TY - CONF
AB - Formal design of embedded and cyber-physical systems relies on mathematical modeling. In this paper, we consider the model class of hybrid automata whose dynamics are defined by affine differential equations. Given a set of time-series data, we present an algorithmic approach to synthesize a hybrid automaton exhibiting behavior that is close to the data, up to a specified precision, and changes in synchrony with the data. A fundamental problem in our synthesis algorithm is to check membership of a time series in a hybrid automaton. Our solution integrates reachability and optimization techniques for affine dynamical systems to obtain both a sufficient and a necessary condition for membership, combined in a refinement framework. The algorithm processes one time series at a time and hence can be interrupted, provide an intermediate result, and be resumed. We report experimental results demonstrating the applicability of our synthesis approach.
AU - Garcia Soto, Miriam
AU - Henzinger, Thomas A
AU - Schilling, Christian
ID - 9200
KW - hybrid automaton
KW - membership
KW - system identification
SN - 9781450383394
T2 - HSCC '21: Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control
TI - Synthesis of hybrid automata with affine dynamics from time-series data
ER -
TY - CONF
AB - Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functionsthat facilitates the efficient search for new materials and material properties. We prove invarianceunder isometries, continuity, and completeness in the generic case, which are necessary featuresfor the reliable comparison of crystals. The proof of continuity integrates methods from discretegeometry and lattice theory, while the proof of generic completeness combines techniques fromgeometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and relatedinclusion-exclusion formulae. We have implemented the algorithm and describe its application tocrystal structure prediction.
AU - Edelsbrunner, Herbert
AU - Heiss, Teresa
AU - Kurlin , Vitaliy
AU - Smith, Philip
AU - Wintraecken, Mathijs
ID - 9345
SN - 1868-8969
T2 - 37th International Symposium on Computational Geometry (SoCG 2021)
TI - The density fingerprint of a periodic point set
VL - 189
ER -
TY - CONF
AB - matching is compatible to two or more labeled point sets of size n with labels {1,…,n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of n points there exists a compatible matching with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(logn) copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge.
AU - Aichholzer, Oswin
AU - Arroyo Guevara, Alan M
AU - Masárová, Zuzana
AU - Parada, Irene
AU - Perz, Daniel
AU - Pilz, Alexander
AU - Tkadlec, Josef
AU - Vogtenhuber, Birgit
ID - 9296
SN - 03029743
T2 - 15th International Conference on Algorithms and Computation
TI - On compatible matchings
VL - 12635
ER -
TY - CONF
AB - In this work, we apply the dynamical systems analysis of Hanrot et al. (CRYPTO’11) to a class of lattice block reduction algorithms that includes (natural variants of) slide reduction and block-Rankin reduction. This implies sharper bounds on the polynomial running times (in the query model) for these algorithms and opens the door to faster practical variants of slide reduction. We give heuristic arguments showing that such variants can indeed speed up slide reduction significantly in practice. This is confirmed by experimental evidence, which also shows that our variants are competitive with state-of-the-art reduction algorithms.
AU - Walter, Michael
ID - 9466
SN - 03029743
T2 - Public-Key Cryptography – PKC 2021
TI - The convergence of slide-type reductions
VL - 12710
ER -
TY - CONF
AB - Modern neural networks can easily fit their training set perfectly. Surprisingly, despite being “overfit” in this way, they tend to generalize well to future data, thereby defying the classic bias–variance trade-off of machine learning theory. Of the many possible explanations, a prevalent one is that training by stochastic gradient descent (SGD) imposes an implicit bias that leads it to learn simple functions, and these simple functions generalize well. However, the specifics of this implicit bias are not well understood.
In this work, we explore the smoothness conjecture which states that SGD is implicitly biased towards learning functions that are smooth. We propose several measures to formalize the intuitive notion of smoothness, and we conduct experiments to determine whether SGD indeed implicitly optimizes for these measures. Our findings rule out the possibility that smoothness measures based on first-order derivatives are being implicitly enforced. They are supportive, though, of the smoothness conjecture for measures based on second-order derivatives.
AU - Volhejn, Vaclav
AU - Lampert, Christoph
ID - 9210
SN - 03029743
T2 - 42nd German Conference on Pattern Recognition
TI - Does SGD implicitly optimize for smoothness?
