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Chemotaxis describes the intricate interplay of cellular motion in response to a chemical signal. We here consider the case of slab geometry which models chemotactic motion between two infinite membranes. Like previous works, we are particularly interested in the asymptotic regime of high tumbling rates. We establish local existence and uniqueness of solutions to the kinetic equation and show their convergence towards solutions of a parabolic Keller-Segel model in the asymptotic limit. In addition, we prove convergence rates with respect to the asymptotic parameter under additional regularity assumptions on the problem data. Particular difficulties in our analysis are caused by vanishing velocities in the kinetic model as well as the occurrence of boundary terms.

Motivated by applications to crystalline materials, we generalize the merge tree and the related barcode of a filtered complex to the periodic setting in Euclidean space. They are invariant under isometries, changing bases, and indeed changing lattices. In addition, we prove stability under perturbations and provide an algorithm that under mild geometric conditions typically satisfied by crystalline materials takes $\mathcal{O}({(n+m) \log n})$ time, in which $n$ and $m$ are the numbers of vertices and edges in the quotient complex, respectively.

Several quantum and classical Monte Carlo algorithms for Betti Number Estimation (BNE) on clique complexes have recently been proposed, though it is unclear how their performances compare. We review these algorithms, emphasising their common Monte Carlo structure within a new modular framework. This framework allows us to directly compare these algorithms by calculating upper bounds on the minimum number of samples needed for convergence. By recombining the different modules, we create a new quantum algorithm with an exponentially-improved dependence in the sample complexity. We run classical simulations to verify convergence within the theoretical bounds and observe the predicted exponential separation, even though empirical convergence occurs substantially earlier than the conservative theoretical bounds.

While control barrier functions are employed to ensure in addressing safety, control synthesis methods based on them generally rely on accurate system dynamics. This is a critical limitation, since the dynamics of complex systems are often not fully known. Supervised machine learning techniques hold great promise for alleviating this weakness by inferring models from data. We propose a novel control barrier function-based framework for safe control through event-triggered learning, which switches between prioritizing control performance and improving model accuracy based on the uncertainty of the learned model. By updating a Gaussian process model with training points gathered online, the approach guarantees the feasibility of control barrier function conditions with high probability, such that safety can be ensured in a data-efficient manner. Furthermore, we establish the absence of Zeno behavior in the triggering scheme, and extend the algorithm to sampled-data realizations by accounting for inter-sampling effects. The effectiveness of the proposed approach and theory is demonstrated in simulations., Comment: The first two authors contributed equally to the work

The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of such devices. We study the numerical solution of the vector potential formulation of nonlinear magnetostatics by means of higher-order finite element methods. Numerical quadrature is used for the efficient handling of the nonlinearities and domain mappings are employed for the consideration of curved boundaries. The existence of a unique solution is proven on the continuous and discrete level and a full convergence analysis of the resulting finite element schemes is presented indicating order optimal convergence rates under appropriate smoothness assumptions. For the solution of the nonlinear discretized problems, we consider a Newton method with line search for which we establish global linear convergence with convergence rates that are independent of the discretization parameters. We further prove local quadratic convergence in a mesh-dependent neighborhood of the solution which becomes effective when high accuracy of the nonlinear solver is demanded. The assumptions required for our analysis cover inhomogeneous, nonlinear, and anisotropic materials, which may arise in typical applications, including the presence of permanent magnets. The theoretical results are illustrated by numerical tests for some typical benchmark problems.

Let $ \{P_n\}_{n\geq 0} $ be the sequence of Perrin numbers defined by $P_0=3$, $P_1=0$,$P_2=2$ and $P_{n+3}=P_{n+1}+P_{n}$ for all $n \geq 0$. In this paper, we determine all Perrin numbers that are palindromic concatenations of two repdigits., Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:2401.05361

Cracking Elements Method (CEM) is a numerical tool to simulate quasi-brittle fractures, which does not need remeshing, nodal enrichment, or complicated crack tracking strategy. The cracking elements used in the CEM can be considered as a special type of finite element implemented in the standard finite element frameworks. One disadvantage of CEM is that it uses nonlinear interpolation of the displacement field (Q8 or T6 elements), introducing more nodes and consequent computing efforts than the cases with elements using linear interpolation of the displacement field. Aiming at solving this problem, we propose a simple hybrid linear and non-linear interpolation finite element for adaptive cracking elements method in this work. A simple strategy is proposed for treating the elements with $p$ edge nodes $p\in\left[0,n\right]$ and $n$ being the edge number of the element. Only a few codes are needed. Then, by only adding edge and center nodes on the elements experiencing cracking and keeping linear interpolation of the displacement field for the elements outside the cracking domain, the number of total nodes was reduced almost to half of the case using the conventional cracking elements. Numerical investigations prove that the new approach inherits all the advantages of CEM with greatly improved computing efficiency., Comment: It is very useful for FEM researchers

