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We provide a solution for decoherence in spatial superpositions due to scattering/collision with air molecules. This result reproduces the short- and long-wavelength limits known in the literature. We compare the decoherence rate with several existing interpolations in the literature and evaluate the decoherence rate and experimental parameters when creating macroscopic quantum spatial superpositions (i.e., micron-size spheres). Finally, we consider the decoherence rate's time dependence while creating and closing the spatial superposition in an interferometer setup., Comment: 4 figures, 1 table

In Group Testing, the objective is to identify K defective items out of N, K<

In this paper, we study the data-dependent convergence and generalization behavior of gradient methods for neural networks with smooth activation. Our first result is a novel bound on the excess risk of deep networks trained by the logistic loss, via an alogirthmic stability analysis. Compared to previous works, our results improve upon the shortcomings of the well-established Rademacher complexity-based bounds. Importantly, the bounds we derive in this paper are tighter, hold even for neural networks of small width, do not scale unfavorably with width, are algorithm-dependent, and consequently capture the role of initialization on the sample complexity of gradient descent for deep nets. Specialized to noiseless data separable with margin $\gamma$ by neural tangent kernel (NTK) features of a network of width $\Omega(\poly(\log(n)))$, we show the test-error rate to be $e^{O(L)}/{\gamma^2 n}$, where $n$ is the training set size and $L$ denotes the number of hidden layers. This is an improvement in the test loss bound compared to previous works while maintaining the poly-logarithmic width conditions. We further investigate excess risk bounds for deep nets trained with noisy data, establishing that under a polynomial condition on the network width, gradient descent can achieve the optimal excess risk. Finally, we show that a large step-size significantly improves upon the NTK regime's results in classifying the XOR distribution. In particular, we show for a one-hidden-layer neural network of constant width $m$ with quadratic activation and standard Gaussian initialization that mini-batch SGD with linear sample complexity and with a large step-size $\eta=m$ reaches the perfect test accuracy after only $\ceil{\log(d)}$ iterations, where $d$ is the data dimension.

This paper presents a method for detecting and estimating vehicle speeds using PlanetScope SuperDove satellite imagery, offering a scalable solution for global vehicle traffic monitoring. Conventional methods such as stationary sensors and mobile systems like UAVs are limited in coverage and constrained by high costs and legal restrictions. Satellite-based approaches provide broad spatial coverage but face challenges, including high costs, low frame rates, and difficulty detecting small vehicles in high-resolution imagery. We propose a Keypoint R-CNN model to track vehicle trajectories across RGB bands, leveraging band timing differences to estimate speed. Validation is performed using drone footage and GPS data covering highways in Germany and Poland. Our model achieved a Mean Average Precision of 0.53 and velocity estimation errors of approximately 3.4 m/s compared to GPS data. Results from drone comparison reveal underestimations, with average speeds of 112.85 km/h for satellite data versus 131.83 km/h from drone footage. While challenges remain with high-speed accuracy, this approach demonstrates the potential for scalable, daily traffic monitoring across vast areas, providing valuable insights into global traffic dynamics.

Standard multi-agent reinforcement learning (MARL) algorithms are vulnerable to sim-to-real gaps. To address this, distributionally robust Markov games (RMGs) have been proposed to enhance robustness in MARL by optimizing the worst-case performance when game dynamics shift within a prescribed uncertainty set. Solving RMGs remains under-explored, from problem formulation to the development of sample-efficient algorithms. A notorious yet open challenge is if RMGs can escape the curse of multiagency, where the sample complexity scales exponentially with the number of agents. In this work, we propose a natural class of RMGs where the uncertainty set of each agent is shaped by both the environment and other agents' strategies in a best-response manner. We first establish the well-posedness of these RMGs by proving the existence of game-theoretic solutions such as robust Nash equilibria and coarse correlated equilibria (CCE). Assuming access to a generative model, we then introduce a sample-efficient algorithm for learning the CCE whose sample complexity scales polynomially with all relevant parameters. To the best of our knowledge, this is the first algorithm to break the curse of multiagency for RMGs.