VL - 12544 LNCS
ER -
TY - JOUR
AB - Selection and random drift determine the probability that novel mutations fixate in a population. Population structure is known to affect the dynamics of the evolutionary process. Amplifiers of selection are population structures that increase the fixation probability of beneficial mutants compared to well-mixed populations. Over the past 15 years, extensive research has produced remarkable structures called strong amplifiers which guarantee that every beneficial mutation fixates with high probability. But strong amplification has come at the cost of considerably delaying the fixation event, which can slow down the overall rate of evolution. However, the precise relationship between fixation probability and time has remained elusive. Here we characterize the slowdown effect of strong amplification. First, we prove that all strong amplifiers must delay the fixation event at least to some extent. Second, we construct strong amplifiers that delay the fixation event only marginally as compared to the well-mixed populations. Our results thus establish a tight relationship between fixation probability and time: Strong amplification always comes at a cost of a slowdown, but more than a marginal slowdown is not needed.
AU - Tkadlec, Josef
AU - Pavlogiannis, Andreas
AU - Chatterjee, Krishnendu
AU - Nowak, Martin A.
ID - 9640
IS - 1
JF - Nature Communications
TI - Fast and strong amplifiers of natural selection
VL - 12
ER -
TY - THES
AB - Deep learning is best known for its empirical success across a wide range of applications
spanning computer vision, natural language processing and speech. Of equal significance,
though perhaps less known, are its ramifications for learning theory: deep networks have
been observed to perform surprisingly well in the high-capacity regime, aka the overfitting
or underspecified regime. Classically, this regime on the far right of the bias-variance curve
is associated with poor generalisation; however, recent experiments with deep networks
challenge this view.
This thesis is devoted to investigating various aspects of underspecification in deep learning.
First, we argue that deep learning models are underspecified on two levels: a) any given
training dataset can be fit by many different functions, and b) any given function can be
expressed by many different parameter configurations. We refer to the second kind of
underspecification as parameterisation redundancy and we precisely characterise its extent.
Second, we characterise the implicit criteria (the inductive bias) that guide learning in the
underspecified regime. Specifically, we consider a nonlinear but tractable classification
setting, and show that given the choice, neural networks learn classifiers with a large margin.
Third, we consider learning scenarios where the inductive bias is not by itself sufficient to
deal with underspecification. We then study different ways of ‘tightening the specification’: i)
In the setting of representation learning with variational autoencoders, we propose a hand-
crafted regulariser based on mutual information. ii) In the setting of binary classification, we
consider soft-label (real-valued) supervision. We derive a generalisation bound for linear
networks supervised in this way and verify that soft labels facilitate fast learning. Finally, we
explore an application of soft-label supervision to the training of multi-exit models.
AU - Bui Thi Mai, Phuong
ID - 9418
TI - Underspecification in Deep Learning
ER -
TY - CONF
AB - We consider the problem ofdistributed mean estimation (DME), in which n machines are each given a local d-dimensional vector xv∈Rd, and must cooperate to estimate the mean of their inputs μ=1n∑nv=1xv, while minimizing total communication cost. DME is a fundamental construct in distributed machine learning, and there has been considerable work on variants of this problem, especially in the context of distributed variance reduction for stochastic gradients in parallel SGD. Previous work typically assumes an upper bound on the norm of the input vectors, and achieves an error bound in terms of this norm. However, in many real applications, the input vectors are concentrated around the correct output μ, but μ itself has large norm. In such cases, previous output error bounds perform poorly. In this paper, we show that output error bounds need not depend on input norm. We provide a method of quantization which allows distributed mean estimation to be performed with solution quality dependent only on the distance between inputs, not on input norm, and show an analogous result for distributed variance reduction. The technique is based on a new connection with lattice theory. We also provide lower bounds showing that the communication to error trade-off of our algorithms is asymptotically optimal. As the lattices achieving optimal bounds under l2-norm can be computationally impractical, we also present an extension which leverages easy-to-use cubic lattices, and is loose only up to a logarithmic factor ind. We show experimentally that our method yields practical improvements for common applications, relative to prior approaches.