This survey paper delves into the emerging and critical area of symbolic knowledge distillation in Large Language Models (LLMs). As LLMs like Generative Pre-trained Transformer-3 (GPT-3) and Bidirectional Encoder Representations from Transformers (BERT) continue to expand in scale and complexity, the challenge of effectively harnessing their extensive knowledge becomes paramount. This survey concentrates on the process of distilling the intricate, often implicit knowledge contained within these models into a more symbolic, explicit form. This transformation is crucial for enhancing the interpretability, efficiency, and applicability of LLMs. We categorize the existing research based on methodologies and applications, focusing on how symbolic knowledge distillation can be used to improve the transparency and functionality of smaller, more efficient Artificial Intelligence (AI) models. The survey discusses the core challenges, including maintaining the depth of knowledge in a comprehensible format, and explores the various approaches and techniques that have been developed in this field. We identify gaps in current research and potential opportunities for future advancements. This survey aims to provide a comprehensive overview of symbolic knowledge distillation in LLMs, spotlighting its significance in the progression towards more accessible and efficient AI systems., Comment: 21 pages, 7 figures

Recent literature has proposed approaches that learn control policies with high performance while maintaining safety guarantees. Synthesizing Hamilton-Jacobi (HJ) reachable sets has become an effective tool for verifying safety and supervising the training of reinforcement learning-based control policies for complex, high-dimensional systems. Previously, HJ reachability was restricted to verifying low-dimensional dynamical systems primarily because the computational complexity of the dynamic programming approach it relied on grows exponentially with the number of system states. In recent years, a litany of proposed methods addresses this limitation by computing the reachability value function simultaneously with learning control policies to scale HJ reachability analysis while still maintaining a reliable estimate of the true reachable set. These HJ reachability approximations are used to improve the safety, and even reward performance, of learned control policies and can solve challenging tasks such as those with dynamic obstacles and/or with lidar-based or vision-based observations. In this survey paper, we review the recent developments in the field of HJ reachability estimation in reinforcement learning that would provide a foundational basis for further research into reliability in high-dimensional systems., Comment: Accepted in IEEE Open Journal of Control Systems (OJ-CSYS)

The European Union Artificial Intelligence Act mandates clear stakeholder responsibilities in developing and deploying machine learning applications to avoid substantial fines, prioritizing private and secure data processing with data remaining at its origin. Federated Learning (FL) enables the training of generative AI Models across data siloes, sharing only model parameters while improving data security. Since FL is a cooperative learning paradigm, clients and servers naturally share legal responsibility in the FL pipeline. Our work contributes to clarifying the roles of both parties, explains strategies for shifting responsibilities to the server operator, and points out open technical challenges that we must solve to improve FL's practical applicability under the EU AI Act., Comment: Accepted at the GenLaw'24 workshop in conjunction with ICML'24

Experimentally monitoring the kinematics of branching network growth is a tricky task, given the complexity of the structures generated in three dimensions. One option is to drive the network in such a way as to obtain two-dimensional growth, enabling a collection of independent images to be obtained. The density of the network generates ambiguous structures, such as overlaps and meetings, which hinder the reconstruction of the chronology of connections. In this paper, we propose a general method for global network reconstruction. Each network connection is defined by a unique label, enabling it to be tracked in time and space. In this work, we distinguish between lateral and apical branches on the one hand, and extremities on the other. Finally, we reconstruct the network after identifying and eliminating overlaps. This method is then applied to the model filamentous fungus Podospora anserina to reconstruct its growing thallus. We derive criteria for differentiating between apical and lateral branches. We find that the outer ring is favorably composed of apical branches, while densification within the network comes from lateral branches. From this, we derive the specific dynamics of each of the two types. Finally, in the absence of any latency phase during growth initiation, we can reconstruct a time based on the equality of apical and lateral branching collections. This makes it possible to directly compare the growth dynamics of different thalli., Comment: 23 pages, 10 figures

