regime. We calculate this value, finding good agreement with numerical evidence. We also show that the crossover to the true asymptotic regime occurs for sizes much beyond currently feasible simulations. Our findings allow us to rationalize and reconcile all previously published results (both analytical and numerical), thus ending a long-standing debate.

There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community of individuals which undergoes local birth-death, immigration, and local jumps on a regular lattice. We study its properties when the system is close to its critical point. Even if this model violates detailed balance, within a physically relevant regime dominated by fluctuations, it is possible to calculate analytically the probability density function of the number of individuals living in a given volume, which captures the close-to-critical behavior of the community across spatial scales. We find that the resulting distribution satisfies an equation where spatial effects are encoded in appropriate functions of space, which we calculate explicitly. The validity of the analytical formulae is confirmed by simulations in the expected regimes. We finally discuss how this model in the critical-like regime is in agreement with several biodiversity patterns observed in tropical rain forests.

While there have been many calls to improve the quality of instructional physics labs, there exists little research on the effectiveness of lab instruction. This study provides a direct comparison between labs that have goals to reinforce physics content to those that emphasize experimentation skills. In this controlled study, all students attended the same lecture and discussion sections, had the same homework and exams, but attended labs that had one of two aims: teaching experimentation or reinforcing content. We compare students’ engagement with experimentation during the lab as well as the impacts on students’ exam performance and attitudes and beliefs about experimental physics. We find no measurable differences between lab conditions on students’ exam performance. Nonetheless, we find measurable and significant improvements in students’ engagement in expertlike experimentation practices and attitudes and beliefs about experimental physics for students in the experimentation labs. The benefits of the experimentation labs are stable across two subsequent semesters of implementation, as measured via standardized assessments. The results provide direct evidence of the extensive benefits of using labs to teach experimentation while directly demonstrating that shifting instructional goals and structure in labs can occur without cost to performance on course exams.

Recent studies of holographic tensor network models defined on regular tessellations of hyperbolic space have not yet addressed the underlying discrete geometry of the boundary. We show that the boundary degrees of freedom naturally live on a novel structure, a “conformal quasicrystal,” that provides a discrete model of conformal geometry. We introduce and construct a class of one-dimensional conformal quasicrystals and discuss a higher-dimensional example (related to the Penrose tiling). Our construction permits discretizations of conformal field theories that preserve an infinite discrete subgroup of the global conformal group at the cost of lattice periodicity.

Despite recent progress in our understanding of complex dynamic networks, it remains challenging to devise sufficiently accurate models to observe, control, or predict the state of real systems in biology, economics, or other fields. A largely overlooked fact is that these systems are typically open and receive unknown inputs from their environment. A further fundamental obstacle is structural model errors caused by insufficient or inaccurate knowledge about the quantitative interactions in the real system. Here, we show that unknown inputs to open systems and model errors can be treated under the common framework of invertibility, which is a requirement for reconstructing these disturbances from output measurements. By exploiting the fact that invertibility can be decided from the influence graph of the system, we analyze the relationship between structural network properties and invertibility under different realistic scenarios. We show that sparsely connected scale-free networks are the most difficult to invert. We introduce a new sensor node placement algorithm to select a minimum set of measurement positions in the network required for invertibility. This algorithm facilitates optimal experimental design for the reconstruction of inputs or model errors from output measurements. Our results have both fundamental and practical implications for nonlinear systems analysis, modeling, and design.

We introduce an ordinate method for noisy data analysis, based solely on rank information and thus insensitive to outliers. The method is nonparametric and objective, and the required data processing is parsimonious. The main ingredients include a rank-order data matrix and its transform to a stable form, which provide linear trends in excellent agreement with least squares regression, despite the loss of magnitude information. A group symmetry orthogonal decomposition of the 2D rank-order transform for iid (white) noise is further ordered by principal component analysis. This two-step procedure provides a noise “etalon” used to characterize arbitrary stationary stochastic processes. The method readily distinguishes both the Ornstein-Uhlenbeck process and chaos generated by the logistic map from white noise. Ranking within randomness differs fundamentally from that in deterministic chaos and signals, thus forming the basis for signal detection. To further illustrate the breadth of applications, we apply this ordinate method to the canonical nonlinear parameter estimation problem of two-species radioactive decay, outperforming special-purpose least squares software. We demonstrate that the method excels when extracting trends in heavy-tailed noise and, unlike the Thiele-Sen estimator, is not limited to linear regression. A simple expression is given that yields a close approximation for signal extraction of an underlying, generally nonlinear signal.