AU - Davies, Peter
AU - Gurunanthan, Vijaykrishna
AU - Moshrefi, Niusha
AU - Ashkboos, Saleh
AU - Alistarh, Dan-Adrian
ID - 9543
T2 - 9th International Conference on Learning Representations
TI - New bounds for distributed mean estimation and variance reduction
ER -
TY - CONF
AB - We study the inductive bias of two-layer ReLU networks trained by gradient flow. We identify a class of easy-to-learn (`orthogonally separable') datasets, and characterise the solution that ReLU networks trained on such datasets converge to. Irrespective of network width, the solution turns out to be a combination of two max-margin classifiers: one corresponding to the positive data subset and one corresponding to the negative data subset. The proof is based on the recently introduced concept of extremal sectors, for which we prove a number of properties in the context of orthogonal separability. In particular, we prove stationarity of activation patterns from some time onwards, which enables a reduction of the ReLU network to an ensemble of linear subnetworks.
AU - Bui Thi Mai, Phuong
AU - Lampert, Christoph
ID - 9416
T2 - 9th International Conference on Learning Representations
TI - The inductive bias of ReLU networks on orthogonally separable data
ER -
TY - JOUR
AB - Turbulence in the flow of fluid through a pipe can be suppressed by buoyancy forces. As the suppression of turbulence leads to severe heat transfer deterioration, this is an important and undesirable phenomenon in both heating and cooling applications. Vertical flow is often considered, as the axial buoyancy force can help drive the flow. With heating measured by the buoyancy parameter 𝐶, our direct numerical simulations show that shear-driven turbulence may either be completely laminarised or it transitions to a relatively quiescent convection-driven state. Buoyancy forces cause a flattening of the base flow profile, which in isothermal pipe flow has recently been linked to complete suppression of turbulence (Kühnen et al., Nat. Phys., vol. 14, 2018, pp. 386–390), and the flattened laminar base profile has enhanced nonlinear stability (Marensi et al., J. Fluid Mech., vol. 863, 2019, pp. 50–875). In agreement with these findings, the nonlinear lower-branch travelling-wave solution analysed here, which is believed to mediate transition to turbulence in isothermal pipe flow, is shown to be suppressed by buoyancy. A linear instability of the laminar base flow is responsible for the appearance of the relatively quiescent convection driven state for 𝐶≳4 across the range of Reynolds numbers considered. In the suppression of turbulence, however, i.e. in the transition from turbulence, we find clearer association with the analysis of He et al. (J. Fluid Mech., vol. 809, 2016, pp. 31–71) than with the above dynamical systems approach, which describes better the transition to turbulence. The laminarisation criterion He et al. propose, based on an apparent Reynolds number of the flow as measured by its driving pressure gradient, is found to capture the critical 𝐶=𝐶𝑐𝑟(𝑅𝑒) above which the flow will be laminarised or switch to the convection-driven type. Our analysis suggests that it is the weakened rolls, rather than the streaks, which appear to be critical for laminarisation.
AU - Marensi, Elena
AU - He, Shuisheng
AU - Willis, Ashley P.
ID - 9467
JF - Journal of Fluid Mechanics
SN - 00221120
TI - Suppression of turbulence and travelling waves in a vertical heated pipe
VL - 919
ER -
TY - THES
AB - Most real-world flows are multiphase, yet we know little about them compared to their single-phase counterparts. Multiphase flows are more difficult to investigate as their dynamics occur in large parameter space and involve complex phenomena such as preferential concentration, turbulence modulation, non-Newtonian rheology, etc. Over the last few decades, experiments in particle-laden flows have taken a back seat in favour of ever-improving computational resources. However, computers are still not powerful enough to simulate a real-world fluid with millions of finite-size particles. Experiments are essential not only because they offer a reliable way to investigate real-world multiphase flows but also because they serve to validate numerical studies and steer the research in a relevant direction. In this work, we have experimentally investigated particle-laden flows in pipes, and in particular, examined the effect of particles on the laminar-turbulent transition and the drag scaling in turbulent flows.
For particle-laden pipe flows, an earlier study [Matas et al., 2003] reported how the sub-critical (i.e., hysteretic) transition that occurs via localised turbulent structures called puffs is affected by the addition of particles. In this study, in addition to this known transition, we found a super-critical transition to a globally fluctuating state with increasing particle concentration. At the same time, the Newtonian-type transition via puffs is delayed to larger Reynolds numbers. At an even higher concentration, only the globally fluctuating state is found. The dynamics of particle-laden flows are hence determined by two competing instabilities that give rise to three flow regimes: Newtonian-type turbulence at low, a particle-induced globally fluctuating state at high, and a coexistence state at intermediate concentrations.
