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In this paper, we present new necessary conditions and sufficient conditions for the (positive parts of) the varieties of vertically parametrized systems to admit monomial parametrizations. The conditions are based on a combination of polyhedral geometry and previously known results about injectivity of monomial maps. The motivation arises from the study of steady state varieties of reaction networks, as toricity simplifies the determination of multistationarity substantially., Comment: 30 pages, 3 figures. Comments welcome!

Methylglyoxal (MGO) is an endogenous, highly reactive dicarbonyl metabolite generated under hyperglycaemic conditions. MGO plays a role in developing pathophysiological conditions, including diabetic cardiomyopathy. However, the mechanisms involved and the molecular targets of MGO in the heart have not been elucidated. In this work, we studied the exposure-related effects of MGO on cardiac function in an isolated perfused rat heart ex vivo model. The effect of MGO on calcium homeostasis in cardiomyocytes was studied in vitro by the fluorescence indicator of intracellular calcium Fluo-4. We demonstrated that MGO induced cardiac dysfunction, both in contractility and diastolic function. In rat heart, the effects of MGO treatment were significantly limited by aminoguanidine, a scavenger of MGO, ruthenium red, a general cation channel blocker, and verapamil, an L-type voltage-dependent calcium channel blocker, demonstrating that this dysfunction involved alteration of calcium regulation. MGO induced a significant concentration-dependent increase of intracellular calcium in neonatal rat cardiomyocytes, which was limited by aminoguanidine and verapamil. These results suggest that the functionality of various calcium channels is altered by MGO, particularly the L-type calcium channel, thus explaining its cardiac toxicity. Therefore, MGO could participate in the development of diabetic cardiomyopathy through its impact on calcium homeostasis in cardiac cells.

Phosphorylation networks, representing the mechanisms by which proteins are phosphorylated at one or multiple sites, are ubiquitous in cell signalling and display rich dynamics such as unlimited multistability. Dual-site phosphorylation networks are known to exhibit oscillations in the form of periodic trajectories, when phosphorylation and dephosphorylation occurs as a mixed mechanism: phosphorylation of the two sites requires one encounter of the kinase, while dephosphorylation of the two sites requires two encounters with the phosphatase. A still open question is whether a mechanism requiring two encounters for both phosphorylation and dephosphorylation also admits oscillations. In this work we provide evidence in favor of the absence of oscillations of this network by precluding Hopf bifurcations in any reduced network comprising three out of its four intermediate protein complexes. Our argument relies on a novel network reduction step that preserves the absence of Hopf bifurcations, and on a detailed analysis of the semi-algebraic conditions precluding Hopf bifurcations obtained from Hurwitz determinants of the characteristic polynomial of the Jacobian of the system. We conjecture that the removal of certain reverse reactions appearing in Michaelis-Menten-type mechanisms does not have an impact on the presence or absence of Hopf bifurcations. We prove an implication of the conjecture under certain favorable scenarios and support the conjecture with additional example-based evidence.

Soft robots offer remarkable adaptability and safety advantages over rigid robots, but modeling their complex, nonlinear dynamics remains challenging. Strain-based models have recently emerged as a promising candidate to describe such systems, however, they tend to be high-dimensional and time consuming. This paper presents a novel model order reduction approach for soft and hybrid robots by combining strain-based modeling with Proper Orthogonal Decomposition (POD). The method identifies optimal coupled strain basis functions -- or mechanical synergies -- from simulation data, enabling the description of soft robot configurations with a minimal number of generalized coordinates. The reduced order model (ROM) achieves substantial dimensionality reduction while preserving accuracy. Rigorous testing demonstrates the interpolation and extrapolation capabilities of the ROM for soft manipulators under static and dynamic conditions. The approach is further validated on a snake-like hyper-redundant rigid manipulator and a closed-chain system with soft and rigid components, illustrating its broad applicability. Finally, the approach is leveraged for shape estimation of a real six-actuator soft manipulator using only two position markers, showcasing its practical utility. This POD-based ROM offers significant computational speed-ups, paving the way for real-time simulation and control of complex soft and hybrid robots.

