Simplified Setting Research Articles

Self-induced transparency of long water waves over bathymetry: the dispersive shock mechanism

The shoreline hazard posed by ocean long waves such as tsunamis and meteotsunamis critically depends on the fraction of energy transmitted across the shallow near-shore shelf. In linear setting, bathymetric inhomogeneities of length comparable to the incident wavelength act as a protective high-pass filter, reflecting long waves and allowing only shorter waves to pass through. Here, we show that, for weakly nonlinear waves, the transmitted energy flux fraction can significantly depend on the amplitude of the incoming wave. The basis of this mechanism is the formation of dispersive shock waves (DSWs), a salient feature of nonlinear evolution of long water waves, often observed in tidal bores and tsunami/meteotsunami evolution. Within the framework of the Boussinesq equations, we show that the DSWs efficiently transfer wave energy into the high wavenumber band, where reflection is negligible. This is phenomenologically similar to self-induced transparency in nonlinear optics: small amplitude long waves are reflected by the bathymetric inhomogeneity, while larger amplitude waves that develop DSWs blueshift into the transparency regime and pass through. We investigate this mechanism in a simplified setting that retains only the key processes of DSW disintegration and reflection, while the effects such as bottom dissipation and breaking are ignored. The results suggests that the phenomenon is a robust, order-one effect. In contrast, the increased transmission due to the growth of bound harmonics associated with the steepening of the wave is weak. The results of the simplified modelling are validated by simulations with the FUNWAVE-TVD Boussinesq model.

Mapless navigation via Hierarchical Reinforcement Learning with memory-decaying novelty

Hierarchical Reinforcement Learning (HRL) has shown superior performance for mapless navigation tasks. However, it remains limited in unstructured environments that might contain terrains like long corridors and dead corners, which can lead to local minima. This is because most HRL-based mapless navigation methods employ a simplified reward setting and exploration strategy. In this work, we propose a novel reward function for training the high-level (HL) policy, which contains two components: extrinsic reward and intrinsic reward. The extrinsic reward encourages the robot to move towards the target location, while the intrinsic reward is computed based on novelty, episode memory and memory decaying, making the agent capable of accomplishing spontaneous exploration. We also design a novel neural network structure that incorporates an LSTM network to augment the agent with memory and reasoning capabilities. We test our method in unknown environments and specific scenarios prone to the local minimum problem to evaluate the navigation performance and local minimum resolution ability. The results show that our method significantly increases the success rate when compared to advanced RL-based methods, achieving a maximum improvement of nearly 28%. Our method demonstrates effective improvement in addressing the local minimum issue, especially in cases where the baselines fail completely. Additionally, numerous ablation studies consistently confirm the effectiveness of our proposed reward function and neural network structure.

Multiscale homogenization for dual porosity time-dependent Darcy-Brinkman/Darcy coupling and its application to the lymphnode.

We study the coupling between time-dependent Darcy-Brinkman and the Darcy equations at the microscale subjected to inhomogeneous body forces and initial conditions to describe a double porosity problem. We derive the homogenized governing equations for this problem using the asymptotic homogenization technique, and as macroscopic results, we obtain a coupling between two Darcy equations, one of which with memory effects, with mass exchange between phases. The memory effects are a consequence of considering the time dependence in the Darcy-Brinkman equation, and they allow us to study in more detail the role of time in the problem under consideration. After the formulation of the model, we solve it in a simplified setting and we use it to describe the movement of fluid within a vascularized lymph node.

Imitation versus serendipity in ranking dynamics.