The effect of particles on turbulent drag is ambiguous, with studies reporting drag reduction, no net change, and even drag increase. The ambiguity arises because, in addition to particle concentration, particle shape, size, and density also affect the net drag. Even similar particles might affect the flow dissimilarly in different Reynolds number and concentration ranges. In the present study, we explored a wide range of both Reynolds number and concentration, using spherical as well as cylindrical particles. We found that the spherical particles do not reduce drag while the cylindrical particles are drag-reducing within a specific Reynolds number interval. The interval strongly depends on the particle concentration and the relative size of the pipe and particles. Within this interval, the magnitude of drag reduction reaches a maximum. These drag reduction maxima appear to fall onto a distinct power-law curve irrespective of the pipe diameter and particle concentration, and this curve can be considered as the maximum drag reduction asymptote for a given fibre shape. Such an asymptote is well known for polymeric flows but had not been identified for particle-laden flows prior to this work.
AU - Agrawal, Nishchal
ID - 9728
KW - Drag Reduction
KW - Transition to Turbulence
KW - Multiphase Flows
KW - particle Laden Flows
KW - Complex Flows
KW - Experiments
KW - Fluid Dynamics
SN - 2663-337X
TI - Transition to turbulence and drag reduction in particle-laden pipe flows
ER -
TY - JOUR
AB - The important roles of mitochondrial function and dysfunction in the process of neurodegeneration are widely acknowledged. Retinal ganglion cells (RGCs) appear to be a highly vulnerable neuronal cell type in the central nervous system with respect to mitochondrial dysfunction but the actual reasons for this are still incompletely understood. These cells have a unique circumstance where unmyelinated axons must bend nearly 90° to exit the eye and then cross a translaminar pressure gradient before becoming myelinated in the optic nerve. This region, the optic nerve head, contains some of the highest density of mitochondria present in these cells. Glaucoma represents a perfect storm of events occurring at this location, with a combination of changes in the translaminar pressure gradient and reassignment of the metabolic support functions of supporting glia, which appears to apply increased metabolic stress to the RGC axons leading to a failure of axonal transport mechanisms. However, RGCs themselves are also extremely sensitive to genetic mutations, particularly in genes affecting mitochondrial dynamics and mitochondrial clearance. These mutations, which systemically affect the mitochondria in every cell, often lead to an optic neuropathy as the sole pathologic defect in affected patients. This review summarizes knowledge of mitochondrial structure and function, the known energy demands of neurons in general, and places these in the context of normal and pathological characteristics of mitochondria attributed to RGCs.
AU - Muench, Nicole A.
AU - Patel, Sonia
AU - Maes, Margaret E
AU - Donahue, Ryan J.
AU - Ikeda, Akihiro
AU - Nickells, Robert W.
ID - 9761
IS - 7
JF - Cells
TI - The influence of mitochondrial dynamics and function on retinal ganglion cell susceptibility in optic nerve disease
VL - 10
ER -
TY - JOUR
AB - In mammalian genomes, differentially methylated regions (DMRs) and histone marks including trimethylation of histone 3 lysine 27 (H3K27me3) at imprinted genes are asymmetrically inherited to control parentally-biased gene expression. However, neither parent-of-origin-specific transcription nor imprints have been comprehensively mapped at the blastocyst stage of preimplantation development. Here, we address this by integrating transcriptomic and epigenomic approaches in mouse preimplantation embryos. We find that seventy-one genes exhibit previously unreported parent-of-origin-specific expression in blastocysts (nBiX: novel blastocyst-imprinted expressed). Uniparental expression of nBiX genes disappears soon after implantation. Micro-whole-genome bisulfite sequencing (µWGBS) of individual uniparental blastocysts detects 859 DMRs. We further find that 16% of nBiX genes are associated with a DMR, whereas most are associated with parentally-biased H3K27me3, suggesting a role for Polycomb-mediated imprinting in blastocysts. nBiX genes are clustered: five clusters contained at least one published imprinted gene, and five clusters exclusively contained nBiX genes. These data suggest that early development undergoes a complex program of stage-specific imprinting involving different tiers of regulation.