We draw the current landscape of quantum algorithms, by classifying about 130 quantum algorithms, according to the fundamental mathematical problems they solve, their real-world applications, the main subroutines they employ, and several other relevant criteria. The primary objectives include revealing trends of algorithms, identifying promising fields for implementations in the NISQ era, and identifying the key algorithmic primitives that power quantum advantage., Comment: 60 pages, 7 figures

We consider systematic numerical approximation of a viscoelastic phase separation model that describes the demixing of a polymer solvent mixture. An unconditionally stable discretisation method is proposed based on a finite element approximation in space and a variational time discretization strategy. The proposed method preserves the energy-dissipation structure of the underlying system exactly and allows to establish a fully discrete nonlinear stability estimate in natural norms based on the concept of relative energy. These estimates are used to derive order optimal error estimates for the method under minimal smoothness assumptions on the problem data, despite the presence of various strong nonlinearities in the equations. The theoretical results and main properties of the method are illustrated by numerical simulations which also demonstrate the capability to reproduce the relevant physical effects observed in experiments., Comment: 31 pages; 1 figure

Reproducibility is a foundational standard for validating scientific claims in computational research. Stochastic computational models are employed across diverse fields such as systems biology, financial modelling and environmental sciences. Existing infrastructure and software tools support various aspects of reproducible model development, application, and dissemination, but do not adequately address independently reproducing simulation results that form the basis of scientific conclusions. To bridge this gap, we introduce the Empirical Characteristic Function Equality Convergence Test (EFECT), a data-driven method to quantify the reproducibility of stochastic simulation results. EFECT employs empirical characteristic functions to compare reported results with those independently generated by assessing distributional inequality, termed EFECT error, a metric to quantify the likelihood of equality. Additionally, we establish the EFECT convergence point, a metric for determining the required number of simulation runs to achieve an EFECT error value of a priori statistical significance, setting a reproducibility benchmark. EFECT supports all real-valued and bounded results irrespective of the model or method that produced them, and accommodates stochasticity from intrinsic model variability and random sampling of model inputs. We tested EFECT with stochastic differential equations, agent-based models, and Boolean networks, demonstrating its broad applicability and effectiveness. EFECT standardizes stochastic simulation reproducibility, establishing a workflow that guarantees reliable results, supporting a wide range of stakeholders, and thereby enhancing validation of stochastic simulation studies, across a model's lifecycle. To promote future standardization efforts, we are developing open source software library libSSR in diverse programming languages for easy integration of EFECT., Comment: 25 pages, 4 figures

We present the overview and first results from the North-PHASE Legacy Survey, which follows six young clusters for five years, using the 2 deg$^2$ FoV of the JAST80 telescope from the Javalambre Observatory (Spain). North-PHASE investigates stellar variability on timescales from days to years for thousands of young stars distributed over entire clusters. This allows us to find new YSO, characterise accretion and study inner disk evolution within the cluster context. Each region (Tr37, CepOB3, IC5070, IC348, NGC2264, and NGC1333) is observed in six filters (SDSS griz, u band, and J0660, which covers H$\alpha$), detecting cluster members as well as field variable stars. Tr37 is used to prove feasibility and optimise the variability analysis techniques. In Tr37, variability reveals 50 new YSO, most of them proper motion outliers. North-PHASE independently confirms the youth of astrometric members, efficiently distinguishes accreting and non-accreting stars, reveals the extent of the cluster populations along Tr37/IC1396 bright rims, and detects variability resulting from rotation, dips, and irregular bursts. The proper motion outliers unveil a more complex star formation history than inferred from Gaia alone, and variability highlights previously hidden proper motion deviations in the surrounding clouds. We also find that non-YSO variables identified by North-PHASE cover a different variability parameter space and include long-period variables, eclipsing binaries, RR Lyr, and $\delta$ Scuti stars. These early results also emphasize the power of variability to complete the picture of star formation where it is missed by astrometry., Comment: Accepted by MNRAS

In this paper, a set of Python methods is described that can be used to compute the frequency response of an arbitrary biochemical network given any input and output. Models can be provided in standard SBML or Antimony format. The code takes into account any conserved moieties so that this software can be used to also study signaling networks where moiety cycles are common. A utility method is also provided to make it easy to plot standard Bode plots from the generated results. The code also takes into account the possibility that the phase shift could exceed 180 degrees which can result in ugly discontinuities in the Bode plot. In the paper, some of the theory behind the method is provided as well as some commentary on the code and several illustrative examples to show the code in operation. Illustrative examples include linear reaction chains of varying lengths and the effect of negative feedback on the frequency response. Software License: MIT Open Source Availability: The code is available from https://github.com/sys-bio/frequencyResponse., Comment: Fixed some minor typos