The reduced state of a small system strongly coupled to a thermal bath may be athermal and used as a small battery once disconnected. If the disconnecting process is too slow, the coupling between the battery and the bath weakens, and at some point, the battery will be in a thermal state that can not be used as a battery. Thus, the unitarily extractable energy (a.k.a ergotropy) decreases with the disconnection time. The work required to disconnect the battery also depends on the disconnection time. We study the efficiency of this battery, defined as the ratio between the ergotropy to the work cost of disconnecting and connecting the battery back to the bath to close the cycle, as a function of the disconnecting time in the Caldeira-Leggett model of a quantum battery. We consider two scenarios. In the first scenario, we assume that the discharged battery is uncorrelated to the bath at the connecting time and find that the efficiency peaks at an optimal disconnecting time. In the second scenario, the discharged battery is correlated to the bath, and find that the optimal efficiency corresponds to an instantaneous disconnection. On top of these results, we analyze various thermodynamic quantities for these Caldeira-Leggett quantum batteries that allow us to express the first and second laws of thermodynamics in the mentioned cycles in simple form despite the system-bath initial correlations and strong coupling regime of the working device., Comment: 22 pages, 4 figures

Simultaneous multithreading processors improve throughput over single-threaded processors thanks to sharing internal core resources among instructions from distinct threads. However, resource sharing introduces inter-thread interference within the core, which has a negative impact on individual application performance and can significantly increase the turnaround time of multi-program workloads. The severity of the interference effects depends on the competing co-runners sharing the core. Thus, it can be mitigated by applying a thread-to-core allocation policy that smartly selects applications to be run in the same core to minimize their interference. This paper presents SYNPA, a simple approach that dynamically allocates threads to cores in an SMT processor based on their run-time dynamic behavior. The approach uses a regression model to select synergistic pairs to mitigate intra-core interference. The main novelty of SYNPA is that it uses just three variables collected from the performance counters available in current ARM processors at the dispatch stage. Experimental results show that SYNPA outperforms the default Linux scheduler by around 36%, on average, in terms of turnaround time in 8-application workloads combining frontend bound and backend bound benchmarks., Comment: 11 pages, 9 figures

In this work, we present an experimental setup and guide to enable the perching of large flapping-wing robots. The combination of forward flight, limited payload, and flight oscillations imposes challenging conditions for localized perching. The described method details the different operations that are concurrently performed within the 4 second perching flight. We validate this experiment with a 700 g ornithopter and demonstrate the first autonomous perching flight of a flapping-wing robot on a branch. This work paves the way towards the application of flapping-wing robots for long-range missions, bird observation, manipulation, and outdoor flight., Comment: IROS 2022 Workshop: Agile Robotics: Perception, Learning, Planning, and Control, 2022

We determine the generic consistency, dimension and nondegeneracy of the zero locus over $\mathbb{C}^*$, $\mathbb{R}^*$ and $\mathbb{R}_{>0}$ of vertically parametrized systems: parametric polynomial systems consisting of linear combinations of monomials scaled by free parameters. These systems generalize sparse systems with fixed monomial support and freely varying parametric coefficients. As our main result, we establish the equivalence among three key properties: the existence of nondegenerate zeros, the zero set having generically the expected dimension, and the system being generically consistent. Importantly, we prove that checking whether a vertically parametrized system has these properties amounts to an easily computed matrix rank condition., Comment: Major rewriting and improvement of previous version. The last section has been removed and will be included in an upcoming follow-up manuscript

Switch-like responses arising from bistability have been linked to cell signaling processes and memory. Revealing the shape and properties of the set of parameters that lead to bistability is necessary to understand the underlying biological mechanisms, but is a complex mathematical problem. We present an efficient approach to determine a basic topological property of the parameter region of multistationary, namely whether it is connected or not. The connectivity of this region can be interpreted in terms of the biological mechanisms underlying bistability and the switch-like patterns that the system can create. We provide an algorithm to assert that the parameter region of multistationarity is connected, targeting reaction networks with mass-action kinetics. We show that this is the case for numerous relevant cell signaling motifs, previously described to exhibit bistability. However, we show that for a motif displaying a phosphorylation cycle with allosteric enzyme regulation, the region of multistationarity has two distinct connected components, corresponding to two different, but symmetric, biological mechanisms. The method relies on linear programming and bypasses the expensive computational cost of direct and generic approaches to study parametric polynomial systems. This characteristic makes it suitable for mass-screening of reaction networks., Comment: Accepted in Plos Computational Biology

