Topological learning in multiclass data sets.

We specialize techniques from topological data analysis to the problem of characterizing the topological complexity (as defined in the body of the paper) of a multiclass data set. As a by-product, a topological classifier is defined that uses an open subcovering of the data set. This subcovering can be used to construct a simplicial complex whose topological features (e.g., Betti numbers) provide information about the classification problem. We use these topological constructs to study the impact of topological complexity on learning in feedforward deep neural networks (DNNs). We hypothesize that topological complexity is negatively correlated with the ability of a fully connected feedforward deep neural network to learn to classify data correctly. We evaluate our topological classification algorithm on multiple constructed and open-source data sets. We also validate our hypothesis regarding the relationship between topological complexity and learning in DNN's on multiple data sets.

The metabolomic physics of complex diseases.

Human diseases involve metabolic alterations. Metabolomic profiles have served as a vital biomarker for the early identification of high-risk individuals and disease prevention. However, current approaches can only characterize individual key metabolites, without taking into account the reality that complex diseases are multifactorial, dynamic, heterogeneous, and interdependent. Here, we leverage a statistical physics model to combine all metabolites into bidirectional, signed, and weighted interaction networks and trace how the flow of information from one metabolite to the next causes changes in health state. Viewing a disease outcome as the consequence of complex interactions among its interconnected components (metabolites), we integrate concepts from ecosystem theory and evolutionary game theory to model how the health state-dependent alteration of a metabolite is shaped by its intrinsic properties and through extrinsic influences from its conspecifics. We code intrinsic contributions as nodes and extrinsic contributions as edges into quantitative networks and implement GLMY homology theory to analyze and interpret the topological change of health state from symbiosis to dysbiosis and vice versa. The application of this model to real data allows us to identify several hub metabolites and their interaction webs, which play a part in the formation of inflammatory bowel diseases. The findings by our model could provide important information on drug design to treat these diseases and beyond.

A pleiotropic-epistatic entangelement model of drug response.

Because drug response is multifactorial, graph models are uniquely powerful for comprehending its genetic architecture. We deconstruct drug response into many different and interdependent sub-traits, with each sub-trait controlled by multiple genes that act and interact in a complicated manner. The outcome of drug response is the consequence of multileveled intertwined interactions between pleiotropic effects and epistatic effects. Here, we propose a general statistical physics framework to chart the 3D geometric network that codes how epistasis pleiotropically influences a complete set of sub-traits to shape body-drug interactions. This model can dissect the topological architecture of epistatically induced pleiotropic networks (EiPN) and pleiotropically influenced epistatic networks (PiEN). We analyze and interpret the practical implications of the pleiotropic-epistatic entanglement model for pharmacogenomic studies.

Completely integrable replicator dynamics associated to competitive networks.

The replicator equations are a family of ordinary differential equations that arise in evolutionary game theory, and are closely related to Lotka-Volterra. We produce an infinite family of replicator equations which are Liouville-Arnold integrable. We show this by explicitly providing conserved quantities and a Poisson structure. As a corollary, we classify all tournament replicators up to dimension 6 and most of dimension 7. As an application, we show that Fig. 1 of Allesina and Levine [Proc. Natl. Acad. Sci. USA 108, 5638 (2011)10.1073/pnas.1014428108] produces quasiperiodic dynamics.

A personalized pharmaco-epistatic network model of precision medicine.

Precision medicine, the utilization of targeted treatments to address an individual's disease, relies on knowledge about the genetic cause of that individual's drug response. Here, we present a functional graph (FunGraph) theory to chart comprehensive pharmacogenetic architecture for each and every patient. FunGraph is the combination of functional mapping - a dynamic model for genetic mapping and evolutionary game theory guiding interactive strategies. It coalesces all pharmacogenetic factors into multilayer and multiplex networks that fully capture bidirectional, signed and weighted epistasis. It can visualize and interrogate how epistasis moves in the cell and how this movement leads to patient- and context-specific genetic architecture in response to organismic physiology. We discuss the future implementation of FunGraph to achieve precision medicine.

Race, employment, and the pandemic: An exploration of covariate explanations of COVID-19 case fatality rate variance.