AU - Santini, Laura
AU - Halbritter, Florian
AU - Titz-Teixeira, Fabian
AU - Suzuki, Toru
AU - Asami, Maki
AU - Ma, Xiaoyan
AU - Ramesmayer, Julia
AU - Lackner, Andreas
AU - Warr, Nick
AU - Pauler, Florian
AU - Hippenmeyer, Simon
AU - Laue, Ernest
AU - Farlik, Matthias
AU - Bock, Christoph
AU - Beyer, Andreas
AU - Perry, Anthony C.F.
AU - Leeb, Martin
ID - 9601
IS - 1
JF - Nature Communications
TI - Genomic imprinting in mouse blastocysts is predominantly associated with H3K27me3
VL - 12
ER -
TY - JOUR
AB - An ordered graph is a graph with a linear ordering on its vertex set. We prove that for every positive integer k, there exists a constant ck > 0 such that any ordered graph G on n vertices with the property that neither G nor its complement contains an induced monotone path of size k, has either a clique or an independent set of size at least n^ck . This strengthens a result of Bousquet, Lagoutte, and Thomassé, who proved the analogous result for unordered graphs.
A key idea of the above paper was to show that any unordered graph on n vertices that does not contain an induced path of size k, and whose maximum degree is at most c(k)n for some small c(k) > 0, contains two disjoint linear size subsets with no edge between them. This approach fails for ordered graphs, because the analogous statement is false for k ≥ 3, by a construction of Fox. We provide some further examples showing that this statement also fails for ordered graphs avoiding other ordered trees.
AU - Pach, János
AU - Tomon, István
ID - 9602
JF - Journal of Combinatorial Theory. Series B
SN - 00958956
TI - Erdős-Hajnal-type results for monotone paths
VL - 151
ER -
TY - JOUR
AU - Bartlett, Michael John
AU - Arslan, Feyza N
AU - Bankston, Adriana
AU - Sarabipour, Sarvenaz
ID - 9759
IS - 7
JF - PLoS Computational Biology
SN - 1553734X
TI - Ten simple rules to improve academic work- life balance
VL - 17
ER -
TY - JOUR
AB - The quantum approximate optimization algorithm (QAOA) is a prospective near-term quantum algorithm due to its modest circuit depth and promising benchmarks. However, an external parameter optimization required in the QAOA could become a performance bottleneck. This motivates studies of the optimization landscape and search for heuristic ways of parameter initialization. In this work we visualize the optimization landscape of the QAOA applied to the MaxCut problem on random graphs, demonstrating that random initialization of the QAOA is prone to converging to local minima with suboptimal performance. We introduce the initialization of QAOA parameters based on the Trotterized quantum annealing (TQA) protocol, parameterized by the Trotter time step. We find that the TQA initialization allows to circumvent
the issue of false minima for a broad range of time steps, yielding the same performance as the best result out of an exponentially scaling number of random initializations. Moreover, we demonstrate that the optimal value of the time step coincides with the point of proliferation of Trotter errors in quantum annealing. Our results suggest practical ways of initializing QAOA protocols on near-term quantum devices and reveal new connections between QAOA and quantum annealing.
AU - Sack, Stefan
AU - Serbyn, Maksym
ID - 9760
JF - Quantum
TI - Quantum annealing initialization of the quantum approximate optimization algorithm
VL - 5
ER -
TY - JOUR
AB - Normative theories and statistical inference provide complementary approaches for the study of biological systems. A normative theory postulates that organisms have adapted to efficiently solve essential tasks, and proceeds to mathematically work out testable consequences of such optimality; parameters that maximize the hypothesized organismal function can be derived ab initio, without reference to experimental data. In contrast, statistical inference focuses on efficient utilization of data to learn model parameters, without reference to any a priori notion of biological function, utility, or fitness. Traditionally, these two approaches were developed independently and applied separately. Here we unify them in a coherent Bayesian framework that embeds a normative theory into a family of maximum-entropy “optimization priors.” This family defines a smooth interpolation between a data-rich inference regime (characteristic of “bottom-up” statistical models), and a data-limited ab inito prediction regime (characteristic of “top-down” normative theory). We demonstrate the applicability of our framework using data from the visual cortex, and argue that the flexibility it affords is essential to address a number of fundamental challenges relating to inference and prediction in complex, high-dimensional biological problems.