Flapping wings are a bio-inspired method to produce lift and thrust in aerial robots, leading to quiet and efficient motion. The advantages of this technology are safety and maneuverability, and physical interaction with the environment, humans, and animals. However, to enable substantial applications, these robots must perch and land. Despite recent progress in the perching field, flapping-wing vehicles, or ornithopters, are to this day unable to stop their flight on a branch. In this paper, we present a novel method that defines a process to reliably and autonomously land an ornithopter on a branch. This method describes the joint operation of a flapping-flight controller, a close-range correction system and a passive claw appendage. Flight is handled by a triple pitch-yaw-altitude controller and integrated body electronics, permitting perching at 3 m/s. The close-range correction system, with fast optical branch sensing compensates for position misalignment when landing. This is complemented by a passive bistable claw design can lock and hold 2 Nm of torque, grasp within 25 ms and can re-open thanks to an integrated tendon actuation. The perching method is supplemented by a four-step experimental development process which optimizes for a successful design. We validate this method with a 700 g ornithopter and demonstrate the first autonomous perching flight of a flapping-wing robot on a branch, a result replicated with a second robot. This work paves the way towards the application of flapping-wing robots for long-range missions, bird observation, manipulation, and outdoor flight.

Multisite phosphorylation is a signaling mechanism well known to give rise to multiple steady states, a property termed multistationarity. When phosphorylation occurs in a sequential and distributive manner, we obtain a family of networks indexed by the number of phosphorylation sites $n$. This work addresses the problem of understanding the parameter region where this family of networks displays multistationarity, by focusing on the projection of this region onto the set of kinetic parameters. The problem is phrased in the context of real algebraic geometry and reduced to studying whether a polynomial, defined as the determinant of a parametric matrix of size three, attains negative values over the positive orthant. The coefficients of the polynomial are functions of the kinetic parameters. For any $n$, we provide sufficient conditions for the polynomial to be positive and hence, preclude multistationarity, and also sufficient conditions for it to attain negative values and hence, enable multistationarity. These conditions are derived by exploiting the structure of the polynomial, its Newton polytope, and employing circuit polynomials. A relevant consequence of our results is that the set of kinetic parameters that enable or preclude multistationarity are both connected for all $n$., Comment: 23 pages

CMMI and Agile can work together. Over 80% of CMMI appraisals in 2018 were conducted at agile organizations, even though pre-2018 CMMI versions do not provide guidelines for agile contexts. A number of experience reports and research studies address the alignment between the two approaches but also pinpoint open tactical and organizational challenges. CMMI V2.0, published in 2018, was designed to be understandable, accessible, and flexible. It was intended to be integrated with other methodologies such as Agile. In this paper, we discuss to what extent the new CMMI V2.0 addresses the existing Agile-CMMI alignment challenges. We identify the two most significant CMMI V2.0 artifacts for this aim, the context-specific sections provided for most of the practice areas, and the value statements linked to the practices. We analyze how they contribute to each of the existing challenges and highlight important issues that organizations still need to tackle regarding this alignment., Comment: Accepted in Computer on November 9th 2020,11 pages, 1 figure

We are concerned with polynomial ordinary differential systems that arise from modelling chemical reaction networks. For such systems, which may be of high dimension and may depend on many parameters, it is frequently of interest to obtain a reduction of dimension in certain parameter ranges. Singular perturbation theory, as initiated by Tikhonov and Fenichel, provides a path toward such reductions. In the present paper we discuss parameter values that lead to singular perturbation reductions (so-called Tikhonov-Fenichel parameter values, or TFPVs). An algorithmic approach is known, but it is feasible for small dimensions only. Here we characterize conditions for classes of reaction networks for which TFPVs arise by turning off reactions (by setting rate parameters to zero), or by removing certain species (which relates to the classical quasi-steady state approach to model reduction). In particular, we obtain definitive results for the class of complex balanced reaction networks (of deficiency zero) and first order reaction networks.