Participants in socio-economic systems are often ranked based on their performance. Rankings conveniently reduce the complexity of such systems to ordered lists. Yet, it has been shown in many contexts that those who reach the top are not necessarily the most talented, as chance plays a role in shaping rankings. Nevertheless, the role played by chance in determining success, i.e. serendipity, is underestimated, and top performers are often imitated by others under the assumption that adopting their strategies will lead to equivalent results. We investigate the tradeoff between imitation and serendipity in an agent-based model. Agents in the model receive payoffs based on their actions and may switch to different actions by either imitating others or through random selection. When imitation prevails, most agents coordinate on a single action, leading to non-meritocratic outcomes, as a minority of them accumulate the majority of payoffs. Yet, such agents are not necessarily the most skilled ones. When serendipity dominates, instead, we observe more egalitarian outcomes. The two regimes are separated by a sharp transition, which we characterize analytically in a simplified setting. We discuss the implications of our findings in a variety of contexts, ranging from academic research to business.

A source-to-surface model of heat and fluid transport in the Taupō Rift, New Zealand

We construct 2-D numerical models of bulk heat and water transport from the mid-crust (10 km depth) to the surface in a 20 km-wide continental rift, based on observations from the Taupō Rift in the central Taupō Volcanic Zone (TVZ) of New Zealand.The model represents a simplified geological setting with two low-permeability basement-like rock-types, the first defining the margins of the rift and the second a distinct ‘rifted basement’. The rift is overlain with a 2 km-thick, 20 km-wide layer of shallow volcanic infill. At the base of model there is a 10 km-deep heat source (the ‘hotplate’) with a specified TVZ-like heat flux of 0.77 Wm−2 and a ‘target’ average hotplate temperature of 700o to 900 °C, required to maintain the low melt fractions at ∼10 km depth inferred from geophysics.Parameterising the permeability of the rifted basement is a key part of the paper as it enables both the heat flux boundary condition and a temperature constraint to be satisfied at the hotplate. More generally, it allows the flexibility to control the depth of temperature contours which represent proxies for geophysical measurements. It is described as a power-law for log10(horizontal component of permeability, kh) with specified values of kh at two depths and a power law exponent as free parameters. Viable models which satisfy all constraints for the hydrothermal system beneath the TVZ rift have a power-law exponent less than ∼0.4, shallow (2 km deep) kh's of 10–14.0 to 10–13.0 m2, and deep (10 km) kh‘s <10–16.5 m2. The vertical component of the rifted basement permeability, kv, is ten times higher than kh.A generic feature of the models is that irregular, unsteady convection occurs in the upper ∼5 km of the rift. This results in temporal and spatial fluctuations in heat and fluid flow which are interpreted as high-temperature TVZ-like geothermal systems which have temperatures of ca. 300 °C at 2 km depth. Over the nominal simulation time of 3 Myr, approximately 40% of the geothermal systems are clustered within ∼2 km of the rift margins, with the remainder distributed roughly uniformly across the rift. Between the geothermal systems cool recharge from the surface occurs, with temperatures as low as 50 °C occurring at 5 km depth. The models successfully match temperature proxies for the depths of maximum seismicity (450 °C) and shallowest partial melt (> 700 °C) inferred from geophysical observations.Heat transport within the rift is dominated by convection. This is true even at 10 km depth, at the base of the geothermal systems, where kh in the rifted basement approaches 10−17 m2. In this situation, the relatively large value of vertical permeability kv, ∼ 10−16 m2, allows convection to occur. Conductive heat transport dominates in regions ∼1 km in vertical extent immediately above the hotplate and between the geothermal systems.The vigour of the hydrothermal systems is controlled by the permeability of the shallow volcanics, through which all cold surface recharge and hot outflows of fluid occur. Models with low permeability for the shallow volcanics produce longer lasting and higher temperature geothermal systems, and those with high permeability produce fewer and cooler geothermal systems.