We derive a simple asymptotic approximation for the long-run case fatality rate of COVID-19 (alpha and delta variants) and show that these estimations are highly correlated to the interaction between US State median age and projected US unemployment rate (Adj. r2 = 60%). We contrast this to the high level of correlation between point (instantaneous) estimates of per state case fatality rates and the interaction of median age, population density and current unemployment rates (Adj. r2 = 50.2%). To determine whether this is caused by a "race effect," we then analyze unemployment, race, median age and population density across US states and show that adding the interaction of African American population and unemployment explains 53.5% of the variance in COVID case fatality rates for the alpha and delta variants when considering instantaneous case fatality rate. Interestingly, when the asymptotic case fatality rate is used, the dependence on the African American population disappears, which is consistent with the fact that in the long-run COVID does not discriminate on race, but may discriminate on access to medical care which is highly correlated to employment in the US. The results provide further evidence of the impact inequality can have on case fatality rates in COVID-19 and the impact complex social, health and economic factors can have on patient survival.

Community formation in wealth-mediated thermodynamic strategy evolution.

We study a dynamical system defined by a repeated game on a 1D lattice, in which the players keep track of their gross payoffs over time in a bank. Strategy updates are governed by a Boltzmann distribution, which depends on the neighborhood bank values associated with each strategy, relative to a temperature scale, which defines the random fluctuations. Players with higher bank values are, thus, less likely to change strategy than players with a lower bank value. For a parameterized rock-paper-scissors game, we derive a condition under which communities of a given strategy form with either fixed or drifting boundaries. We show the effect of a temperature increase on the underlying system and identify surprising properties of this model through numerical simulations.

Osteohistology of a Triassic dinosaur population reveals highly variable growth trajectories typified early dinosaur ontogeny.

Intraspecific variation in growth trajectories provides a fundamental source of variation upon which natural selection acts. Recent work hints that early dinosaurs possessed elevated levels of such variation compared to other archosaurs, but comprehensive data uniting body size, bone histology, and morphological variation from a stratigraphically constrained early dinosaur population are needed to test this hypothesis. The Triassic theropod Coelophysis bauri, known from a bonebed preserving a single population of coeval individuals, provides an exceptional system to assess whether highly variable growth patterns were present near the origin of Dinosauria. Twenty-four histologically sampled individuals were less than a year to at least four years old and confirm the right-skewed age distribution of the Coelophysis assemblage. Poor correlations among size, age, and morphological maturity strongly support the presence of unique, highly variable growth trajectories in early dinosaurs relative to coeval archosaurs and their living kin.

The dinosaurian femoral head experienced a morphogenetic shift from torsion to growth along the avian stem.

Significant evolutionary shifts in locomotor behaviour often involve comparatively subtle anatomical transitions. For dinosaurian and avian evolution, medial overhang of the proximal femur has been central to discussions. However, there is an apparent conflict with regard to the evolutionary origin of the dinosaurian femoral head, with neontological and palaeontological data suggesting seemingly incongruent hypotheses. To reconcile this, we reconstructed the evolutionary history of morphogenesis of the proximal end of the femur from early archosaurs to crown birds. Embryological comparison of living archosaurs (crocodylians and birds) suggests the acquisition of the greater overhang of the femoral head in dinosaurs results from additional growth of the proximal end in the medial-ward direction. On the other hand, the fossil record suggests that this overhang was acquired by torsion of the proximal end, which projected in a more rostral direction ancestrally. We reconcile this apparent conflict by inferring that the medial overhang of the dinosaur femoral head was initially acquired by torsion, which was then superseded by mediad growth. Details of anatomical shifts in fossil forms support this hypothesis, and their biomechanical implications are congruent with the general consensus regarding broader morpho-functional evolution on the avian stem.

An eco-evo-devo genetic network model of stress response.