We give partial generalizations of the classical Descartes' rule of signs to multivariate polynomials (with real exponents), in the sense that we provide upper bounds on the number of connected components of the complement of a hypersurface in the positive orthant. In particular, we give conditions based on the geometrical configuration of the exponents and the sign of the coefficients that guarantee that the number of connected components where the polynomial attains a negative value is at most one or two. Our results fully cover the cases where such an upper bound provided by the univariate Descartes' rule of signs is one. This approach opens a new route to generalize Descartes' rule of signs to the multivariate case, differing from previous works that aim at counting the number of positive solutions of a system of multivariate polynomial equations., Comment: Final version to appear in Advances in Mathematics

In recent years wildfires have caused havoc across the world, especially aggravated in certain regions, due to climate change. Remote sensing has become a powerful tool for monitoring fires, as well as for measuring their effects on vegetation over the following years. We aim to explain the dynamics of wildfires' effects on a vegetation index (previously estimated by causal inference through synthetic controls) from pre-wildfire available information (mainly proceeding from satellites). For this purpose, we use regression models from Functional Data Analysis, where wildfire effects are considered functional responses, depending on elapsed time after each wildfire, while pre-wildfire information acts as scalar covariates. Our main findings show that vegetation recovery after wildfires is a slow process, affected by many pre-wildfire conditions, among which the richness and diversity of vegetation is one of the best predictors for the recovery., Comment: 35 Pages, 8 Figures, 4 Tables

This paper introduces a factorization for the inverse of discrete Fourier integral operators that can be applied in quasi-linear time. The factorization starts by approximating the operator with the butterfly factorization. Next, a hierarchical matrix representation is constructed for the hermitian matrix arising from composing the Fourier integral operator with its adjoint. This representation is inverted efficiently with a new algorithm based on the hierarchical interpolative factorization. By combining these two factorizations, an approximate inverse factorization for the Fourier integral operator is obtained as a product of $O(\log N)$ sparse matrices of size $N\times N$. The resulting approximate inverse factorization can be used as a direct solver or as a preconditioner. Numerical examples on 1D and 2D Fourier integral operators, including a generalized Radon transform, demonstrate the performance of this new approach.

As cities expand, human mobility has become a central focus of urban planning and policy making to make cities more inclusive and sustainable. Initiatives such as the "15-minutes city" have been put in place to shift the attention from monocentric city configurations to polycentric structures, increasing the availability and diversity of local urban amenities. Ultimately they expect to increase local walkability and increase mobility within residential areas. While we know how urban amenities influence human mobility at the city level, little is known about spatial variations in this relationship. Here, we use mobile phone, census, and volunteered geographical data to measure geographic variations in the relationship between origin-destination flows and local urban accessibility in Barcelona. Using a Negative Binomial Geographically Weighted Regression model, we show that, globally, people tend to visit neighborhoods with better access to education and retail. Locally, these and other features change in sign and magnitude through the different neighborhoods of the city in ways that are not explained by administrative boundaries, and that provide deeper insights regarding urban characteristics such as rental prices. In conclusion, our work suggests that the qualities of a 15-minutes city can be measured at scale, delivering actionable insights on the polycentric structure of cities, and how people use and access this structure., Comment: 32 pages, 7 figures

Wildfires have become one of the biggest natural hazards for environments worldwide. The effects of wildfires are heterogeneous, meaning that the magnitude of their effects depends on many factors such as geographical region, climate and land cover/vegetation type. Yet, which areas are more affected by these events remains unclear. Here we present a novel application of the Generalised Synthetic Control (GSC) method that enables quantification and prediction of vegetation changes due to wildfires through a time-series analysis of in situ and satellite remote sensing data. We apply this method to medium to large wildfires ($>$ 1000 acres) in California throughout a time-span of two decades (1996--2016). The method's ability for estimating counterfactual vegetation characteristics for burned regions is explored in order to quantify abrupt system changes. We find that the GSC method is better at predicting vegetation changes than the more traditional approach of using nearby regions to assess wildfire impacts. We evaluate the GSC method by comparing its predictions of spectral vegetation indices to observations during pre-wildfire periods and find improvements in correlation coefficient from $R^2 = 0.66$ to $R^2 = 0.93$ in Normalised Difference Vegetation Index (NDVI), from $R^2 = 0.48$ to $R^2 = 0.81$ for Normalised Burn Ratio (NBR), and from $R^2 = 0.49$ to $R^2 = 0.85$ for Normalised Difference Moisture Index (NDMI). Results show greater changes in NDVI, NBR, and NDMI post-fire on regions classified as having a lower Burning Index. The GSC method also reveals that wildfire effects on vegetation can last for more than a decade post-wildfire, and in some cases never return to their previous vegetation cycles within our study period. Lastly, we discuss the usefulness of using GSC in remote sensing analyses., Comment: 29 pages, 7 figures