Recovering the underlying clustering of a set $U$ of $n$ points by asking pair-wise same-cluster queries has garnered significant interest in the last decade. Given a query $S \subset U$, $|S|=2$, the oracle returns yes if the points are in the same cluster and no otherwise. For adaptive algorithms with pair-wise queries, the number of required queries is known to be $\Theta(nk)$, where $k$ is the number of clusters. However, non-adaptive schemes require $\Omega(n^2)$ queries, which matches the trivial $O(n^2)$ upper bound attained by querying every pair of points. To break the quadratic barrier for non-adaptive queries, we study a generalization of this problem to subset queries for $|S|>2$, where the oracle returns the number of clusters intersecting $S$. Allowing for subset queries of unbounded size, $O(n)$ queries is possible with an adaptive scheme (Chakrabarty-Liao, 2024). However, the realm of non-adaptive algorithms is completely unknown. In this paper, we give the first non-adaptive algorithms for clustering with subset queries. Our main result is a non-adaptive algorithm making $O(n \log k \cdot (\log k + \log\log n)^2)$ queries, which improves to $O(n \log \log n)$ when $k$ is a constant. We also consider algorithms with a restricted query size of at most $s$. In this setting we prove that $\Omega(\max(n^2/s^2,n))$ queries are necessary and obtain algorithms making $\tilde{O}(n^2k/s^2)$ queries for any $s \leq \sqrt{n}$ and $\tilde{O}(n^2/s)$ queries for any $s \leq n$. We also consider the natural special case when the clusters are balanced, obtaining non-adaptive algorithms which make $O(n \log k) + \tilde{O}(k)$ and $O(n\log^2 k)$ queries. Finally, allowing two rounds of adaptivity, we give an algorithm making $O(n \log k)$ queries in the general case and $O(n \log \log k)$ queries when the clusters are balanced.

In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix games are based on the smoothed best-response dynamics, while the learning dynamics for stochastic games build upon those for matrix games, with additional incorporation of the minimax value iteration. To our knowledge, our theoretical results present the first finite-sample analysis of such learning dynamics with last-iterate guarantees. In the matrix game setting, the results imply a sample complexity of $O(\epsilon^{-1})$ to find the Nash distribution and a sample complexity of $O(\epsilon^{-8})$ to find a Nash equilibrium. In the stochastic game setting, the results also imply a sample complexity of $O(\epsilon^{-8})$ to find a Nash equilibrium. To establish these results, the main challenge is to handle stochastic approximation algorithms with multiple sets of coupled and stochastic iterates that evolve on (possibly) different time scales. To overcome this challenge, we developed a coupled Lyapunov-based approach, which may be of independent interest to the broader community studying the convergence behavior of stochastic approximation algorithms., Comment: A preliminary version [arXiv:2303.03100] of this paper, with a subset of the results that are presented here, was presented at NeurIPS 2023

This article focuses on the study of zero-sum invariants of finite non-abelian groups. We address two main problems: the first centers on the ordered Davenport constant and the second on Gao's constant. We establish a connection between the ordered Davenport constant and the small Davenport constant for a finite non-abelian group of even order, which in turn gives a relation with the Noether number. Additionally, we confirm a conjecture of Gao and Li for a non-abelian group of order $2p^{\alpha}$, where $p$ is a prime. Furthermore, we prove a conjecture that connects the ordered Davenport constant to the Loewy length for certain classes of finite $2$-groups., Comment: 15 pages