The capacity of plants to resist abiotic stresses is of great importance to agricultural, ecological and environmental sustainability, but little is known about its genetic underpinnings. Existing genetic tools can identify individual genetic variants mediating biochemical, physiological, and cellular defenses, but fail to chart an overall genetic atlas behind stress resistance. We view stress response as an eco-evo-devo process by which plants adaptively respond to stress through complex interactions of developmental canalization, phenotypic plasticity, and phenotypic integration. As such, we define and quantify stress response as the developmental change of adaptive traits from stress-free to stress-exposed environments. We integrate composite functional mapping and evolutionary game theory to reconstruct omnigenic, information-flow interaction networks for stress response. Using desert-adapted Euphrates poplar as an example, we infer salt resistance-related genome-wide interactome networks and trace the roadmap of how each SNP acts and interacts with any other possible SNPs to mediate salt resistance. We characterize the previously unknown regulatory mechanisms driving trait variation; i.e. the significance of a SNP may be due to the promotion of positive regulators, whereas the insignificance of a SNP may result from the inhibition of negative regulators. The regulator-regulatee interactions detected are not only experimentally validated by two complementary experiments, but also biologically interpreted by their encoded protein-protein interactions. Our eco-evo-devo model of genetic interactome networks provides an approach to interrogate the genetic architecture of stress response and informs precise gene editing for improving plants' capacity to live in stress environments.

Africa's oldest dinosaurs reveal early suppression of dinosaur distribution.

The vertebrate lineages that would shape Mesozoic and Cenozoic terrestrial ecosystems originated across Triassic Pangaea1-11. By the Late Triassic (Carnian stage, ~235 million years ago), cosmopolitan 'disaster faunas' (refs. 12-14) had given way to highly endemic assemblages12,13 on the supercontinent. Testing the tempo and mode of the establishment of this endemism is challenging-there were few geographic barriers to dispersal across Pangaea during the Late Triassic. Instead, palaeolatitudinal climate belts, and not continental boundaries, are proposed to have controlled distribution15-18. During this time of high endemism, dinosaurs began to disperse and thus offer an opportunity to test the timing and drivers of this biogeographic pattern. Increased sampling can test this prediction: if dinosaurs initially dispersed under palaeolatitudinal-driven endemism, then an assemblage similar to those of South America4,19-21 and India19,22-including the earliest dinosaurs-should be present in Carnian deposits in south-central Africa. Here we report a new Carnian assemblage from Zimbabwe that includes Africa's oldest definitive dinosaurs, including a nearly complete skeleton of the sauropodomorph Mbiresaurus raathi gen. et sp. nov. This assemblage resembles other dinosaur-bearing Carnian assemblages, suggesting that a similar vertebrate fauna ranged high-latitude austral Pangaea. The distribution of the first dinosaurs is correlated with palaeolatitude-linked climatic barriers, and dinosaurian dispersal to the rest of the supercontinent was delayed until these barriers relaxed, suggesting that climatic controls influenced the initial composition of the terrestrial faunas that persist to this day.

The developing bird pelvis passes through ancestral dinosaurian conditions.

Living birds (Aves) have bodies substantially modified from the ancestral reptilian condition. The avian pelvis in particular experienced major changes during the transition from early archosaurs to living birds1,2. This stepwise transformation is well documented by an excellent fossil record2-4; however, the ontogenetic alterations that underly it are less well understood. We used embryological imaging techniques to examine the morphogenesis of avian pelvic tissues in three dimensions, allowing direct comparison with the fossil record. Many ancestral dinosaurian features2 (for example, a forward-facing pubis, short ilium and pubic 'boot') are transiently present in the early morphogenesis of birds and arrive at their typical 'avian' form after transitioning through a prenatal developmental sequence that mirrors the phylogenetic sequence of character acquisition. We demonstrate quantitatively that avian pelvic ontogeny parallels the non-avian dinosaur-to-bird transition and provide evidence for phenotypic covariance within the pelvis that is conserved across Archosauria. The presence of ancestral states in avian embryos may stem from this conserved covariant relationship. In sum, our data provide evidence that the avian pelvis, whose early development has been little studied5-7, evolved through terminal addition-a mechanism8-10 whereby new apomorphic states are added to the end of a developmental sequence, resulting in expression8,11 of ancestral character states earlier in that sequence. The phenotypic integration we detected suggests a previously unrecognized mechanism for terminal addition and hints that retention of ancestral states in development is common during evolutionary transitions.

A Single-Cell Omics Network Model of Cell Crosstalk during the Formation of Primordial Follicles.