This paper presents a strategy for efficient quantum circuit design for density estimation. The strategy is based on a quantum-inspired algorithm for density estimation and a circuit optimisation routine based on memetic algorithms. The model maps a training dataset to a quantum state represented by a density matrix through a quantum feature map. This training state encodes the probability distribution of the dataset in a quantum state, such that the density of a new sample can be estimated by projecting its corresponding quantum state onto the training state. We propose the application of a memetic algorithm to find the architecture and parameters of a variational quantum circuit that implements the quantum feature map, along with a variational learning strategy to prepare the training state. Demonstrations of the proposed strategy show an accurate approximation of the Gaussian kernel density estimation method through shallow quantum circuits illustrating the feasibility of the algorithm for near-term quantum hardware., Comment: 15 pages, 10 figures, presented at QTML 2023

Exploring bodies of water on their surface allows robots to efficiently communicate and harvest energy from the sun. On the water surface, however, robots often face highly unstructured environments, cluttered with plant matter, animals, and debris. We report a fast (5.1 cm/s translation and 195 {\deg}/s rotation), centimeter-scale swimming robot with high maneuverability and autonomous untethered operation. Locomotion is enabled by a pair of soft, millimeter-thin, undulating pectoral fins, in which traveling waves are electrically excited to generate propulsion. The robots navigate through narrow spaces, through grassy plants, and push objects weighing over 16x their body weight. Such robots can allow distributed environmental monitoring as well as continuous measurement of plant and water parameters for aqua-farming.

We consider cubic NLS in dimensions 2, 3, 4 and we prove that almost surely solutions with randomized initial data at low regularity scatter. Moreover, we establish some smoothing properties of the associated scattering operator and precise the rate of convergence., Comment: 23 pages

Exploring the shape of point configurations has been a key driver in the evolution of TDA (short for topological data analysis) since its infancy. This survey illustrates the recent efforts to broaden these ideas to model spatial interactions among multiple configurations, each distinguished by a color. It describes advances in this area and prepares the ground for further exploration by mentioning unresolved questions and promising research avenues while focusing on the overlap with discrete geometry.

Mosaic crystals, with their high integrated reflectivities, are widely-employed in spectrometers used to diagnose high energy density systems. X-ray Thomson scattering (XRTS) has emerged as a powerful diagnostic tool of these systems, providing in principle direct access to important properties such as the temperature via detailed balance. However, the measured XRTS spectrum is broadened by the spectrometer instrument function (IF), and without careful consideration of the IF one risks misdiagnosing system conditions. Here, we consider in detail the IF of 40 $\mu$m and 100 $\mu$m mosaic HAPG crystals, and how the broadening varies across the spectrometer in an energy range of 6.7-8.6 keV. Notably, we find a strong asymmetry in the shape of the IF towards higher energies. As an example, we consider the effect of the asymmetry in the IF on the temperature inferred via XRTS for simulated 80 eV CH plasmas, and find that the temperature can be overestimated if an approximate symmetric IF is used. We therefore expect a detailed consideration of the full IF will have an important impact on system properties inferred via XRTS in both forward modelling and model-free approaches., Comment: 19 pages, 13 figures

Extreme events are the major weather related hazard for humanity. It is then of crucial importance to have a good understanding of their statistics and to be able to forecast them. However, lack of sufficient data makes their study particularly challenging. In this work we provide a simple framework to study extreme events that tackles the lack of data issue by using the whole dataset available, rather than focusing on the extremes in the dataset. To do so, we make the assumption that the set of predictors and the observable used to define the extreme event follow a jointly Gaussian distribution. This naturally gives the notion of an optimal projection of the predictors for forecasting the event. We take as a case study extreme heatwaves over France, and we test our method on an 8000-year-long intermediate complexity climate model time series and on the ERA5 reanalysis dataset. For a-posteriori statistics, we observe and motivate the fact that composite maps of very extreme events look similar to less extreme ones. For prediction, we show that our method is competitive with off-the-shelf neural networks on the long dataset and outperforms them on reanalysis. The optimal projection pattern, which makes our forecast intrinsically interpretable, highlights the importance of soil moisture deficit and quasi-stationary Rossby waves as precursors to extreme heatwaves., Comment: 40 pages, 11 figures, 6 tables

This paper proposes the utilization of a periodic Parareal with a periodic coarse problem to efficiently perform adjoint sensitivity analysis for the steady state of time-periodic nonlinear circuits. In order to implement this method, a modified formulation for adjoint sensitivity analysis based on the transient approach is derived.