Creating macroscopic spatial superposition states is crucial for investigating matter-wave interferometry and advancing quantum sensor technology. Currently, two potential methods exist to achieve this objective. The first involves using inverted harmonic potential (IHP) to spatially delocalize quantum states through coherent inflation [1]. The second method employs a spin-dependent force to separate two massive wave packets spatially [2]. The disadvantage of the former method is the slow initial coherent inflation, while the latter is hindered by the diamagnetism of spin-embedded nanocrystals, which suppresses spatial separation. In this study, we integrate two methods: first, we use the spin-dependent force to generate initial spatial separation, and second, we use IHP to achieve coherent inflating trajectories of the wavepackets. This approach enables the attainment of massive large spatial superposition in minimal time. For instance, a spatial superposition with a mass of $10^{-15}$ kg and a size of 50 $\mu$m is realized in $0.1$ seconds. We also calculate the evolution of wave packets in both harmonic potential (HP) and IHP using path integral approach., Comment: 14 pages, 6 figures

Creating macroscopic spatial quantum superposition with a nanoparticle has a multitude of applications, ranging from testing the foundations of quantum mechanics, matter-wave interferometer for detecting gravitational waves and probing the electromagnetic vacuum, dark matter detection and quantum sensors to testing the quantum nature of gravity in a lab. In this paper, we investigate the role of rotation in a matter-wave interferometer, where we show that imparting angular momentum along the direction of a defect, such as one present in the nitrogen-vacancy centre of a nanodiamond can cause an enhancement in spin contrast for a wide-ranging value of the angular momentum, e.g. $10^{3}-10^{6}$~Hz for a mass of order $10^{-14}-10^{-17}$ Kg nanodiamond. Furthermore, the imparted angular momentum can enhance the spatial superposition by almost a factor of two and possibly average out any potential permanent dipoles in the nanodiamond., Comment: 12pages, 8 figures

In this work, we have studied how incorporating viscous fluids leads to exact bounce cosmological solutions in general relativity (GR) framework. Specifically, we propose a novel parameterization of bulk viscosity coefficient of the form $\zeta = \zeta_0 (t-t_0)^{-2n} H$, where $\zeta_0$, $n$ being some positive constants and $t_0$ is the bounce epoch. We investigate how this form of bulk viscosity may assist in explaining the early universe's behaviour, with a particular focus on non-singular bounce scenario by studying the various energy conditions and other related cosmological observables and how the model parameters affect the evolution of the Universe. We demonstrate that the NEC and SEC violation occurs at the bounce point while DEC is satisfied. Finally, we carried out a stability check based on linear order perturbation to the Hubble parameter. We found that the perturbation vanishes asymptotically at later times, which indicates a stable behaviour of the bounce scenario, Comment: 8 figures, 2 tables, Accepted for publication in Int. J. Geom. Methods. Mod. Phys. arXiv admin note: text overlap with arXiv:2208.03171 by other authors

For a finite group $G,$ $D(G)$ is defined as the least positive integer $k$ such that for every sequence $S=g_1 g_2\cdots g_k$ of length $k$ over $G$, there exist $1 \le i_1 < i_2 <\cdots < i_m \le k $ such that $\prod_{j=1}^{m} g_{i_{\sigma(j)}}=1$ holds for $\sigma = id,$ identity element of $S_m.$ For a finite abelian group, this group invariant, known as the Davenport constant, is crucial in the theory of non-unique factorization domains. The precise value of this invariant, even for a finite abelian group of rank greater than $2$, is not known yet. In 1977, Olson and White first worked with this invariant for finite non-abelian groups. After that in 2004, Dimitrov dealt with it, where he proved that $D(G)\leq L(G)$ for a finite $p$-group $G$, where $p$ is a prime and $L(G)$ is the Loewy length of $\mathbb{F}_pG.$ He conjectured that equality holds for all finite $p$-groups. In this article, we compute $D(G)$ for a certain subclass of $2$-generated finite $p$-groups of nilpotency class two and show that the conjecture is true by determining the precise value of the Loewy length of $\mathbb{F}_pG.$ We also evaluate $D(G)$ for finite dicyclic, semi-dihedral and some other groups.

