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This work proposes a fairness monitoring approach for machine learning models that predict patient mortality in the ICU. We investigate how well models perform for patient groups with different race, sex and medical diagnoses. We investigate Documentation bias in clinical measurement, showing how fairness analysis provides a more detailed and insightful comparison of model performance than traditional accuracy metrics alone., Comment: 8 pages

We use symplectic tools to establish a smooth variant of Franks theorem for a closed orientable surface of positive genus $g$; it implies that a symplectic diffeomorphism isotopic to the identity with more than $2g-2$ fixed points, counted homologically, has infinitely many periodic points. Furthermore, we present examples of symplectic diffeomorphisms with a prescribed number of periodic points. In particular, we construct symplectic flows on surfaces possessing only one fixed point and no other periodic orbits., Comment: v2: few changes in the Introduction regarding references

The Fuel Refueling Location Problem (FRLP) is a stylized model for determining the optimal siting of refueling stations for vehicles with limited travel ranges, such as hydrogen fuel cell vehicles and electric vehicles. This problem becomes particularly relevant when the goal is to facilitate long-distance travel using these vehicles. A variant of the FRLP, known as the Deviation Fuel Refueling Location Problem, accounts for the possibility that drivers may deviate from their preferred routes to ensure sufficient fuel or charging to complete their trips. While solution techniques based on various mathematical programming formulations have been thoroughly explored for these problems, there is a lack of theoretical insights into the relationships and strengths of these formulations. In this work, we study formulations of these problems used in the literature and compare their strengths in terms of linear programming relaxations. Furthermore, we explore approaches to tighten the formulations., Comment: 24 pages, 2 figures

In this paper, novel approaches are developed to explore the dynamics of motion in periodic orbits near libration points in cislunar space using the Differential Algebra (DA) framework. The Circular Restricted Three-Body Problem (CR3BP) models the motion, with initial states derived numerically via differential correction. Periodic orbit families are computed using the Pseudo-Arclength Continuation (PAC) method and fitted. Two newly developed polynomial regression models (PRMs) express initial states as functions of predefined parameters and are used in the DA framework to evaluate propagated states. The initial states, expressed via PRM, are propagated in the DA framework using the fourth-order Runge-Kutta (RK4) method. The resultant polynomials of both PRM and DA are employed to develop a control law that shows significantly reduced control effort compared to the traditional tracking control law, demonstrating their potential for cislunar space applications, particularly those requiring computationally inexpensive low-energy transfers., Comment: 20 pages, 19 figures

The spectral diameter of a symplectic ball is shown to be equal to its capacity; this result upgrades the known bound by a factor of two and yields a simple formula for the spectral diameter of a symplectic ellipsoid. We also study the relationship between the spectral diameter and packings by two balls., Comment: 21 pages

Federated Learning enables diverse devices to collaboratively train a shared model while keeping training data locally stored, avoiding the need for centralized cloud storage. Despite existing privacy measures, concerns arise from potential reverse engineering of gradients, even with added noise, revealing private data. To address this, recent research emphasizes using encrypted model parameters during training. This paper introduces a novel federated learning algorithm, leveraging coded local gradients without encryption, exchanging coded proxies for model parameters, and injecting surplus noise for enhanced privacy. Two algorithm variants are presented, showcasing convergence and learning rates adaptable to coding schemes and raw data characteristics. Two encryption-free implementations with fixed and random coding matrices are provided, demonstrating promising simulation results from both federated optimization and machine learning perspectives.

The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational physics and engineering applications across a number of domains. This paper describes some of the recent research and development in MFEM, focusing on performance portability across leadership-class supercomputing facilities, including exascale supercomputers, as well as new capabilities and functionality, enabling a wider range of applications. Much of this work was undertaken as part of the Department of Energy's Exascale Computing Project (ECP) in collaboration with the Center for Efficient Exascale Discretizations (CEED)., Comment: 19 pages, 19 figures

We explore three-body binary formation (3BBF), the formation of a bound system via gravitational scattering of three initially unbound bodies (3UB), using direct numerical integrations. For the first time, we consider systems with unequal masses, as well as finite-size and post-Newtonian effects. Our analytically derived encounter rates and numerical scattering results reproduce the 3BBF rate predicted by Goodman \& Hut (1993) for hard binaries in dense star clusters. We find that 3BBF occurs overwhelmingly through nonresonant encounters and that the two most massive bodies are never the most likely to bind. Instead, 3BBF favors pairing the two least massive bodies (for wide binaries) or the most plus least massive bodies (for hard binaries). 3BBF overwhelmingly favors wide binary formation with super-thermal eccentricities, perhaps helping to explain the eccentric wide binaries observed by Gaia. Hard binary formation is far rarer, but with a thermal eccentricity distribution. The semimajor axis distribution scales cumulatively as $a^3$ for hard and slightly wider binaries. Though mergers are rare between black holes when including relativistic effects, direct collisions occur frequently between main-sequence stars -- more often than hard 3BBF. Yet, these collisions do not significantly suppress hard 3BBF at the low velocity dispersions typical of open or globular clusters. Energy dissipation through gravitational radiation leads to a small probability of a bound, hierarchical triple system forming directly from 3UB., Comment: 28 pages, 16 figures, submitted to ApJ. Comments welcome