We investigate collider signatures of standard model extensions featuring vector-like leptons and a flavorful scalar sector. Such a framework arises naturally within asymptotically safe model building, which tames the UV behavior of the standard model towards the Planck scale and beyond. We focus on values of Yukawa couplings and masses which allow to explain the present data on the muon and electron anomalous magnetic moments. Using a CMS search based on $77.4 \, \rm{fb}^{-1}$ at the $\sqrt{s}=13$ TeV LHC we find that flavorful vector-like leptons are excluded for masses below around $300$ GeV if they are singlets under $SU(2)_L$, and around $800$ GeV if they are doublets. Exploiting the flavor-violating-like decays of the scalars, we design novel null test observables based on opposite sign opposite flavor invariant masses. These multi-lepton distributions allow to signal new physics and to extract mass hierarchies in reach of near-future searches at the LHC and the HL-LHC., Comment: 32 pages, 17 figures

Understanding inter-VM interference is of paramount importance to provide a sound knowledge and understand where performance degradation comes from in the current public cloud. With this aim, this paper devises a workload taxonomy that classifies applications according to how the major system resources affect their performance (e.g., tail latency) as a function of the level of load (e.g., QPS). After that, we present three main studies addressing three major concerns to improve the cloud performance: impact of the level of load on performance, impact of hyper-threading on performance, and impact of limiting the major system resources (e.g., last level cache) on performance. In all these studies we identified important findings that we hope help cloud providers improve their system utilization., Comment: 16 pages, 17 figures. Submitted to Journal of Parallel and Distributed Computing

Kac-Rice formulas express the expected number of elements a fiber of a random field has in terms of a multivariate integral. We consider here parametrized systems of polynomial equations that are linear in enough parameters, and provide a Kac-Rice formula for the expected number of solutions of the system when the parameters follow continuous distributions. Combined with Monte Carlo integration, we apply the formula to partition the parameter region according to the number of solutions or find a region in parameter space where the system has the maximal number of solutions. The motivation stems from the study of steady states of chemical reaction networks and gives new tools for the open problem of identifying the parameter region where the network has at least two positive steady states. We illustrate with numerous examples that our approach successfully handles a larger number of parameters than exact methods., Comment: To appear in Mathematics of Computation

We perform a comprehensive search for Standard Model extensions inspired by asymptotic safety. Our models feature a singlet matrix scalar field, three generations of vector-like leptons, and direct links to the Higgs and flavor sectors via new Yukawa and portal couplings. A novel feature is that the enlarged scalar sector may spontaneously break lepton flavor universality. We provide a complete two-loop renormalization group analysis of the running gauge, Yukawa, and quartic couplings to find ultraviolet fixed points and the BSM critical surface of parameters, $i.e.$ the set of boundary conditions at the TeV scale for which models remain well-behaved and predictive up to the Planck scale without encountering Landau poles or instabilities. This includes templates for asymptotically safe Standard Model extensions which match the measured values of gauge couplings and the Higgs, top, and bottom masses. We further detail the phenomenology of our models covering production, decay, fermion mixing, anomalous magnetic moments, effects from scalar mixing and chiral enhancement, and constraints on model parameters from data. Signatures at proton-proton and lepton colliders such as lepton flavor violation and displaced vertices, and the prospect for electric dipole moments or charged lepton-flavor-violating type processes, are also indicated., Comment: 40 pages, 23 figures, 11 tables

We study the robustness of the steady states of a class of systems of autonomous ordinary differential equations (ODEs), having as a central example those arising from (bio)chemical reaction networks. More precisely, we study under what conditions the steady states of the system are contained in a parallel translate of a coordinate hyperplane. To this end, we focus mainly on ODEs consisting of generalized polynomials, and make use of algebraic and geometric tools to relate the local and global structure of the set of steady states. Specifically, we consider the local property termed zero sensitivity at a coordinate $x_i$, which means that the tangent space is contained in a hyperplane of the form $x_i=c$, and provide a criterion to identify it. We consider the global property termed absolute concentration robustness (ACR), meaning that all steady states are contained in a hyperplane of the form $x_i=c$. We clarify and formalise the relation between the two approaches. In particular, we show that ACR implies zero sensitivity, and identify when the two properties do not agree, via an intermediate property we term local ACR. For families of systems arising from modelling biochemical reaction networks, we obtain the first practical and automated criterion to decide upon (local) ACR., Comment: To appear in Mathematical Methods in the Applied Sciences