The manipulation of individual charged particles has been deeply explored in physics's theoretical and experimental domains during the past decades. It is the pillar of several existing devices used for metrology and sensing and is a promising platform for realizing future technologies, such as quantum computers. It is also known that in the relativistic regime, interactions between charged particles become affected by post-Coulombian corrections, with the dominant couplings encoded in the Darwin Hamiltonian. The Darwin term has been extensively studied in atomic physics, where the interaction range is confined to the sub-angstrom scale. Still, there is a lack of understanding about whether (and when) Darwin's contributions are relevant at larger scales. In this paper, we explore the effects of these corrections in a system of two harmonically trapped electrons, where we look into the behaviour of quantum entanglement present in the static and dynamical regimes. We explore the parameter space of the developed model and seek frequencies, distances, and squeezing parameters for which relativistic effects become relevant for the generation of entanglement., Comment: 12 pages, 3 figures

There has been strong interest recently in the so-called Cooper pair density wave, subsequent to the proposition that such a state occurs in the hole-doped cuprate superconductors. As of now there is no convincing demonstration of such a state in the cuprate theoretical literature. We present here a brief but complete review of our theoretical and computational work on the paired-electron crystal (PEC), which has been also experimentally seen in the insulating phase proximate to superconductivity (SC) in organic charge-transfer solid (CTS) superconductors. Within our theory, SC in the CTS does indeed evolve from the PEC. A crucial requirement for the finding of the PEC is that the proper carrier density of one charge carrier per two sites is taken into consideration at the outset. Following the discussion of CTS superconductors, we briefly discuss how the theory can be extended to understand the phase diagram of the cuprate superconductors that has remained mysterious after nearly four decades of the discovery of SC in this family., Comment: To appear in special issue of Chaos

This article focuses on training work carried out in artificial intelligence (AI) at the National Center for Supercomputing Applications (NCSA) at the University of Illinois Urbana-Champaign via a research experience for undergraduates (REU) program named FoDOMMaT. It also describes why we are interested in AI, and concludes by discussing what we've learned from running this program and its predecessor over six years.

A significant roadblock to the development of principled multi-agent reinforcement learning is the fact that desired solution concepts like Nash equilibria may be intractable to compute. To overcome this obstacle, we take inspiration from behavioral economics and show that -- by imbuing agents with important features of human decision-making like risk aversion and bounded rationality -- a class of risk-averse quantal response equilibria (RQE) become tractable to compute in all $n$-player matrix and finite-horizon Markov games. In particular, we show that they emerge as the endpoint of no-regret learning in suitably adjusted versions of the games. Crucially, the class of computationally tractable RQE is independent of the underlying game structure and only depends on agents' degree of risk-aversion and bounded rationality. To validate the richness of this class of solution concepts we show that it captures peoples' patterns of play in a number of 2-player matrix games previously studied in experimental economics. Furthermore, we give a first analysis of the sample complexity of computing these equilibria in finite-horizon Markov games when one has access to a generative model and validate our findings on a simple multi-agent reinforcement learning benchmark., Comment: preprint of multi-agent RL with risk-averse equilibria

We study the primordial spectra and the gravitational-wave background (GWB) of three models of semi-classical, quantum or string gravity where the big bang is replaced by a bounce and the primordial tensor spectrum is blue: ekpyrotic universe with fast-rolling Galileons, string-gas cosmology with Atick-Witten conjecture and pre-big-bang cosmology. We find that the ekpyrotic scenario with Galileons does not produce a GWB amplitude detectable by present or third-generation interferometers, while the Atick-Witten-based string-gas model is ruled out in its present form for violating the big-bang-nucleosynthesis bound, contrary to the original string-gas scenario. In contrast, the GWB of the pre-big-bang scenario falls within the sensitivity window of both LISA and Einstein Telescope, where it takes the form of a single or a broken power law depending on the choice of parameters. The latter will be tightly constrained by both detectors., Comment: 1+36 pages, 4 figures. v2: Einstein Telescope sensitivity curve updated, several parts clarified, results unchanged, references added