We introduce a novel method for safe mobile robot navigation in dynamic, unknown environments, utilizing onboard sensing to impose safety constraints without the need for accurate map reconstruction. Traditional methods typically rely on detailed map information to synthesize safe stabilizing controls for mobile robots, which can be computationally demanding and less effective, particularly in dynamic operational conditions. By leveraging recent advances in distributionally robust optimization, we develop a distributionally robust control barrier function (DR-CBF) constraint that directly processes range sensor data to impose safety constraints. Coupling this with a control Lyapunov function (CLF) for path tracking, we demonstrate that our CLF-DR-CBF control synthesis method achieves safe, efficient, and robust navigation in uncertain dynamic environments. We demonstrate the effectiveness of our approach in simulated and real autonomous robot navigation experiments, marking a substantial advancement in real-time safety guarantees for mobile robots., Comment: Submitted to the International Journal of Robotics Research (IJRR). Project page: https://existentialrobotics.org/DR_Safe_Navigation_Webpage

In numerous fields, dynamic time series data require continuous updates, necessitating efficient data processing techniques for accurate analysis. This paper examines the banana tree data structure, specifically designed to efficiently maintain persistent homology -- a multi-scale topological descriptor -- for dynamically changing time series data. We implement this data structure and conduct an experimental study to assess its properties and runtime for update operations. Our findings indicate that banana trees are highly effective with unbiased random data, outperforming state-of-the-art static algorithms in these scenarios. Additionally, our results show that real-world time series share structural properties with unbiased random walks, suggesting potential practical utility for our implementation.

Policy gradient methods have enabled deep reinforcement learning (RL) to approach challenging continuous control problems, even when the underlying systems involve highly nonlinear dynamics that generate complex non-smooth optimization landscapes. We develop a rigorous framework for understanding how policy gradient methods mollify non-smooth optimization landscapes to enable effective policy search, as well as the downside of it: while making the objective function smoother and easier to optimize, the stochastic objective deviates further from the original problem. We demonstrate the equivalence between policy gradient methods and solving backward heat equations. Following the ill-posedness of backward heat equations from PDE theory, we present a fundamental challenge to the use of policy gradient under stochasticity. Moreover, we make the connection between this limitation and the uncertainty principle in harmonic analysis to understand the effects of exploration with stochastic policies in RL. We also provide experimental results to illustrate both the positive and negative aspects of mollification effects in practice., Comment: 19 pages, 41 figures

Antimony is a high-level, human-readable text-based language designed for defining and sharing models in the systems biology community. It enables scientists to describe biochemical networks and systems using a simple and intuitive syntax. It allows users to easily create, modify, and distribute reproducible computational models. By allowing the concise representation of complex biological processes, Antimony enhances collaborative efforts, improves reproducibility, and accelerates the iterative development of models in systems biology. This paper provides an update to the Antimony language since it was introduced in 2009. In particular, we highlight new annotation features, support for flux balance analysis, a new rateOf method, support for probability distributions and uncertainty, named stochiometries, and algebraic rules. Antimony is also now distributed as a C/C++ library, together with python and Julia bindings, as well as a JavaScript version for use within a web browser. Availability: https://github.com/sys-bio/antimony.

Efficient computation of sensitivities is a promising approach for efficiently of designing and optimizing high voltage direct current cable joints. This paper presents the adjoint variable method for coupled nonlinear transient electrothermal problems as an efficient approach to compute sensitivities with respect to a large number of design parameters. The method is used to compute material sensitivities of a 320kV high voltage direct current cable joint specimen. The results are validated against sensitivities obtained via the direct sensitivity method.