This note proposes an efficient preconditioner for solving linear and semi-linear parabolic equations. With the Crank-Nicholson time stepping method, the algebraic system of equations at each time step is solved with the conjugate gradient method, preconditioned with hierarchical interpolative factorization. Stiffness matrices arising in the discretization of parabolic equations typically have large condition numbers, and therefore preconditioning becomes essential, especially for large time steps. We propose to use the hierarchical interpolative factorization as the preconditioning for the conjugate gradient iteration. Computed only once, the hierarchical interpolative factorization offers an efficient and accurate approximate inverse of the linear system. As a result, the preconditioned conjugate gradient iteration converges in a small number of iterations. Compared to other classical exact and approximate factorizations such as Cholesky or incomplete Cholesky, the hierarchical interpolative factorization can be computed in linear time and the application of its inverse has linear complexity. Numerical experiments demonstrate the performance of the method and the reduction of conjugate gradient iterations.

Urban population grows constantly. By 2050 two thirds of the world population will reside in urban areas. This growth is faster and more complex than the ability of cities to measure and plan for their sustainability. To understand what makes a city inclusive for all, we define a methodology to identify and characterize spatial subdivisions: areas with over- and under-representation of specific population groups, named hot and cold spots respectively. Using aggregated mobile phone data, we apply this methodology to the city of Barcelona to assess the mobility of three groups of people: women, elders, and tourists. We find that, within the three groups, cold spots have a lower diversity of amenities and services than hot spots. Also, cold spots of women and tourists tend to have lower population income. These insights apply to the floating population of Barcelona, thus augmenting the scope of how inclusiveness can be analyzed in the city., Comment: 10 pages, 10 figures. To be presented at the Data Science for Social Good workshop at The Web Conference 2020

Multistationarity in molecular systems underlies switch-like responses in cellular decision making. Determining whether and when a system displays multistationarity is in general a difficult problem. In this work we completely determine the set of kinetic parameters that enable multistationarity in a ubiquitous motif involved in cell signaling, namely a dual phosphorylation cycle. In addition we show that the regions of multistationarity and monostationarity are both path connected. We model the dynamics of the concentrations of the proteins over time by means of a parametrized polynomial ordinary differential equation (ODE) system arising from the mass-action assumption. Since this system has three linear first integrals defined by the total amounts of the substrate and the two enzymes, we study for what parameter values the ODE system has at least two positive steady states after suitably choosing the total amounts. We employ a suite of techniques from (real) algebraic geometry, which in particular concern the study of the signs of a multivariate polynomial over the positive orthant and sums of nonnegative circuit polynomials.

The measurements of the muon and electron anomalous magnetic moments hint at physics beyond the standard model. We show why and how models inspired by asymptotic safety can explain deviations from standard model predictions naturally. Our setup features an enlarged scalar sector and Yukawa couplings between leptons and new vector-like fermions. Using the complete two-loop running of couplings, we observe a well-behaved high energy limit of models including a stabilization of the Higgs. We find that a manifest breaking of lepton universality beyond standard model Yukawas is not necessary to explain the muon and electron anomalies. We further predict the tau anomalous magnetic moment, and new particles in the TeV energy range whose signatures at colliders are indicated. With small CP phases, the electron EDM can be as large as the present bound., Comment: 5 pages, 4 figures; v2: explanations expanded and references added, conclusions unchanged; match with published version

Deciding whether and where a system of parametrized ordinary differential equations displays bistability, that is, has at least two asymptotically stable steady states for some choice of parameters, is a hard problem. For systems modeling biochemical reaction networks, we introduce a procedure to determine, exclusively via symbolic computations, the stability of the steady states for unspecified parameter values. In particular, our approach fully determines the stability type of all steady states of a broad class of networks. To this end, we combine the Hurwitz criterion, reduction of the steady state equations to one univariate equation, and structural reductions of the reaction network. Using our method, we prove that bistability occurs in open regions in parameter space for many relevant motifs in cell signaling., Comment: To appear in SIAM Journal of Applied Dynamical Systems