We study transfer learning for estimation in latent variable network models. In our setting, the conditional edge probability matrices given the latent variables are represented by $P$ for the source and $Q$ for the target. We wish to estimate $Q$ given two kinds of data: (1) edge data from a subgraph induced by an $o(1)$ fraction of the nodes of $Q$, and (2) edge data from all of $P$. If the source $P$ has no relation to the target $Q$, the estimation error must be $\Omega(1)$. However, we show that if the latent variables are shared, then vanishing error is possible. We give an efficient algorithm that utilizes the ordering of a suitably defined graph distance. Our algorithm achieves $o(1)$ error and does not assume a parametric form on the source or target networks. Next, for the specific case of Stochastic Block Models we prove a minimax lower bound and show that a simple algorithm achieves this rate. Finally, we empirically demonstrate our algorithm's use on real-world and simulated graph transfer problems.

Ru$_{2-x}$Fe$_x$CrSi ( 0 $<$ x $<$1) system is theoretically predicted to be one of the very few known examples of robust half-metallic ferromagnet with 100\% spin polarization. Since Cr is considered to be the main contributor to magnetism, the Fe/Ru substitution is not expected to disturb its magnetic properties any significantly, and hence all Fe-containing members of the series are predicted to follow Slater-Pauling rule with a saturation magnetic moment of 2 ${\mu_B}$/f.u. However, contrarily to the theoretical expectations, some experiments rather show a linear variation of the saturation magnetization and Curie temperature with Fe (\textit{x}) substitution. The equiatomic member FeRuCrSi of this family is also considered as a technologically important material, where the band structure calculations suggest the material to be spin gapless semiconductor. Through our in-depth structural analysis of FeRuCrSi using X-ray diffraction, extended X-ray absorption fine structure and $^{57}$Fe M\"{o}ssbauer spectrometry, we found a random disorder between Fe and Ru sites, while the magnetic moment in this system is actually contributed by Fe atoms, questioning the very basic foundation of the half-metallic character proposed by all theoretical calculations on Ru$_{2-x}$Fe$_x$CrSi series. Our M\"{o}ssbauer result also envisions a rather rare scenario where the main physical properties are intricately correlated to the chemistry of the material in the form of random atomic disorder on a localised scale.

The delicate nature of the half-metallic ferromagnetic (HMF) property in Heusler alloys is often compromised by inherent structural disorder within the systems. Fe2VSi is a prime example, where such disorder prevents the realization of the theoretically proposed HMF state as the anti-site disorder leads to the formation of two anti-parallel magnetic lattices resulting in antiferromagnetic order. In this study, we propose an innovative and simple strategy to prevent this atomic disorder by replacing 50% of the magnetic element Fe by a large, isoelectronic, non-magnetic element, Ru. In this way, one of the magnetic sublattices of the antiferromagnetic lattice ceases to order while ferromagnetic order is restored, an essential criterion for exhibiting HMF properties. Through various experimental measurements and theoretical calculations, we have shown that such partial replacement of Fe by Ru prevents the cross-site substitution of V/Si sites and the system regains its ferromagnetic order. Our theoretical calculations suggest that a perfect structural arrangement in Fe and Ru would have restored the HMF property in FeRuVSi. However, the local atomic disorder of Fe and Ru was found to decrease the spin polarization value. The present work sheds light on the complex interplay between structural disorder and magnetic properties in Heusler alloys and provides insights for future design strategies in the pursuit of robust half-metallic ferromagnets.

Mixed linear regression is a well-studied problem in parametric statistics and machine learning. Given a set of samples, tuples of covariates and labels, the task of mixed linear regression is to find a small list of linear relationships that best fit the samples. Usually it is assumed that the label is generated stochastically by randomly selecting one of two or more linear functions, applying this chosen function to the covariates, and potentially introducing noise to the result. In that situation, the objective is to estimate the ground-truth linear functions up to some parameter error. The popular expectation maximization (EM) and alternating minimization (AM) algorithms have been previously analyzed for this. In this paper, we consider the more general problem of agnostic learning of mixed linear regression from samples, without such generative models. In particular, we show that the AM and EM algorithms, under standard conditions of separability and good initialization, lead to agnostic learning in mixed linear regression by converging to the population loss minimizers, for suitably defined loss functions. In some sense, this shows the strength of AM and EM algorithms that converges to ``optimal solutions'' even in the absence of realizable generative models., Comment: To appear in ICML 2024