AU - Mlynarski, Wiktor F
AU - Hledik, Michal
AU - Sokolowski, Thomas R
AU - Tkačik, Gašper
ID - 7553
IS - 7
JF - Neuron
TI - Statistical analysis and optimality of neural systems
VL - 109
ER -
TY - JOUR
AB - Embryo morphogenesis is impacted by dynamic changes in tissue material properties, which have been proposed to occur via processes akin to phase transitions (PTs). Here, we show that rigidity percolation provides a simple and robust theoretical framework to predict material/structural PTs of embryonic tissues from local cell connectivity. By using percolation theory, combined with directly monitoring dynamic changes in tissue rheology and cell contact mechanics, we demonstrate that the zebrafish blastoderm undergoes a genuine rigidity PT, brought about by a small reduction in adhesion-dependent cell connectivity below a critical value. We quantitatively predict and experimentally verify hallmarks of PTs, including power-law exponents and associated discontinuities of macroscopic observables. Finally, we show that this uniform PT depends on blastoderm cells undergoing meta-synchronous divisions causing random and, consequently, uniform changes in cell connectivity. Collectively, our theoretical and experimental findings reveal the structural basis of material PTs in an organismal context.
AU - Petridou, Nicoletta
AU - Corominas-Murtra, Bernat
AU - Heisenberg, Carl-Philipp J
AU - Hannezo, Edouard B
ID - 9316
IS - 7
JF - Cell
SN - 00928674
TI - Rigidity percolation uncovers a structural basis for embryonic tissue phase transitions
VL - 184
ER -
TY - JOUR
AB - While recent advancements in computation and modelling have improved the analysis of complex traits, our understanding of the genetic basis of the time at symptom onset remains limited. Here, we develop a Bayesian approach (BayesW) that provides probabilistic inference of the genetic architecture of age-at-onset phenotypes in a sampling scheme that facilitates biobank-scale time-to-event analyses. We show in extensive simulation work the benefits BayesW provides in terms of number of discoveries, model performance and genomic prediction. In the UK Biobank, we find many thousands of common genomic regions underlying the age-at-onset of high blood pressure (HBP), cardiac disease (CAD), and type-2 diabetes (T2D), and for the genetic basis of onset reflecting the underlying genetic liability to disease. Age-at-menopause and age-at-menarche are also highly polygenic, but with higher variance contributed by low frequency variants. Genomic prediction into the Estonian Biobank data shows that BayesW gives higher prediction accuracy than other approaches.
AU - Ojavee, Sven E
AU - Kousathanas, Athanasios
AU - Trejo Banos, Daniel
AU - Orliac, Etienne J
AU - Patxot, Marion
AU - Lall, Kristi
AU - Magi, Reedik
AU - Fischer, Krista
AU - Kutalik, Zoltan
AU - Robinson, Matthew Richard
ID - 8430
IS - 1
JF - Nature Communications
TI - Genomic architecture and prediction of censored time-to-event phenotypes with a Bayesian genome-wide analysis
VL - 12
ER -
TY - JOUR
AB - High impact epidemics constitute one of the largest threats humanity is facing in the 21st century. In the absence of pharmaceutical interventions, physical distancing together with testing, contact tracing and quarantining are crucial in slowing down epidemic dynamics. Yet, here we show that if testing capacities are limited, containment may fail dramatically because such combined countermeasures drastically change the rules of the epidemic transition: Instead of continuous, the response to countermeasures becomes discontinuous. Rather than following the conventional exponential growth, the outbreak that is initially strongly suppressed eventually accelerates and scales faster than exponential during an explosive growth period. As a consequence, containment measures either suffice to stop the outbreak at low total case numbers or fail catastrophically if marginally too weak, thus implying large uncertainties in reliably estimating overall epidemic dynamics, both during initial phases and during second wave scenarios.
AU - Scarselli, Davide
AU - Budanur, Nazmi B
AU - Timme, Marc
AU - Hof, Björn
ID - 9407
IS - 1
JF - Nature Communications
TI - Discontinuous epidemic transition due to limited testing
VL - 12
ER -