We introduce an extension of the non-equilibrium dynamical mean field theory to incorporate the effects of static random disorder in the dynamics of a many-particle system by integrating out different disorder configurations resulting in an effective time-dependent density-density interaction. We use this method to study the non-equilibrium transient dynamics of a system described by the Fermi Anderson-Hubbard model following an interaction and disorder quench. The method recovers the solution of the disorder-free case for which the system exhibits qualitatively distinct dynamical behaviors in the weak-coupling (prethermalization) and strong-coupling regimes (collapse-and-revival oscillations). However, we find that weak random disorder promotes thermalization. In the weak coupling regime, the jump in the quasiparticle weight in the prethermal regime is suppressed by random disorder while in the strong-coupling regime, random disorder reduces the amplitude of the quasiparticle weight oscillations. These results highlight the importance of disorder in the dynamics of realistic many-particle systems., Comment: 6 pages, 3 figures

Surgical automation can improve the accessibility and consistency of life saving procedures. Most surgeries require separating layers of tissue to access the surgical site, and suturing to reattach incisions. These tasks involve deformable manipulation to safely identify and alter tissue attachment (boundary) topology. Due to poor visual acuity and frequent occlusions, surgeons tend to carefully manipulate the tissue in ways that enable inference of the tissue's attachment points without causing unsafe tearing. In a similar fashion, we propose JIGGLE, a framework for estimation and interactive sensing of unknown boundary parameters in deformable surgical environments. This framework has two key components: (1) a probabilistic estimation to identify the current attachment points, achieved by integrating a differentiable soft-body simulator with an extended Kalman filter (EKF), and (2) an optimization-based active control pipeline that generates actions to maximize information gain of the tissue attachments, while simultaneously minimizing safety costs. The robustness of our estimation approach is demonstrated through experiments with real animal tissue, where we infer sutured attachment points using stereo endoscope observations. We also demonstrate the capabilities of our method in handling complex topological changes such as cutting and suturing., Comment: Accepted at RSS 2024

The biomolecular networks underpinning cell function exhibit canalization, or the buffering of fluctuations required to function in a noisy environment. One understudied putative mechanism for canalization is the functional equivalence of a biomolecular entity's regulators (e.g., among the transcription factors for a gene). In these discrete dynamical systems, activation and inhibition of biomolecular entities (e.g., transcription of genes) are modeled as the activity of coupled 2-state automata, and thus the equivalence of regulators can be studied using the theory of symmetry in discrete functions. To this end, we present a new exact algorithm for finding maximal symmetry groups among the inputs to discrete functions. We implement this algorithm in Rust as a Python package, schematodes. We include schematodes in the new CANA v1.0.0 release, an open source Python library for analyzing canalization in Boolean networks, which we also present here. We compare our exact method implemented in schematodes to the previously published inexact method used in earlier releases of CANA and find that schematodes significantly outperforms the prior method both in speed and accuracy. We also apply CANA v1.0.0 to study the symmetry properties of regulatory function from an ensemble of experimentally-supported Boolean networks from the Cell Collective. Using CANA v1.0.0, we find that the distribution of a previously reported symmetry parameter, $k_s/k$, is statistically significantly different in the Cell Collective than in random automata with the same in-degree and activation bias (Kolmogorov-Smirnov test, $p<0.001$). In particular, its spread is much wider than in our null model (IQR 0.31 vs IQR 0.20 with equal medians), demonstrating that the Cell Collective is enriched in functions with extreme symmetry or asymmetry., Comment: 5 pages 1 figure (two images in figure)

Estimates of future migration patterns are a crucial input to world population projections. Forced migration, including refugee and asylum seekers, plays an important role in overall migration patterns, but is notoriously difficult to forecast. We propose a modeling pipeline based on Bayesian hierarchical time-series modeling for projecting combined refugee and asylum seeker populations by country of origin using data from the United Nations High Commissioner for Human Rights (UNHCR). Our approach is based on a conceptual model of refugee crises following growth and decline phases, separated by a peak. The growth and decline phases are modeled by logistic growth and decline through an interrupted logistic process model. We evaluate our method through a set of validation exercises that show it has good performance for forecasts at 1, 5, and 10 year horizons, and we present projections for 35 countries with ongoing refugee crises., Comment: 31 pages, 3 tables, 6 figures

Longitudinal Modified Treatment Policies (LMTPs) provide a framework for defining a broad class of causal target parameters for continuous and categorical exposures. We propose Local LMTPs, a generalization of LMTPs to settings where the target parameter is conditional on subsets of units defined by the treatment or exposure. Such parameters have wide scientific relevance, with well-known parameters such as the Average Treatment Effect on the Treated (ATT) falling within the class. We provide a formal causal identification result that expresses the Local LMTP parameter in terms of sequential regressions, and derive the efficient influence function of the parameter which defines its semi-parametric and local asymptotic minimax efficiency bound. Efficient semi-parametric inference of Local LMTP parameters requires estimating the ratios of functions of complex conditional probabilities (or densities). We propose an estimator for Local LMTP parameters that directly estimates these required ratios via empirical loss minimization, drawing on the theory of Riesz representers. The estimator is implemented using a combination of ensemble machine learning algorithms and deep neural networks, and evaluated via simulation studies. We illustrate in simulation that estimation of the density ratios using Riesz representation might provide more stable estimators in finite samples in the presence of empirical violations of the overlap/positivity assumption., Comment: 28 pages, 1 figure