The fate of fetal germ cells (FGCs) in primordial follicles is largely determined by how they interact with the surrounding granulosa cells. However, the molecular mechanisms underlying this interactive process remain poorly understood. Here, we develop a computational model to characterize how individual genes program and rewire cellular crosstalk across FGCs and somas, how gene regulatory networks mediate signaling pathways that functionally link these two cell types, and how different FGCs diversify and evolve through cooperation and competition during embryo development. We analyze single-cell RNA-seq data of human female embryos using the new model, identifying previously uncharacterized mechanisms behind follicle development. The majority of genes (70%) promote FGC-soma synergism, only with a small portion (4%) that incur antagonism; hub genes function reciprocally between the FGC network and soma network; and germ cells tend to cooperate between different stages of development but compete in the same stage within a developmental embryo. Our network model could serve as a powerful tool to unravel the genomic signatures that mediate folliculogenesis from single-cell omics data.

Development of a polymeric biomedical device platform with controlled disassembly and in vivo testing in a swine intestinal model.

The aim of this study was to create a surgical guide platform that maintains its integrity while the surgeon performs an intestinal anastomosis or another similar procedure, which then breaks apart and is eliminated from the body in a controlled manner. The device contains mixed polymeric structures that give it a controlled rate of disassembly that could meet the requirements of a specific surgical purpose. The intraluminal anastomotic guide was manufactured as a hollow cylinder composed of layers of porous polyurethane/PCL with polyvinylpyrrolidone as the binding agent similar to a "brick-mortar" architecture. This combination of polymeric structures is a promising manufacturing method from which a variety of tunable devices can be fabricated for specific medical procedures and site-specific indications. The guide was designed to rapidly disassemble within the intestinal lumen after use, reliably degrading while maintaining sufficient mechanical rigidity and stability to support manipulation during complex surgical procedures. The nature of the device's disassembly makes it suitable for use in hollow structures that discharge their contents, resulting in their elimination from the body. A swine model of intestinal anastomosis was utilized to validate the use and function of the device.

A graph model of combination therapies.

The simultaneous use of multiple medications causes drug-drug interactions (DDI) that impact therapeutic efficacy. Here, we argue that graph theory, in conjunction with game theory and ecosystem theory, can address this issue. We treat the coexistence of multiple drugs as a system in which DDI is modeled by game theory. We develop an ordinary differential equation model to characterize how the concentration of a drug changes as a result of its independent capacity and the dependent influence of other drugs through the metabolic response of the host. We coalesce all drugs into personalized and context-specific networks, which can reveal key DDI determinants of therapeutical efficacy. Our model can quantify drug synergy and antagonism and test the translational success of combination therapies to the clinic.

A Comment on and Correction to: Opinion Dynamics in the Presence of Increasing Agreement Pressure.

We identify counterexamples to the consensus result given in Semonsen et al. (2018). We resolve the counterexamples by replacing Lemma 5 in the given reference with a novel variation of the Banach fixed-point theorem, which explains both the numerical results in the reference and the counterexample(s) in this note and provides a sufficient condition for consensus in systems with increasing peer-pressure. This work is relevant for other papers that have used the proof technique from Semonsen et al. and establishes the veracity of their claims assuming the new sufficient condition.

Developing and testing an automated qualitative assistant (AQUA) to support qualitative analysis.

Qualitative research remains underused, in part due to the time and cost of annotating qualitative data (coding). Artificial intelligence (AI) has been suggested as a means to reduce those burdens, and has been used in exploratory studies to reduce the burden of coding. However, methods to date use AI analytical techniques that lack transparency, potentially limiting acceptance of results. We developed an automated qualitative assistant (AQUA) using a semiclassical approach, replacing Latent Semantic Indexing/Latent Dirichlet Allocation with a more transparent graph-theoretic topic extraction and clustering method. Applied to a large dataset of free-text survey responses, AQUA generated unsupervised topic categories and circle hierarchical representations of free-text responses, enabling rapid interpretation of data. When tasked with coding a subset of free-text data into user-defined qualitative categories, AQUA demonstrated intercoder reliability in several multicategory combinations with a Cohen's kappa comparable to human coders (0.62-0.72), enabling researchers to automate coding on those categories for the entire dataset. The aim of this manuscript is to describe pertinent components of best practices of AI/machine learning (ML)-assisted qualitative methods, illustrating how primary care researchers may use AQUA to rapidly and accurately code large text datasets. The contribution of this article is providing guidance that should increase AI/ML transparency and reproducibility.