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Humans appear to have a critical period (CP) for language acquisition: Second language (L2) acquisition becomes harder after early childhood, and ceasing exposure to a first language (L1) after this period (but not before) typically does not lead to substantial loss of L1 proficiency. It is unknown whether these CP effects result from innately determined brain maturation or as a stabilization of neural connections naturally induced by experience. In this study, we use language models (LMs) to test the extent to which these phenomena are peculiar to humans, or shared by a broader class of language learners. We vary the age of exposure by training LMs on language pairs in various experimental conditions, and find that LMs, which lack any direct analog to innate maturational stages, do not show CP effects when trained sequentially on L1 and L2. Our results contradict the claim that CP effects are an inevitable result of learning in statistical learners, and they are consistent with an innate mechanism for CP effects. We show that we can reverse-engineer the CP by introducing a regularizer partway through training to simulate a maturational decrease in plasticity. All in all, our results suggest that L1 learning on its own may not be enough to induce a CP, and additional engineering is necessary to make language models more cognitively plausible.

A generalized two-dimensional cubic Lotka-Volterra model with infinitesimal parameters is studied. Three different cases have been considered, one non-degenerate and two degenerate. The local behavior of the model has been studied in the three cases. Six bifurcation diagrams with thirty different regions have been obtained in the non-degenerate case, respectively, sixteen diagrams with forty regions in the two degenerate cases.

The design of low-power wearables for the biomedical domain has received a lot of attention in recent decades, as technological advances in chip manufacturing have allowed real-time monitoring of patients using low-complexity ML within the mW range. Despite advances in application and hardware design research, the domain lacks a systematic approach to hardware evaluation. In this work, we propose BiomedBench, a new benchmark suite composed of complete end-to-end TinyML biomedical applications for real-time monitoring of patients using wearable devices. Each application presents different requirements during typical signal acquisition and processing phases, including varying computational workloads and relations between active and idle times. Furthermore, our evaluation of five state-of-the-art low-power platforms in terms of energy efficiency shows that modern platforms cannot effectively target all types of biomedical applications. BiomedBench is released as an open-source suite to standardize hardware evaluation and guide hardware and application design in the TinyML wearable domain., Comment: 7 pages, 5 figures. Sumbitted to Design & Test Special Issue TinyML

We investigate quotients by radical monomial ideals for which $T^2$, the second cotangent cohomology module, vanishes. The dimension of the graded components of $T^2$, and thus their vanishing, depends only on the combinatorics of the corresponding simplicial complex. We give both a complete characterization and a full list of one dimensional complexes with $T^2=0$. We characterize the graded components of $T^2$ when the simplicial complex is a uniform matroid. Finally, we show that $T^2$ vanishes for all matroids of corank at most two and conjecture that all connected matroids with vanishing $T^2$ are of corank at most two., Comment: 13 pages

The distributed computing literature considers multiple options for modeling communication. Most simply, communication is categorized as either synchronous or asynchronous. Synchronous communication assumes that messages get delivered within a publicly known timeframe and that parties' clocks are synchronized. Asynchronous communication, on the other hand, only assumes that messages get delivered eventually. A more nuanced approach, or a middle ground between the two extremes, is given by the partially synchronous model, which is arguably the most realistic option. This model comes in two commonly considered flavors: (i) The Global Stabilization Time (GST) model: after an (unknown) amount of time, the network becomes synchronous. This captures scenarios where network issues are transient. (ii) The Unknown Latency (UL) model: the network is, in fact, synchronous, but the message delay bound is unknown. This work formally establishes that any time-agnostic property that can be achieved by a protocol in the UL model can also be achieved by a (possibly different) protocol in the GST model. By time-agnostic, we mean properties that can depend on the order in which events happen but not on time as measured by the parties. Most properties considered in distributed computing are time-agnostic. The converse was already known, even without the time-agnostic requirement, so our result shows that the two network conditions are, under one sensible assumption, equally demanding.

We prove that one hundred percent of closed geodesic periods of a Maa{\ss} form for the modular group are non-vanishing when ordered by length. We present applications to the non-vanishing of central values of Rankin--Selberg $L$-functions. Similar results for holomorphic forms for general Fuchsian groups of the first kind with a cusp are also obtained, as well as results towards normal distribution., Comment: 34 pages, comments welcome!