Turbulence via intermolecular potential: Uncovering the origin

In recent works, we proposed a hypothesis, according to which turbulence in gases is created by the mean field effect of an intermolecular potential. We discovered that, in a numerically simulated inertial flow, turbulent solutions indeed spontaneously emerge from a laminar initial condition, as observed in nature and experiments. To study the origin of turbulent dynamics, in the current work we examine the equations of a two-dimensional inertial flow, linearized around a large scale constant vorticity state. Remarkably, even in this simplified setting, we find that turbulent dynamics emerge as linearly unstable fluctuations of the velocity divergence.In particular, for the linearized dynamics at a high Reynolds number, we find that, at short time scales, the coupling of the mean field potential with the large scale background vorticity creates linearly unstable and rapidly oscillating fluctuations of the divergence of velocity at inertial scales. In the asymptotic time limit, we find a persistent eigenvector, also aligned largely with the divergence of velocity, which allows these fluctuations to propagate in the form of traveling waves in the Fourier domain. Remarkably, these traveling waves decay at a constant, scale-independent exponential rate. Furthermore, it appears that the Kolmogorov scaling of the kinetic energy is produced by this persistent velocity divergence, due to a cubic relation between the physical time variable, and a pseudo-time variable, in which the dynamics become autonomous. These effects vanish when the mean field potential is removed.

On the One‐Dimensional Transition State Theory and the Relation between Statistical and Deterministic Oscillation Frequencies of Anharmonic Energy Wells

AbstractThe transition state theory allows the development of approximated models useful to study the non‐equilibrium evolution of systems undergoing transformations between two states (e.g., chemical reactions). In a simplified 1D setting, the characteristic rate constants are typically written in terms of a temperature‐dependent characteristic oscillation frequency , describing the exploration of the phase space. As a particular case, this statistical oscillation frequency can be defined for an arbitrary convex potential energy well. This value is compared here with the deterministic oscillation frequency of the corresponding anharmonic oscillator. It is proved that there is a universal relationship between statistical and deterministic frequencies, which is the same for classical and relativistic mechanics. The independence of this relationship from the adopted physical laws gives it an interesting thermodynamic and pedagogical meaning. Several examples clarify the meaning of this relationship from both physical and mathematical viewpoints.

Functional rolling circle amplification-based sensitive determination and low-speed centrifugation-based isolation of Staphylococcus aureus

The ability to quickly and accurately analyze Staphylococcus aureus (S. aureus) and isolate the bacteria in a simplified setting is crucial for the early identification and treatment of infectious illnesses. Here, we describe the development of a new aptamer-based detection and separation technique that combines Mg2+-dependent DNAzyme amplification cascades with catalytic hairpin assembly for enhanced sensitivity. This technique uses a rolling circle amplification procedure to build a detection scaffold with a repetitive functional hairpin structure that, upon identifying S. aureus, can launch a catalytic hairpin assembly-mediated DNAzyme-based cascade signal amplification. This allows S. aureus to be isolated using low-speed centrifugation and simultaneously quantified. The approach has a low limit of detection of 21 cfu/mL and a broad detection range of six orders of magnitude due to the inclusion of the catalytic hairpin assembly for signal amplification. In addition to high sensitivity, the method also demonstrates high selectivity for the identification and isolation of S. aureus, making it a useful instrument for reporting S. aureus infections.

Elastic founder graphs improved and enhanced

Indexing labeled graphs for pattern matching is a central challenge of pangenomics. Equi et al. (2022) [14] developed the Elastic Founder Graph (EFG) representing an alignment of m sequences of length n, drawn from alphabet Σ plus the special gap character: the paths spell the original sequences or their recombination. By enforcing the semi-repeat-free property, the EFG admits a polynomial-space index for linear-time pattern matching, breaking through the conditional lower bounds on indexing labeled graphs (Equi et al. [13]). In this work, we improve the space of the EFG index answering pattern matching queries in linear time, from linear in the length of all strings spelled by three consecutive node labels, to linear in the size of the edge labels. Then, we develop linear-time construction algorithms optimizing for different metrics: we improve the existing linearithmic construction algorithms to O(mn), by solving the novel exclusive ancestor set problem on trees; we propose, for the simplified gapless setting, an O(mn)-time solution minimizing the maximum block height, that we generalize by substituting block height with prefix-aware height. Finally, to show the versatility of the framework, we develop a BWT-based EFG index and study how to encode and perform document listing queries on a set of paths of the graphs, reporting which paths present a given pattern as a substring. We propose the EFG framework as an improved and enhanced version of the framework for the gapless setting, along with construction methods that are valid in any setting concerned with the segmentation of aligned sequences.