The detrimental effects of air pollutants on human health have prompted increasing concerns regarding indoor air quality (IAQ). The emergence of digital health interventions and citizen science initiatives has provided new avenues for raising awareness, improving IAQ, and promoting behavioural changes. The Technology Acceptance Model (TAM) offers a theoretical framework to understand user acceptance and adoption of IAQ technology. This paper presents a case study using the COM-B model and Internet of Things (IoT) technology to design a human-centred digital visualisation platform, leading to behavioural changes and improved IAQ. The study also investigates users' acceptance and adoption of the technology, focusing on their experiences, expectations, and the impact on IAQ. Integrating IAQ sensing, digital health-related interventions, citizen science, and the TAM model offers opportunities to address IAQ challenges, enhance public health, and foster sustainable indoor environments. The analytical results show that factors such as human behaviour, indoor activities, and awareness play crucial roles in shaping IAQ., Comment: 10 pages

The robust $\phi$-regularized Markov Decision Process (RRMDP) framework focuses on designing control policies that are robust against parameter uncertainties due to mismatches between the simulator (nominal) model and real-world settings. This work makes two important contributions. First, we propose a model-free algorithm called Robust $\phi$-regularized fitted Q-iteration (RPQ) for learning an $\epsilon$-optimal robust policy that uses only the historical data collected by rolling out a behavior policy (with robust exploratory requirement) on the nominal model. To the best of our knowledge, we provide the first unified analysis for a class of $\phi$-divergences achieving robust optimal policies in high-dimensional systems with general function approximation. Second, we introduce the hybrid robust $\phi$-regularized reinforcement learning framework to learn an optimal robust policy using both historical data and online sampling. Towards this framework, we propose a model-free algorithm called Hybrid robust Total-variation-regularized Q-iteration (HyTQ: pronounced height-Q). To the best of our knowledge, we provide the first improved out-of-data-distribution assumption in large-scale problems with general function approximation under the hybrid robust $\phi$-regularized reinforcement learning framework. Finally, we provide theoretical guarantees on the performance of the learned policies of our algorithms on systems with arbitrary large state space., Comment: To appear in the proceedings of the International Conference on Machine Learning (ICML) 2024

The salient feature of both classical and quantum gravity is its universal and attractive character. However, less is known about the behaviour and build-up of quantum correlations when quantum systems interact via graviton exchange. In this work, we show that quantum correlations can remain strongly suppressed for certain choices of parameters even when considering two adjacent quantum systems in delocalized states. Using the framework of linearized quantum gravity with post-Newtonian contributions, we find that there are special values of delocalization where gravitationally induced entanglement drops to negligible values, albeit non-vanishing. We find a pronounced cancellation point far from the Planck scale, where the system tends towards classicalization. In addition, we show that quantum correlations begin to reemerge for large and tiny delocalizations due to Heisenberg's uncertainty principle and the universal coupling of gravity to the energy-momentum tensor, forming a valley of gravitational entanglement., Comment: 9 pages, 3 figures

To overcome the sim-to-real gap in reinforcement learning (RL), learned policies must maintain robustness against environmental uncertainties. While robust RL has been widely studied in single-agent regimes, in multi-agent environments, the problem remains understudied -- despite the fact that the problems posed by environmental uncertainties are often exacerbated by strategic interactions. This work focuses on learning in distributionally robust Markov games (RMGs), a robust variant of standard Markov games, wherein each agent aims to learn a policy that maximizes its own worst-case performance when the deployed environment deviates within its own prescribed uncertainty set. This results in a set of robust equilibrium strategies for all agents that align with classic notions of game-theoretic equilibria. Assuming a non-adaptive sampling mechanism from a generative model, we propose a sample-efficient model-based algorithm (DRNVI) with finite-sample complexity guarantees for learning robust variants of various notions of game-theoretic equilibria. We also establish an information-theoretic lower bound for solving RMGs, which confirms the near-optimal sample complexity of DRNVI with respect to problem-dependent factors such as the size of the state space, the target accuracy, and the horizon length., Comment: Accepted by International Conference on Machine Learning, 2024