We propose a data-driven approach for propagating uncertainty in stochastic power grid simulations and apply it to the estimation of transmission line failure probabilities. A reduced-order equation governing the evolution of the observed line energy probability density function is derived from the Fokker--Planck equation of the full-order continuous Markov process. Our method consists of estimates produced by numerically integrating this reduced equation. Numerical experiments for scalar- and vector-valued energy functions are conducted using the classical multimachine model under spatiotemporally correlated noise perturbation. The method demonstrates a more sample-efficient approach for computing probabilities of tail events when compared with kernel density estimation. Moreover, it produces vastly more accurate estimates of joint event occurrence when compared with independent models., Comment: 12 pages, 6 figures, and 1 table

We consider binary group decision-making under a rich model of liquid democracy recently proposed by Colley, Grandi, and Novaro (2022): agents submit ranked delegation options, where each option may be a function of multiple agents' votes; e.g., "I vote yes if a majority of my friends vote yes." Such ballots are unravelled into a profile of direct votes by selecting one entry from each ballot so as not to introduce cyclic dependencies. We study delegation via monotonic Boolean functions, and two unravelling procedures: MinSum, which minimises the sum of the ranks of the chosen entries, and its egalitarian counterpart, MinMax. We provide complete computational dichotomies: MinSum is hard to compute (and approximate) as soon as any non-trivial functions are permitted, and polynomial otherwise; for MinMax the easiness results extend to arbitrary-arity logical ORs and ANDs taken in isolation, but not beyond. For the classic model of delegating to individual agents, we give asymptotically near-tight algorithms for carrying out the two procedures and efficient algorithms for finding optimal unravellings with the highest vote count for a given alternative. These algorithms inspire novel tie-breaking rules for the setup of voting to change a status quo. We then introduce a new axiom, which can be viewed as a variant of the participation axiom, and use algorithmic techniques developed earlier in the paper to show that it is satisfied by MinSum and a lexicographic refinement of MinMax (but not MinMax itself)., Comment: To appear in AAAI'24

This paper presents a novel centralized, variational data assimilation approach for calibrating transient dynamic models in electrical power systems, focusing on load model parameters. With the increasing importance of inverter-based resources, assessing power systems' dynamic performance under disturbances has become challenging, necessitating robust model calibration methods. The proposed approach expands on previous Bayesian frameworks by establishing a posterior distribution of parameters using an approximation around the maximum a posteriori value. We illustrate the efficacy of our method by generating events of varying intensity, highlighting its ability to capture the systems' evolution accurately and with associated uncertainty estimates. This research improves the precision of dynamic performance assessments in modern power systems, with potential applications in managing uncertainties and optimizing system operations., Comment: 9 pages, 8 figures, and 1 table

A decade ago, Gerhard Woeginger posed an open problem that became well-known as "Woeginger's Hiking Problem": Consider a group of $n$ people that want to go hiking; everyone expresses preferences over the size of their hiking group in the form of an interval between $1$ and $n$. Is it possible to efficiently assign the $n$ people to a set of hiking subgroups so that every person approves the size of their assigned subgroup? The problem is also known as efficiently deciding if an instance of an anonymous Hedonic Game with interval approval preferences admits a wonderful partition. We resolve the open problem in the affirmative by presenting an $O(n^5)$ time algorithm for Woeginger's Hiking Problem. Our solution is based on employing a dynamic programming approach for a specific rectangle stabbing problem from computational geometry. Moreover, we propose natural, more demanding extensions of the problem, e.g., maximizing the number of satisfied participants and variants with single-peaked preferences, and show that they are also efficiently solvable. Last but not least, we employ our solution to efficiently compute a partition that maximizes the egalitarian welfare for anonymous single-peaked Hedonic Games., Comment: To appear in ICALP 2024; contains omitted material and small writing improvements

The growing computing power over the years has enabled simulations to become more complex and accurate. While immensely valuable for scientific discovery and problem-solving, however, high-fidelity simulations come with significant computational demands. As a result, it is common to run a low-fidelity model with a subgrid-scale model to reduce the computational cost, but selecting the appropriate subgrid-scale models and tuning them are challenging. We propose a novel method for learning the subgrid-scale model effects when simulating partial differential equations augmented by neural ordinary differential operators in the context of discontinuous Galerkin (DG) spatial discretization. Our approach learns the missing scales of the low-order DG solver at a continuous level and hence improves the accuracy of the low-order DG approximations as well as accelerates the filtered high-order DG simulations with a certain degree of precision. We demonstrate the performance of our approach through multidimensional Taylor-Green vortex examples at different Reynolds numbers and times, which cover laminar, transitional, and turbulent regimes. The proposed method not only reconstructs the subgrid-scale from the low-order (1st-order) approximation but also speeds up the filtered high-order DG (6th-order) simulation by two orders of magnitude., Comment: 17 figures, 2 tables, 27 pages