Given a compact Lagrangian $L$ in a semipositive convex-at-infinity symplectic manifold $W$, we establish a cup-length estimate for the action values of $L$ associated to a Hamiltonian isotopy whose spectral norm is smaller than some $\hbar(L)$. When $L$ is rational, this implies a cup-length estimate on the number of intersection points. This Chekanov-type result generalizes a theorem of Kislev and Shelukhin proving non-displaceability in the case when $W$ is closed and monotone. The method of proof is to deform the pair-of-pants product on Hamiltonian Floer cohomology using the Lagrangian $L$., Comment: 45 pages

With the increasing effects of climate change, the urgency to step away from fossil fuels is greater than ever before. Electric vehicles (EVs) are one way to diminish these effects, but their widespread adoption is often limited by the insufficient availability of charging stations. In this work, our goal is to expand the infrastructure of EV charging stations, in order to provide a better quality of service in terms of user satisfaction (and availability of charging stations). Specifically, our focus is directed towards urban areas. We first propose a model for the assignment of EV charging demand to stations, framing it as a maximum flow problem. This model is the basis for the evaluation of user satisfaction with a given charging infrastructure. Secondly, we incorporate the maximum flow model into a mixed-integer linear program, where decisions on the opening of new stations and on the expansion of their capacity through additional outlets is accounted for. We showcase our methodology for the city of Montreal, demonstrating the scalability of our approach to handle real-world scenarios. We conclude that considering both spacial and temporal variations in charging demand is meaningful when solving realistic instances.

This work presents an investigation and assessment framework, which, supported by realistic data, aims at provisioning operators with in-depth insights into the consumer-perceived Quality-of-Experience (QoE) at public Electric Vehicle (EV) charging infrastructures. Motivated by the unprecedented EV market growth, it is suspected that the existing charging infrastructure will soon be no longer capable of sustaining the rapidly growing charging demands; let alone that the currently adopted ad hoc infrastructure expansion strategies seem to be far from contributing any quality service sustainability solutions that tangibly reduce (ultimately mitigate) the severity of this problem. Without suitable QoE metrics, operators, today, face remarkable difficulty in assessing the performance of EV Charging Stations (EVCSs) in this regard. This paper aims at filling this gap through the formulation of novel and original critical QoE performance metrics that provide operators with visibility into the per-EVCS operational dynamics and allow for the optimization of these stations' respective utilization. Such metrics shall then be used as inputs to a Machine Learning model finely tailored and trained using recent real-world data sets for the purpose of forecasting future long-term EVCS loads. This will, in turn, allow for making informed optimal EV charging infrastructure expansions that will be capable of reliably coping with the rising EV charging demands and maintaining acceptable QoE levels. The model's accuracy has been tested and extensive simulations are conducted to evaluate the achieved performance in terms of the above listed metrics and show the suitability of the recommended infrastructure expansions., Comment: Accepted for Publication in IEEE Transactions on Intelligent Transportation Systems

Due to growing environmental concerns, the world's governments have been encouraging the shift of the transportation sector towards the adoption of Electric Vehicles (EVs). As a result, EV numbers have been growing exponentially and are expected to continue growing further which will add a large EV charging load to the power grid. To this end, this paper presents an EV-based defense mechanism against Load-Altering (LA) attacks targeting the grid. The developed mechanism utilizes H-infinity controllers and Linear Matrix Inequalities (LMIs) to mitigate LA attacks. After the controller synthesis and presentation of the attack scenarios, we demonstrate the effectiveness and success of our defense mechanism against the three known types of LA attacks. The scenarios include three 800 MW LA attacks against the New England 39-bus grid. The results demonstrate how our EV-based mitigation scheme eliminates the attack impacts and maintains the grid's stability in face of an unknown persisting attack., Comment: Accepted in the 2023 8th IEEE International Conference on Recent Advances and Innovations in Engineering (ICRAIE)-ICRAIE 2023. arXiv admin note: substantial text overlap with arXiv:2308.07526

Integer factorization is a significant problem, with implications for the security of widely-used cryptographic schemes. No efficient classical algorithm for polynomial-time integer factorization has been found despite extensive research. Although Peter Shor's breakthrough quantum algorithm offers a viable solution, current limitations of noisy intermediate-scale quantum (NISQ) computers hinder its practical implementation. To address this, researchers have explored alternative methods for factorization suitable for NISQ devices. One such method is the Quantum Approximate Optimization Algorithm, which treats factoring as an optimization problem defined over binary bits, resulting in various problematic aspects. In this paper, we explore the Func-QAOA approach for factorization, which premises overcoming some of the limitations of previous approaches and allows the incorporation of more advanced factorization techniques. After reviewing the most promising quantum implementations for integer arithmetics, we present a few illustrative examples to demonstrate the efficacy of the Func-QAOA approach and discuss methods to reduce the search space to speed up the optimization process.

