This work describes experiments on thermal dynamics of pure H2O excited by hydrodynamic cavitation, which has been reported to facilitate the spin conversion of para- and ortho-isomers at water interfaces. Previous measurements by NMR and capillary methods of excited samples demonstrated changes of proton density by 12-15%, the surface tension up to 15.7%, which can be attributed to a non-equilibrium para-/ortho- ratio. Beside these changes, we also expect a variation of heat capacity. Experiments use a differential calorimetric approach with two devices: one with an active thermostat for diathermic measurements, another is fully passive for long-term measurements. Samples after excitation are degassed at -0.09MPa and thermally equalized in a water bath. Conducted attempts demonstrated changes in the heat capacity of experimental samples by 4.17%--5.72% measured in the transient dynamics within 60 min after excitation, which decreases to 2.08% in the steady-state dynamics 90-120 min after excitation. Additionally, we observed occurrence of thermal fluctuations at the level of 10^-3 C relative temperature on 20-40 min mesoscale dynamics and a long-term increase of such fluctuations in experimental samples. Obtained results are reproducible in both devices and are supported by previously published outcomes on four-photon scattering spectra in the range from -1.5 to 1.5 cm^-1 and electrochemical reactivity in CO2 and H2O2 pathways. Based on these results, we propose a hypothesis about ongoing spin conversion process on mesoscopic scales under weak influx of energy caused by thermal, EM or geomagnetic factors; this enables explaining electrochemical and thermal anomalies observed in long-term measurements.
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In applications of group testing in networks, e.g. identifying individuals who are infected by a disease spread over a network, exploiting correlation among network nodes provides fundamental opportunities in reducing the number of tests needed. We model and analyze group testing on $n$ correlated nodes whose interactions are specified by a graph $G$. We model correlation through an edge-faulty random graph formed from $G$ in which each edge is dropped with probability $1-r$, and all nodes in the same component have the same state. We consider three classes of graphs: cycles and trees, $d$-regular graphs and stochastic block models or SBM, and obtain lower and upper bounds on the number of tests needed to identify the defective nodes. Our results are expressed in terms of the number of tests needed when the nodes are independent and they are in terms of $n$, $r$, and the target error. In particular, we quantify the fundamental improvements that exploiting correlation offers by the ratio between the total number of nodes $n$ and the equivalent number of independent nodes in a classic group testing algorithm. The lower bounds are derived by illustrating a strong dependence of the number of tests needed on the expected number of components. In this regard, we establish a new approximation for the distribution of component sizes in "$d$-regular trees" which may be of independent interest and leads to a lower bound on the expected number of components in $d$-regular graphs. The upper bounds are found by forming dense subgraphs in which nodes are more likely to be in the same state. When $G$ is a cycle or tree, we show an improvement by a factor of $log(1/r)$. For grid, a graph with almost $2n$ edges, the improvement is by a factor of ${(1-r) \log(1/r)}$, indicating drastic improvement compared to trees. When $G$ has a larger number of edges, as in SBM, the improvement can scale in $n$.
Accurate analytical and numerical modeling of multiscale systems is a daunting task. The need to properly resolve spatial and temporal scales spanning multiple orders of magnitude pushes the limits of both our theoretical models as well as our computational capabilities. Rigorous upscaling techniques enable efficient computation while bounding/tracking errors and making informed cost-accuracy tradeoffs. The biggest challenges arise when the applicability conditions for upscaled models break down. Here, we present a non-intrusive two-way coupled hybrid model, applied to thermal runaway in battery packs, that combines fine- and upscaled equations in the same numerical simulation to achieve predictive accuracy while limiting computational costs. First, we develop two methods with different orders of accuracy to enforce continuity at the coupling boundary. Then, we derive weak (i.e., variational) formulations of the fine-scale and upscaled governing equations for finite element (FE) discretization and numerical implementation in FEniCS. We demonstrate that hybrid simulations can accurately predict the average temperature fields within error bounds determined a priori by homogenization theory. Finally, we demonstrate the computational efficiency of the hybrid algorithm against fine-scale simulations.