This paper presents the Smooth Number Message Authentication Code (SNMAC) for the context of lightweight IoT devices. The proposal is based on the use of smooth numbers in the field of cryptography, and investigates how one can use them to improve the security and performance of various algorithms or security constructs. The literature findings suggest that current IoT solutions are viable and promising, yet they should explore the potential usage of smooth numbers. The methodology involves several processes, including the design, implementation, and results evaluation. After introducing the algorithm, provides a detailed account of the experimental performance analysis of the SNMAC solution, showcasing its efficiency in real-world scenarios. Furthermore, the paper also explores the security aspects of the proposed SNMAC algorithm, offering valuable insights into its robustness and applicability for ensuring secure communication within IoT environments., Comment: 19 pages, 7 figures

An electorate with fully-ranked innate preferences casts approval votes over a finite set of alternatives. As a result, only partial information about the true preferences is revealed to the voting authorities. In an effort to understand the nature of the true preferences given only partial information, one might ask whether the unknown innate preferences could possibly be single-crossing. The existence of a polynomial time algorithm to determine this has been asked as an outstanding problem in the works of Elkind and Lackner. We hereby give a polynomial time algorithm determining a single-crossing collection of fully-ranked preferences that could have induced the elicited approval ballots, or reporting the nonexistence thereof. Moreover, we consider the problem of identifying negative instances with a set of forbidden sub-ballots, showing that any such characterization requires infinitely many forbidden configurations., Comment: To appear in WINE'23; add acknowledgements, change formatting, minor corrections

In this paper, we consider a risk process with deterministic growth and multiplicative jumps to model the capital of a low-income household. Reflecting the high-risk nature of the low-income environment, capital losses are assumed to be proportional to the level of accumulated capital at the jump time. Our aim is to derive the probability that a household falls below the poverty line, i.e. the trapping probability, where ``trapping" occurs when the level of capital of a household holds falls below the poverty line, to an area from which it is difficult to escape without external help. Considering the remaining proportion of capital to be distributed as a special case of the beta distribution, closed-form expressions for the trapping probability are obtained via analysis of the Laplace transform of the infinitesimal generator of the process. To study the impact of insurance on this probability, introduction of an insurance product offering proportional coverage is presented. The infinitesimal generator of the insured process gives rise to non-local differential equations. To overcome this, we propose a recursive method for deriving a closed-form solution of the integro-differential equation associated with the infinitesimal generator of the insured process and provide a numerical estimation method for obtaining the trapping probability. Constraints on the rate parameters of the process that prevent certain trapping are derived in both the uninsured and insured cases using classical results from risk theory.

A group of $n$ agents with numerical preferences for each other are to be assigned to the $n$ seats of a dining table. We study two natural topologies:~circular (cycle) tables and panel (path) tables. For a given seating arrangement, an agent's utility is the sum of their preference values towards their (at most two) direct neighbors. An arrangement is envy-free if no agent strictly prefers someone else's seat, and it is stable if no two agents strictly prefer each other's seats. Recently, it was shown that for both paths and cycles it is NP-hard to decide whether an envy-free arrangement exists, even for symmetric binary preferences. In contrast, we show that, if agents come from a bounded number of classes, the problem is solvable in polynomial time for arbitrarily-valued possibly asymmetric preferences, including outputting an arrangement if possible. We also give simpler proofs of the previous hardness results if preferences are allowed to be asymmetric. For stability, it is known that deciding the existence of stable arrangements is NP-hard for both topologies, but only if sufficiently-many numerical values are allowed. As it turns out, even constructing unstable instances can be challenging in certain cases, e.g., binary values. We completely characterize the existence of stable arrangements based on the number of distinct values in the preference matrix and the number of agent classes. We also ask the same question for non-negative values and give an almost-complete characterization, the most interesting outstanding case being that of paths with two-valued non-negative preferences, for which we experimentally find that stable arrangements always exist and prove it under the additional constraint that agents can only swap seats when sitting at most two positions away. We moreover give a polynomial algorithm for determining a stable arrangement assuming a bounded number of classes., Comment: To appear in WINE'23; preliminary version presented at COMSOC'23