Powered by large language models (LLMs), AI agents have become capable of many human tasks. Using the most canonical definitions of the Big Five personality, we measure the ability of LLMs to negotiate within a game-theoretical framework, as well as methodological challenges to measuring notions of fairness and risk. Simulations (n=1,500) for both single-issue and multi-issue negotiation reveal increase in domain complexity with asymmetric issue valuations improve agreement rates but decrease surplus from aggressive negotiation. Through gradient-boosted regression and Shapley explainers, we find high openness, conscientiousness, and neuroticism are associated with fair tendencies; low agreeableness and low openness are associated with rational tendencies. Low conscientiousness is associated with high toxicity. These results indicate that LLMs may have built-in guardrails that default to fair behavior, but can be "jail broken" to exploit agreeable opponents. We also offer pragmatic insight in how negotiation bots can be designed, and a framework of assessing negotiation behavior based on game theory and computational social science.

While the currents of the defocusing Ablowitz-Ladik chain are unambiguously defined, no explicit formulas for their densities have been obtained yet. We close this gap. As a consequence, we also complete the argument which establishes the anticipated expression for average currents, averaged over a generalized Gibbs ensemble., Comment: 8 pages

Artificial intelligence systems exhibit many useful capabilities, but they appear to lack understanding. This essay describes how we could go about constructing a machine capable of understanding. As John Locke (1689) pointed out words are signs for ideas, which we can paraphrase as thoughts and concepts. To understand a word is to know and be able to work with the underlying concepts for which it is an indicator. Understanding between a speaker and a listener occurs when the speaker casts his or her concepts into words and the listener recovers approximately those same concepts. Current models rely on the listener to construct any potential meaning. The diminution of behaviorism as a psychological paradigm and the rise of cognitivism provide examples of many experimental methods that can be used to determine whether and to what extent a machine might understand and to make suggestions about how that understanding might be instantiated.

The numerical solution of problems in nonlinear magnetostatics is typically based on a variational formulation in terms of magnetic potentials, the discretization by finite elements, and iterative solvers like the Newton method. The vector potential approach aims at minimizing a certain energy functional and, in three dimensions, requires the use of edge elements and appropriate gauging conditions. The scalar potential approach, on the other hand, seeks to maximize the negative coenergy and can be realized by standard Lagrange finite elements, thus reducing the number of degrees of freedom and simplifying the implementation. The number of Newton iterations required to solve the governing nonlinear system, however, has been observed to be usually higher than for the vector potential formulation. In this paper, we propose a method that combines the advantages of both approaches, i.e., it requires as few Newton iterations as the vector potential formulation while involving the magnetic scalar potential as the primary unknown. We discuss the variational background of the method, its well-posedness, and its efficient implementation. Numerical examples are presented for illustration of the accuracy and the gain in efficiency compared to other approaches.

This paper explores some basic concepts of Biochemical Systems Theory (BST) and Metabolic Control Analysis (MCA), two frameworks developed to understand the behavior of biochemical networks. Initially introduced by Savageau, BST focuses on system stability and employs power laws in modeling biochemical systems. On the other hand, MCA, pioneered by authors such as Kacser and Burns and Heinrich and Rapoport, emphasizes linearization of the governing equations and describes relationships (known as theorems) between different measures. Despite apparent differences, both frameworks are shown to be equivalent in many respects. Through a simple example of a linear chain, the paper demonstrates how BST and MCA yield identical results when analyzing steady-state behavior and logarithmic gains within biochemical pathways. This comparative analysis highlights the interchangeability of concepts such as kinetic orders, elasticities and other logarithmic gains.

A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which explicitly encodes the energy storage, dissipation, and transfer mechanisms. This implies a power balance on the continuous level which can be preserved under appropriate discretization in space and time. The models and main results are presented in detail for linear constitutive models, but the extension to nonlinear elements and more general coupling mechanisms is possible. The theoretical findings are demonstrated by numerical results.