On asymptotic dark energy in string theory

We examine bounds on accelerated expansion in asymptotic regions of the moduli space in string theory compactifications to four spacetime dimensions. While there are conjectures that forbid or constrain accelerated expansion in such asymptotic regions, potential counter examples have been discussed recently in the literature. We check whether such counter examples can arise in explicit string theory constructions, focusing in particular on non-geometric compactifications of type IIB string theory that have no Kähler moduli. We find no violation of the Strong Asymptotic dS Conjecture and thus provide support for the absence of accelerated expansion in asymptotic regions of a barely explored corner of the string landscape. Moreover, working in a simplified setting, we point out a new mechanism for potentially connecting the Sharpened Distance Conjecture and the Strong Asymptotic dS Conjecture. If this argument could be generalized, it would mean that the Sharpened Distance Conjecture is implied by the Strong Asymptotic dS Conjecture, and that their exponential factors are naturally related by a factor of 2.

Transfer Learning with Kernel Methods

Transfer learning refers to the process of adapting a model trained on a source task to a target task. While kernel methods are conceptually and computationally simple models that are competitive on a variety of tasks, it has been unclear how to develop scalable kernel-based transfer learning methods across general source and target tasks with possibly differing label dimensions. In this work, we propose a transfer learning framework for kernel methods by projecting and translating the source model to the target task. We demonstrate the effectiveness of our framework in applications to image classification and virtual drug screening. For both applications, we identify simple scaling laws that characterize the performance of transfer-learned kernels as a function of the number of target examples. We explain this phenomenon in a simplified linear setting, where we are able to derive the exact scaling laws.

Gradient descent for deep matrix factorization: Dynamics and implicit bias towards low rank

In deep learning, it is common to use more network parameters than training points. In such scenario of over-parameterization, there are usually multiple networks that achieve zero training error so that the training algorithm induces an implicit bias on the computed solution. In practice, (stochastic) gradient descent tends to prefer solutions which generalize well, which provides a possible explanation of the success of deep learning. In this paper we analyze the dynamics of gradient descent in the simplified setting of linear networks and of an estimation problem. Although we are not in an overparameterized scenario, our analysis nevertheless provides insights into the phenomenon of implicit bias. In fact, we derive a rigorous analysis of the dynamics of vanilla gradient descent, and characterize the dynamical convergence of the spectrum. We are able to accurately locate time intervals where the effective rank of the iterates is close to the effective rank of a low-rank projection of the ground-truth matrix. In practice, those intervals can be used as criteria for early stopping if a certain regularity is desired. We also provide empirical evidence for implicit bias in more general scenarios, such as matrix sensing and random initialization. This suggests that deep learning prefers trajectories whose complexity (measured in terms of effective rank) is monotonically increasing, which we believe is a fundamental concept for the theoretical understanding of deep learning.

Restricted nonlinear scales of turbulent secondary flows over spanwise heterogeneous roughness

Recent studies, e.g., Wangsawijaya et al. (2020) have revealed the prevalence of streak meandering in turbulent flow over spanwise heterogeneous roughness. Here we exploit the scale decomposition inherent in the Restricted Nonlinear (RNL) modeling approach to further investigate this behavior. The RNL decomposition comprises a large-scale streamwise averaged mean with small-scale fluctuations about that mean defined through a dynamical restriction that leads to computational tractability. The simplified setting facilitates the study of secondary flow interacting with the large-scale streak via one-way coupling, thus enabling additional insight into relevant interaction mechanisms. In agreement with the experimental work, our results indicate that the energy of the large-scales is amplified over the low roughness region due to the secondary flow. The small-scales are shown to play a dominant role in the Reynolds stresses responsible for generation of the secondary flow. Conditional averaging of the RNL mean field reveals stronger momentum pathways and diminished energy over low roughness regions experiencing downwash in instances that differ from the time-averaged trends. Further analysis, via time-filtering, shows long time-scales pertinent to streak meandering are anti-correlated with instantaneous upwash/downwash motions that are the dominant contribution to the increased shear Reynolds stress observed over the low roughness strips.