Traditional blockchain design gives miners or validators full control over transaction ordering, i.e., they can freely choose which transactions to include or exclude, as well as in which order. While not an issue initially, the emergence of decentralized finance has introduced new transaction order dependencies allowing parties in control of the ordering to make a profit by front-running others' transactions. In this work, we present the Decentralized Clock Network, a new approach for achieving fair transaction ordering. Users submit their transactions to the network's clocks, which run an agreement protocol that provides each transaction with a timestamp of receipt which is then used to define the transactions' order. By separating agreement from ordering, our protocol is efficient and has a simpler design compared to other available solutions. Moreover, our protocol brings to the blockchain world the paradigm of asynchronous fallback, where the algorithm operates with stronger fairness guarantees during periods of synchronous use, switching to an asynchronous mode only during times of increased network delay., Comment: In Proceedings of 27th International Conference on Principles of Distributed Systems (OPODIS)

Advanced science and technology provide a wealth of big data from different sources for extreme value analysis. Classical extreme value theory was extended to obtain an accelerated max-stable distribution family for modelling competing risk-based extreme data in Cao and Zhang (2021). In this paper, we establish probability models for power normalized maxima and minima from competing risks. The limit distributions consist of an extensional new accelerated max-stable and min-stable distribution family (termed as the accelerated p-max/p-min stable distribution), and its left-truncated version. The consistency and asymptotic normality are obtained for the maximum likelihood estimation of the parameters involved in the accelerated p-max and p-min stable distributions when it exists. The limit types of distributions are determined principally by the sample generating process and the interplay among the competing risks, which are illustrated by common examples. Further, the statistical inference concerning the maximum likelihood estimation and model diagnosis of this model was investigated. Numerical studies show first the efficient approximation of all limit scenarios as well as its comparable convergence rate in contrast with those under linear normalization, and then present the maximum likelihood estimation and diagnosis of accelerated p-max/p-min stable models for simulated data sets. Finally, two real datasets concerning annual maximum of ground level ozone and survival times of Stanford heart plant demonstrate the performance of our accelerated p-max and accelerated p-min stable models.

In this paper, we prove that in the overparametrized regime, deep neural network provide universal approximations and can interpolate any data set, as long as the activation function is locally in $L^1(\RR)$ and not an affine function. Additionally, if the activation function is smooth and such an interpolation networks exists, then the set of parameters which interpolate forms a manifold. Furthermore, we give a characterization of the Hessian of the loss function evaluated at the interpolation points. In the last section, we provide a practical probabilistic method of finding such a point under general conditions on the activation function., Comment: This is a revised, improved and more general result than the previous version

In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker-Planck operator for small-angle Coulomb collisions, a radiation damping operator, and a secondary knock-on (Boltzmann) collision source. We develop a new scalable fully implicit solver utilizing finite volume and conservative finite difference schemes and dynamic mesh adaptivity. A new data management framework in the PETSc library based on the p4est library is developed to enable simulations with dynamic adaptive mesh refinement (AMR), distributed memory parallelization, and dynamic load balancing of computational work. This framework and the runaway electron solver building on the framework are able to dynamically capture both bulk Maxwellian at the low-energy region and a runaway tail at the high-energy region. To effectively capture features via the AMR algorithm, a new AMR indicator prediction strategy is proposed that is performed alongside the implicit time evolution of the solution. This strategy is complemented by the introduction of computationally cheap feature-based AMR indicators that are analyzed theoretically. Numerical results quantify the advantages of the prediction strategy in better capturing features compared with nonpredictive strategies; and we demonstrate trade-offs regarding computational costs. The robustness with respect to model parameters, algorithmic scalability, and parallel scalability are demonstrated through several benchmark problems including manufactured solutions and solutions of different physics models. We focus on demonstrating the advantages of using implicit time stepping and AMR for runaway electron simulations., Comment: accepted

We prove that various Finsler metrizability problems for sprays can be reformulated in terms of the geodesic invariance of two tensors (metric and angular). We show that gyroscopic sprays is the the largest class of sprays with geodesic invariant angular metric. Scalar functions associated to these geodesically invariant tensors will be invariant as well and therefore will provide first integrals for the given spray.

We find the asymptotics of the value function maximizing the expected utility of discounted dividend payments of an insurance company whose reserves are modeled as a classical Cram\'er risk process, with exponentially distributed claims, when the initial reserves tend to infinity. We focus on the power and logarithmic utility functions. We perform some numerical analysis as well.