Matter-wave interferometry is susceptible to non-inertial noise sources, which can induce dephasing and a resulting loss of interferometric visibility. Here, we focus on inertial torsion noise (ITN), which arises from the rotational motion of the experimental apparatus suspended by a thin wire and subject to random external torques. We provide analytical expressions for the ITN noise starting from Langevin equations describing the experimental box in a thermal environment which can then be used together with the transfer function to obtain the dephasing factor. We verify the theoretical modelling and the validity of the approximations using Monte Carlo simulations obtaining good agreement between theory and numerics. As an application we estimate the size of the effects for the next-generation of interferometery experiments with femtogram particles, which could be used as the building block for entanglement-based tests of the quantum nature of gravity. We find that the ambient gas is a weak source of ITN, posing mild restrictions on the ambient pressure and temperature, and conclude with a discussion about the general ITN constrains by assuming a Langevin equation parameterized by three phenomenological parameters., Comment: 15 pages, 11 figures

A large proportion of jobs submitted to modern computing clusters and data centers are parallelizable and capable of running on a flexible number of computing cores or servers. Although allocating more servers to such a job results in a higher speed-up in the job's execution, it reduces the number of servers available to other jobs, which in the worst case, can result in an incoming job not finding any available server to run immediately upon arrival. Hence, a key question to address is: how to optimally allocate servers to jobs such that (i) the average execution time across jobs is minimized and (ii) almost all jobs find at least one server immediately upon arrival. To address this question, we consider a system with $n$ servers, where jobs are parallelizable up to $d^{(n)}$ servers and the speed-up function of jobs is concave and increasing. Jobs not finding any available servers upon entry are blocked and lost. We propose a simple server allocation scheme that achieves the minimum average execution time of accepted jobs while ensuring that the blocking probability of jobs vanishes as the system becomes large ($n \to \infty$). This result is established for various traffic conditions as well as for heterogeneous workloads. To prove our result, we employ Stein's method which also yields non-asymptotic bounds on the blocking probability and the mean execution time. Furthermore, our simulations show that the performance of the scheme is insensitive to the distribution of job execution times.

Designing tests to evaluate if a given autonomous system satisfies complex specifications is challenging due to the complexity of these systems. This work proposes a flow-based approach for reactive test synthesis from temporal logic specifications, enabling the synthesis of test environments consisting of static and reactive obstacles and dynamic test agents. The temporal logic specifications describe desired test behavior, including system requirements as well as a test objective that is not revealed to the system. The synthesized test strategy places restrictions on system actions in reaction to the system state. The tests are minimally restrictive and accomplish the test objective while ensuring realizability of the system's objective without aiding it (semi-cooperative setting). Automata theory and flow networks are leveraged to formulate a mixed-integer linear program (MILP) to synthesize the test strategy. For a dynamic test agent, the agent strategy is synthesized for a GR(1) specification constructed from the solution of the MILP. If the specification is unrealizable by the dynamics of the test agent, a counterexample-guided approach is used to resolve the MILP until a strategy is found. This flow-based, reactive test synthesis is conducted offline and is agnostic to the system controller. Finally, the resulting test strategy is demonstrated in simulation and experimentally on a pair of quadrupedal robots for a variety of specifications., Comment: Manuscript

Utilizing the Stern-Gerlach apparatus to create matter-wave superposition states is a long-sought-after goal, not only due to its potential applications in the quantum realm but also because of its fundamental implications for studying the quantum properties of gravity. The main challenge in creating a macroscopic quantum interferometer arises from the loss of coherence, primarily through two channels. One channel involves strong coupling with the environment for macroscopic matter, leading to decoherence. The other channel relates to the precision of wave packet overlap, which can occur due to external and internal fluctuations of various sources. The latter introduces a unique challenge for larger-scale masses by perturbing the centre of mass motion of the macroscopic object. Here, we study a particular challenge, namely, the issue of internal degrees of freedom, specifically phonon fluctuations and contrast reduction. This work will investigate the contrast reduction caused by spin-magnetic field and diamagnetic interactions at the phonon occupation level in the quantum gravity-induced entanglement of masses (QGEM) protocol configuration.