Hydrodynamics and Survivability during Post-main-sequence Planetary Engulfment

The engulfment of substellar bodies (SBs), such as brown dwarfs and planets, by giant stars is a possible explanation for rapidly rotating giants, lithium-rich giants, and the presence of SBs in close orbits around subdwarfs and white dwarfs. We perform three-dimensional hydrodynamical simulations of the flow in the vicinity of an engulfed SB. We model the SB as a rigid body with a reflective surface because it cannot accrete. This reflective boundary changes the flow morphology to resemble that of engulfed compact objects with outflows. We measure the drag coefficients for the ram-pressure and gravitational drag forces acting on the SB, and use them to integrate its trajectory inside the star. We find that engulfment can increase the luminosity of a 1 M ⊙ star by up to a few orders of magnitude. The time for the star to return to its original luminosity is up to a few thousand years when the star has evolved to ≈10 R ⊙ and up to a few decades at the tip of the red giant branch (RGB). No SBs can eject the envelope of a 1 M ⊙ star before it evolves to ≈10 R ⊙ if the orbit of the SB is the only energy source contributing to the ejection. In contrast, SBs as small as ≈10 M Jup can eject the envelope at the tip of the RGB. The numerical framework we introduce here can be used to study planetary engulfment in a simplified setting that captures the physics of the flow at the scale of the SB.

Dispersion of expectorated cough droplets with seasonal influenza in an office

We do not fully grasp viral droplet transmission processes in ventilated interior environments. The core focus of our research is to investigate the effectiveness of the protected occupied zone ventilation (POV) through computational fluid dynamics models in a simplified office setting. The large-eddy simulation technique with the Eulerian–Lagrangian model was implemented to address complicated indoor processes such as turbulence, flow–aerosol interaction, and ventilation impact. We computationally investigated the effects of desk partitions and the POV on cough droplets in an office. The ventilation approach was tested using two distinct exhaust layouts and four different ventilation rates (1.0, 1.2, 1.5, and 1.8 m/s). A comparative analysis of the ventilation flow fields, topologies, and particle directions has been studied. The findings indicate that the plane jet's ventilation rates influence the protected occupied zone ventilation performance. The ventilation rates distributed the virus droplets around the room, but compared to the up-exhaust cases, the down-exhaust cases appeared to have better shielded the healthy person. This pattern could indicate that the placement of the exhaust outlet in ventilation systems significantly influences indoor aerosol dispersion. The results also show that substantial flow streams may carry tiny particles (≤70 μm) throughout their path. Large particles (≥100 μm) could not go far in cough gas clouds. Most viral particles deposit on solid surfaces in various work sites per specific ventilation rates. Office workers need to be very cautious around these hazardous areas.

Peptide conformational sampling using the Quantum Approximate Optimization Algorithm

Protein folding has attracted considerable research effort in biochemistry in recent decades. In this work, we explore the potential of quantum computing to solve a simplified version of protein folding. More precisely, we numerically investigate the performance of the Quantum Approximate Optimization Algorithm (QAOA) in sampling low-energy conformations of short peptides. We start by benchmarking the algorithm on an even simpler problem: sampling self-avoiding walks. Motivated by promising results, we then apply the algorithm to a more complete version of protein folding, including a simplified physical potential. In this case, we find less promising results: deep quantum circuits are required to achieve accurate results, and the performance of QAOA can be matched by random sampling up to a small overhead. Overall, these results cast serious doubt on the ability of QAOA to address the protein folding problem in the near term, even in an extremely simplified setting.