An assembly of $n$ voters needs to decide on $t$ independent binary issues. Each voter has opinions about the issues, given by a $t$-bit vector. Anscombe's paradox shows that a policy following the majority opinion in each issue may not survive a vote by the very same set of $n$ voters, i.e., more voters may feel unrepresented by such a majority-driven policy than represented. A natural resolution is to come up with a policy that deviates a bit from the majority policy but no longer gets more opposition than support from the electorate. We show that a Hamming distance to the majority policy of at most $\lfloor (t - 1) / 2 \rfloor$ can always be guaranteed, by giving a new probabilistic argument relying on structure-preserving symmetries of the space of potential policies. Unless the electorate is evenly divided between the two options on all issues, we in fact show that a policy strictly winning the vote exists within this distance bound. Our approach also leads to a deterministic polynomial-time algorithm for finding policies with the stated guarantees, answering an open problem of previous work. For odd $t$, unless we are in the pathological case described above, we also give a simpler and more efficient algorithm running in expected polynomial time with the same guarantees. We further show that checking whether distance strictly less than $\lfloor (t - 1) /2 \rfloor$ can be achieved is NP-hard, and that checking for distance at most some input $k$ is FPT with respect to several natural parameters., Comment: Accepted by AAMAS'23; fixed typos and improved clarity

Existing methods to determine the stability of a power system to small perturbations are based on eigenvalue analysis and focus on the asymptotic (long-term) behavior of the power grid. During the preasymptotic (short-term) transient, however, the system can exhibit large growth that is not explained by eigenvalues alone. In this paper we propose a new framework to determine the maximum (optimal) preasymptotic growth using the singular value decomposition. The approach is tailored to the analysis of quantities of interest in power system dynamics, such as the set of rotor speed deviations. Matrix-free techniques are developed to avoid the explicit formation of dense matrices and enable the analysis of large-scale systems without reaching memory bounds. Extensive results carried out from small to very large-scale systems (e.g., 70k-bus system) verify the theoretical aspects of the technique.

The Lunar Orbital Platform-Gateway (LOP-Gateway, or simply Gateway) is a crewed platform that will be assembled and operated in the vicinity of the Moon by NASA and international partner organizations, including ESA, starting from the mid-2020s. It will offer new opportunities for fundamental and applied scientific research. The Moon is a unique location to study the deep space plasma environment. Moreover, the lunar surface and the surface-bounded exosphere are interacting with this environment, constituting a complex multi-scale interacting system. This paper examines the opportunities provided by externally mounted payloads on the Gateway in the field of space plasma physics, heliophysics and space weather, but also examines the impact of the space environment on an inhabited platform in the vicinity of the Moon. It then presents the conceptual design of a model payload, required to perform these space plasma measurements and observations. It results that the Gateway is very well-suited for space plasma physics research. It allows a series of scientific objectives with a multidisciplinary dimension to be addressed.

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary differential equations (NODEs). Solving systems with fine temporal and spatial grid scales is an ongoing computational challenge, and closure models are generally difficult to tune. Machine learning approaches have increased the accuracy and efficiency of computational fluid dynamics solvers. In this approach neural networks are used to learn the coarse- to fine-grid map, which can be viewed as subgrid-scale parameterization. We propose a strategy that uses the NODE and partial knowledge to learn the source dynamics at a continuous level. Our method inherits the advantages of NODEs and can be used to parameterize subgrid scales, approximate coupling operators, and improve the efficiency of low-order solvers. Numerical results with the two-scale Lorenz 96 ODE, the convection-diffusion PDE, and the viscous Burgers' PDE are used to illustrate this approach., Comment: 28 pages, 21 figures, 2 tables

This paper explores strategies to transform an existing CPU-based high-performance computational fluid dynamics solver, HyPar, for compressible flow simulations on emerging exascale heterogeneous (CPU+GPU) computing platforms. The scientific motivation for developing a GPU-enhanced version of HyPar is to simulate canonical turbulent flows at the highest resolution possible on such platforms. We show that optimizing memory operations and thread blocks results in 200x speedup of computationally intensive kernels compared with a CPU core. Using multiple GPUs and CUDA-aware MPI communication, we demonstrate both strong and weak scaling of our GPU-based HyPar implementation on the NVIDIA Volta V100 GPUs. We simulate the decay of homogeneous isotropic turbulence in a triply periodic box on grids with up to $1024^3$ points (5.3 billion degrees of freedom) and on up to 1,024 GPUs. We compare the wall times for CPU-only and CPU+GPU simulations. The results presented in the paper are obtained on the Summit and Lassen supercomputers at Oak Ridge and Lawrence Livermore National Laboratories, respectively.