We develop an optimization-based algorithm for parametric model order reduction (PMOR) of linear time-invariant dynamical systems. Our method aims at minimizing the $\mathcal{H}_\infty \otimes \mathcal{L}_\infty$ approximation error in the frequency and parameter domain by an optimization of the reduced order model (ROM) matrices. State-of-the-art PMOR methods often compute several nonparametric ROMs for different parameter samples, which are then combined to a single parametric ROM. However, these parametric ROMs can have a low accuracy between the utilized sample points. In contrast, our optimization-based PMOR method minimizes the approximation error across the entire parameter domain. Moreover, due to our flexible approach of optimizing the system matrices directly, we can enforce favorable features such as a port-Hamiltonian structure in our ROMs across the entire parameter domain. Our method is an extension of the recently developed SOBMOR-algorithm to parametric systems. We extend both the ROM parameterization and the adaptive sampling procedure to the parametric case. Several numerical examples demonstrate the effectiveness and high accuracy of our method in a comparison with other PMOR methods.
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.
Linear $L_1$-regularized models have remained one of the simplest and most effective tools in data analysis, especially in information retrieval problems where n-grams over text with TF-IDF or Okapi feature values are a strong and easy baseline. Over the past decade, screening rules have risen in popularity as a way to reduce the runtime for producing the sparse regression weights of $L_1$ models. However, despite the increasing need of privacy-preserving models in information retrieval, to the best of our knoweledge, no differentially private screening rule exists. In this paper, we develop the first differentially private screening rule for linear and logistic regression. In doing so, we discover difficulties in the task of making a useful private screening rule due to the amount of noise added to ensure privacy. We provide theoretical arguments and experimental evidence that this difficulty arises from the screening step itself and not the private optimizer. Based on our results, we highlight that developing an effective private $L_1$ screening method is an open problem in the differential privacy literature.
The flocking motion control is concerned with managing the possible conflicts between local and team objectives of multi-agent systems. The overall control process guides the agents while monitoring the flock-cohesiveness and localization. The underlying mechanisms may degrade due to overlooking the unmodeled uncertainties associated with the flock dynamics and formation. On another side, the efficiencies of the various control designs rely on how quickly they can adapt to different dynamic situations in real-time. An online model-free policy iteration mechanism is developed here to guide a flock of agents to follow an independent command generator over a time-varying graph topology. The strength of connectivity between any two agents or the graph edge weight is decided using a position adjacency dependent function. An online recursive least squares approach is adopted to tune the guidance strategies without knowing the dynamics of the agents or those of the command generator. It is compared with another reinforcement learning approach from the literature which is based on a value iteration technique. The simulation results of the policy iteration mechanism revealed fast learning and convergence behaviors with less computational effort.
Collective motion is an ubiquitous phenomenon in nature, inspiring engineers, physicists and mathematicians to develop mathematical models and bio-inspired designs. Collective motion at small to medium group sizes ($\sim$10-1000 individuals, also called the `mesoscale'), can show nontrivial features due to stochasticity. Therefore, characterizing both the deterministic and stochastic aspects of the dynamics is crucial in the study of mesoscale collective phenomena. Here, we use a physics-inspired, neural-network based approach to characterize the stochastic group dynamics of interacting individuals, through a stochastic differential equation (SDE) that governs the collective dynamics of the group. We apply this technique on both synthetic and real-world datasets, and identify the deterministic and stochastic aspects of the dynamics using drift and diffusion fields, enabling us to make novel inferences about the nature of order in these systems.
Traction parameters, that characterize the ground-wheel contact dynamics, are the central factor in the energy efficiency of vehicles. To optimize fuel consumption, reduce wear of tires, increase productivity etc., knowledge of current traction parameters is unavoidable. Unfortunately, these parameters are difficult to measure and require expensive force and torque sensors. An alternative way is to use system identification to determine them. In this work, we validate such a method in field experiments with a mobile robot. The method is based on an adaptive Kalman filter. We show how it estimates the traction parameters online, during the motion on the field, and compare them to their values determined via a 6-directional force-torque sensor installed for verification. Data of adhesion slip ratio curves is recorded and compared to curves from literature for additional validation of the method. The results can establish a foundation for a number of optimal traction methods.
Like most modern blockchain networks, Ethereum has relied on economic incentives to promote honest participation in the chain's consensus. The distributed character of the platform, together with the "randomness" or "luck" factor that both proof of work (PoW) and proof of stake (PoS) provide when electing the next block proposer, pushed the industry to model and improve the reward system of the system. With several improvements to predict PoW block proposal rewards and to maximize the extractable rewards of the same ones, the ultimate Ethereum's transition to PoS applied in the Paris Hard-Fork, more generally known as "The Merge", has meant a significant modification on the reward system in the platform. In this paper, we aim to break down both theoretically and empirically the new reward system in this post-merge era. We present a highly detailed description of the different rewards and their share among validators' rewards. Ultimately, we offer a study that uses the presented reward model to analyze the performance of the network during this transition.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
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