Premium control with reinforcement learning

AbstractWe consider a premium control problem in discrete time, formulated in terms of a Markov decision process. In a simplified setting, the optimal premium rule can be derived with dynamic programming methods. However, these classical methods are not feasible in a more realistic setting due to the dimension of the state space and lack of explicit expressions for transition probabilities. We explore reinforcement learning techniques, using function approximation, to solve the premium control problem for realistic stochastic models. We illustrate the appropriateness of the approximate optimal premium rule compared with the true optimal premium rule in a simplified setting and further demonstrate that the approximate optimal premium rule outperforms benchmark rules in more realistic settings where classical approaches fail.

Two-channel EEG based diagnosis of panic disorder and major depressive disorder using machine learning and non-linear dynamical methods

The current study aimed to investigate the possibility of rapid and accurate diagnoses of Panic disorder (PD) and Major depressive disorder (MDD) using machine learning. The support vector machine method was applied to 2-channel EEG signals from the frontal lobes (Fp1 and Fp2) of 149 participants to classify PD and MDD patients from healthy individuals using non-linear measures as features. We found significantly lower correlation dimension and Lempel-Ziv complexity in PD patients and MDD patients in the left hemisphere compared to healthy subjects at rest. Most importantly, we obtained a 90% accuracy in classifying MDD patients vs. healthy individuals, a 68% accuracy in classifying PD patients vs. controls, and a 59% classification accuracy between PD and MDD patients. In addition to demonstrating classification performance in a simplified setting, the observed differences in EEG complexity between subject groups suggest altered cortical processing present in the frontal lobes of PD patients that can be captured through non-linear measures. Overall, this study suggests that machine learning and non-linear measures using only 2-channel frontal EEGs are useful for aiding the rapid diagnosis of panic disorder and major depressive disorder.

Computational methods for multiscale modelling of virus infection dynamics

Abstract Virus infection dynamics is governed by the processes on multiple scales: on the whole organism level, tissue level, and intracellular level. In this paper, we develop a multi-scale multi-compartment model of HIV infection in a simplified setting and the computational methods for numerical realization of the model. The multiscale model describes the processes from various scales and of different nature (cell motility, virus diffusion, intracellular virus replication). Intracellular replication model is based on a Markov chain with time-inhomogeneous propensities that depend on the extracellular level of virions. Reaction diffusion equations used to model free virion diffusion in the lymphoid tissue have moving sources, which are determined by the positions of the infected cells (immune cell motility model) and the rate of virion secretion from them (intracellular model). Immune cell motility model parameterizes the intercellular interaction forces, friction and the stochastic force of active cell motility. Together, this allows for a proper description of the intracellular stochasticity that propagates across multiple scales. A hybrid discrete-continuous stochastic-deterministic algorithm for simulation of the multiscale model based on the uniformization Monte Carlo method is implemented.

Body Compression Corrective Garment and Eating Behavioural Change for Weight Reduction: The Mutsu City Randomised Controlled Trial.

Affordable and accessible behaviour-based interventions that do not overwhelm or demoralise overweight/obese individuals are needed. Combining clothing with behaviour change techniques might be an option. This is because clothing is a social norm, and clothing and motivation for weight loss are associated with the common desire to look better. Therefore, we conducted a single-blind randomised controlled trial to examine the effect of an intervention that combined behaviour change techniques, including simplified goal setting and self-monitoring, with a body compression corrective garment (BCCG), which exerts continuous but minimal tactile pressure on the hips and abdomen. We enrolled healthy community-dwelling adults with a body mass index ≥ 25 kg/m2 and assigned 35 and 34 participants to the intervention and control groups, respectively. The reduction in body weight was 1.3 kg more in the intervention group than in the control group after the 12-week intervention period (p < 0.05, repeated-measures mixed model). In addition, eating behaviour and body appreciation showed significant improvement in the intervention group compared with the control group. Our newly developed intervention improved eating behaviour and body appreciation and reduced the body weight of overweight/obese participants. Wearing a BCCG seems to facilitate behavioural changes and lead to weight loss.