We show that, on a closed semipositive symplectic manifold with semisimple quantum homology, any Hamiltonian diffeomorphism possessing more contractible fixed points, counted homologically, than the total Betti number of the manifold, must have infinitely many periodic points. This generalizes to the semipositive setting the beautiful result of Shelukhin on the Hofer-Zehnder conjecture., Comment: 32 pages

We present a new method for two-material Lagrangian hydrodynamics, which combines the Shifted Interface Method (SIM) with a high-order Finite Element Method. Our approach relies on an exact (or sharp) material interface representation, that is, it uses the precise location of the material interface. The interface is represented by the zero level-set of a continuous high-order finite element function that moves with the material velocity. This strategy allows to evolve curved material interfaces inside curved elements. By reformulating the original interface problem over a surrogate (approximate) interface, located in proximity of the true interface, the SIM avoids cut cells and the associated problematic issues regarding implementation, numerical stability, and matrix conditioning. Accuracy is maintained by modifying the original interface conditions using Taylor expansions. We demonstrate the performance of the proposed algorithms on established numerical benchmarks in one, two and three dimensions.

This paper presents an algorithm to apply nonlinear control design approaches in the case of stochastic systems with partial state observation. Deterministic nonlinear control approaches are formulated under the assumption of full state access and, often, relative degree one. We propose a control design approach that first generates a control policy for nonlinear deterministic models with full state observation. The resulting control policy is then used to build an importance-like probability distribution over the space of control sequences which are to be evaluated for the true stochastic and state-uncertain dynamics. This distribution serves in the sampling step within a random search control optimization procedure, to focus the exploration effort on certain regions of the control space. The sampled control sequences are assigned costs determined by a prescribed finite-horizon performance and safety measure, which is based on the stochastic dynamics. This sampling algorithm is parallelizable and shown to have computational complexity indifferent to the state dimension, and to be able to guarantee safety over the prescribed prediction horizon. A numerical simulation is provided to test the applicability and effectiveness of the presented approach and compare it to a certainty equivalence controller.

We propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries. Specifically, the variational formulation is appropriately modified to enforce free-slip wall boundary conditions, without perturbing the structure of the function spaces used to represent the solution, with a considerable simplification with respect to traditional approaches. Total energy is conserved and the resulting mass matrices are constant in time. The robustness and accuracy of the proposed method are validated with an extensive set of tests involving nontrivial curved boundaries.

The maximum covering location problem (MCLP) is a key problem in facility location, with many applications and variants. One such variant is the dynamic (or multi-period) MCLP, which considers the installation of facilities across multiple time periods. To the best of our knowledge, no exact solution method has been proposed to tackle large-scale instances of this problem. To that end, in this work, we expand upon the current state-of-the-art branch-and-Benders-cut solution method in the static case, by exploring several acceleration techniques. Additionally, we propose a specialised local branching scheme, that uses a novel distance metric in its definition of subproblems and features a new method for efficient and exact solving of the subproblems. These methods are then compared through extensive computational experiments, highlighting the strengths of the proposed methodologies., Comment: V2: Minor corrections for references and invalid URL

Due to the growing threat of climate change, the worlds governments have been encouraging the adoption of Electric Vehicles (EVs). As a result, EV numbers have been growing exponentially which will introduce a large EV charging load into the power grid. On this basis, we present a scheme to utilize EVs as a defense mechanism to mitigate Load-Altering (LA) attacks against the grid. The developed scheme relies on robust control theory and Linear Matrix Inequalities (LMIs). Our EV-based defense mechanism is formulated as a feedback controller synthesized using H-2 and H-infinity control techniques to eliminate the impact of unknown LA attacks. The controller synthesis considers the grid topology and the uncertainties of the EV connection to the grid. To demonstrate the effectiveness of the proposed mitigation scheme, it is tested against three types of LA attacks on the New England 39-bus grid. We test our mitigation scheme against 800 MW static, switching, and dynamic attacks in the presence of multiple sources of uncertainty that can affect the EV load during deployment. The results demonstrate how the grid remains stable under the LA attacks that would otherwise lead to serious instabilities., Comment: Accepted for publication in Applied Energy

In a recent work arXiv:2201.07655v2 we showed that there is a constant $\lambda >0$ such that it is possible to efficiently classically simulate a quantum system in which (i) qudits are placed on the nodes of a graph, (ii) each qudit undergoes at most $D$ diagonal gates, (iii) each qudit is destructively measured in the computational basis or bases unbiased to it, and (iv) each qudit is initialised within $\lambda^{-D}$ of a diagonal state according to a particular distance measure. In this work we explicitly compute $\lambda$ for any two qubit diagonal gate, thereby extending the computation of arXiv:2201.07655v2 beyond CZ gates. For any finite degree graph this allows us to describe a two parameter family of pure entangled quantum states (or three parameter family of thermal states) which have a non-trivial classically efficiently simulatable "phase" for the permitted measurements, even though other values of the parameters may enable ideal cluster state quantum computation. The main the technical tool involves considering separability in terms of "cylindrical" sets of operators. We also consider whether a different choice of set can strengthen the algorithm, and prove that they are optimal among a broad class of sets, but also show numerically that outside this class there are choices that can increase the size of the classically efficient regime., Comment: 12 pages, 3 figures