The top-down synthesis of inherently ferroelectric semiconductors and their integration with traditional material platforms have the potential to enable new low power logic devices, and to harness the bulk photoelectric effect for more efficient photovoltaic cells. InSe is a layered van der Waals compound exhibiting multiple polytypes, with semiconducting gamma-InSe revealing a non-centrosymmetric space group and showing a high carrier mobility at room temperature. Here we report the growth of InSe films on close to lattice matched semi-insulating GaAs(111)B substrates by molecular beam epitaxy (MBE). Excellent nucleation behavior resulted in the growth of smooth, single phase InSe films. The dominant polytype determined from X-ray diffraction was the targeted gamma-InSe, however Raman spectroscopy revealed spatial variations in the overall low-intensity non-centrosymmetric vibration modes. Transmission electron microscopy uncovered the presence of the three bulk polytypes beta, gamma, and epsilon-InSe coexisting in the films arranging in nanosized domains. The different polytypes can be interpreted as sequences of stacking faults and rotational twin boundaries of gamma-InSe made from individual non-centrosymmetric Se-In-In-Se layers with P-6m2 symmetry. A second, centrosymmetric Se-In-In-Se layer polymorph was identified with P-3m symmetry, which is typically not present in InSe bulk phases. First principles calculations revealed small formation energy differences between the InSe polymorphs and polytypes, yet sizeable differences in their electronic properties. Nanoscale domain sizes of varying polytypes thus resulted in sizeable electronic disorder in the grown films that dominated the electronic transport properties. Our results indicate that bottom-up thin film synthesis is a viable synthesis route towards stabilization of InSe polytypes not present in the bulk.

Fast and Safe Tracking (FaSTrack) is a modular framework that provides safety guarantees while planning and executing trajectories in real time via value functions of Hamilton-Jacobi (HJ) reachability. These value functions are computed through dynamic programming, which is notorious for being computationally inefficient. Moreover, the resulting trajectory does not adapt online to the environment, such as sudden disturbances or obstacles. DeepReach is a scalable deep learning method to HJ reachability that allows parameterization of states, which opens up possibilities for online adaptation to various controls and disturbances. In this paper, we propose Parametric FaSTrack, which uses DeepReach to approximate a value function that parameterizes the control bounds of the planning model. The new framework can smoothly trade off between the navigation speed and the tracking error (therefore maneuverability) while guaranteeing obstacle avoidance in a priori unknown environments. We demonstrate our method through two examples and a benchmark comparison with existing methods, showing the safety, efficiency, and faster solution times of the framework., Comment: 12 pages, 6 figures, 1 table, to be published in L4DC

The Ablowitz-Ladik chain is an integrable discretized version of the nonlinear Schr\"{o}dinger equation. We report on a novel underlying Hamiltonian particle system with properties similar to the ones known for the classical Toda chain and Calogero fluid with $1/\sinh^2$ pair interaction. Boundary conditions are imposed such that, both in the distant past and future, particles have a constant velocity. We establish the many-particle scattering for the Ablowitz-Ladik chain and obtain properties known for generic integrable many-body systems. For a specific choice of the chain, real initial data remain real in the course of time. Then, asymptotically, particles move in pairs with a velocity-dependent size and scattering shifts are governed by the fusion rule., Comment: 32 pages, 5 figures, 2 appendices

Reliable prediction of protein variant effects is crucial for both protein optimization and for advancing biological understanding. For practical use in protein engineering, it is important that we can also provide reliable uncertainty estimates for our predictions, and while prediction accuracy has seen much progress in recent years, uncertainty metrics are rarely reported. We here provide a Gaussian process regression model, Kermut, with a novel composite kernel for modelling mutation similarity, which obtains state-of-the-art performance for protein variant effect prediction while also offering estimates of uncertainty through its posterior. An analysis of the quality of the uncertainty estimates demonstrates that our model provides meaningful levels of overall calibration, but that instance-specific uncertainty calibration remains more challenging. We hope that this will encourage future work in this promising direction., Comment: 10 pages (36 in total with appendix), 4 figures (26 figures in total with appendix)

Advances in large language models have notably enhanced the efficiency of information extraction from unstructured and semi-structured data sources. As these technologies become integral to various applications, establishing an objective measure for the quality of information extraction becomes imperative. However, the scarcity of labeled data presents significant challenges to this endeavor. In this paper, we introduce an automatic framework to assess the quality of the information extraction/retrieval and its completeness. The framework focuses on information extraction in the form of entity and its properties. We discuss how to handle the input/output size limitations of the large language models and analyze their performance when extracting the information. In particular, we introduce scores to evaluate the quality of the extraction and provide an extensive discussion on how to interpret them.