This paper presents a closed-form notion of controllability and observability for systems with communication delays, actuation delays, and locality constraints. The formulation reduces to classical notions of controllability and observability in the unconstrained setting. As a consequence of our formulation, we show that the addition of locality and communication constraints may not affect the controllability and observability of the system, and we provide an efficient sufficient condition under which this phenomenon occurs. This contrasts with actuation and sensing delays, which cause a gradual loss of controllability and observability as the delays increase. We illustrate our results using linearized swing equations for the power grid, showing how actuation delay and locality constraints affect controllability.

In this paper, we present an online reinforcement learning algorithm for constrained Markov decision processes with a safety constraint. Despite the necessary attention of the scientific community, considering stochastic stopping time, the problem of learning optimal policy without violating safety constraints during the learning phase is yet to be addressed. To this end, we propose an algorithm based on linear programming that does not require a process model. We show that the learned policy is safe with high confidence. We also propose a method to compute a safe baseline policy, which is central in developing algorithms that do not violate the safety constraints. Finally, we provide simulation results to show the efficacy of the proposed algorithm. Further, we demonstrate that efficient exploration can be achieved by defining a subset of the state-space called proxy set.

In view to scrutinize the idea that nonlocal modifications of General Relativity could dynamically address the dark energy problem, we investigate the evolution of the Universe at infrared scales as an Infinite Derivative Gravity model of the Ricci scalar, without introducing the cosmological constant $\Lambda$ or any scalar field. The accelerated expansion of the late Universe is shown to be compatible with the emergence of nonlocal gravitational effects at sufficiently low energies. A technique for circumventing the mathematical complexity of the nonlocal cosmological equations is developed and, after drawing a connection with the Starobinsky gravity, verifiable predictions are considered, like a possible decreasing in the strength of the effective gravitational constant. In conclusion, the emergence of nonlocal gravity corrections at given scales could be an efficient mechanism to address the dark energy problem., Comment: 16 pages, 2 figures, accepted for publication in Physics of the Dark Universe

In the context of ghost-free infinite derivative gravity we consider the single graviton exchange either between two spinless particles or between a spinless particle and a photon. To this end, we compute the gravitational potential for both cases and derive the quantum correction that arises at the linearized level. In the local theory it is well-known that such a correction is in the form of a Dirac delta function. Here we show that, for the nonlocal theory and in contrast to the local theory, the quantum correction is smeared out and takes on non-zero values for a non-zero separation between the two particles., Comment: 6 pages, no figures

In this paper, we study the implications of conformal invariance in momentum space for correlation functions in quantum mechanics. We find that three point functions of arbitrary operators can be written in terms of the $_2 F_1$ hypergeometric function. We then show that generic four-point functions can be expressed in terms of Appell's generalized hypergeometric function $F_2$ with one undetermined parameter that plays the role of the conformal cross ratio in momentum space. We also construct momentum space conformal partial waves, which we compare with the Appell $F_2$ representation. We test our expressions against free theory and DFF model correlators, finding an exact agreement. We then analyze five, six, and all higher point functions. We find, quite remarkably, that $n$-point functions can be expressed in terms of the Lauricella generalized hypergeometric function, $E_A$, with $n-3$ undetermined parameters, which is in one-to-one correspondence with the number of conformal cross ratios. This analysis provides the first instance of a closed form for generic momentum space conformal correlators in contrast to the situation in higher dimensions. Further, we show that the existence of multiple solutions to the momentum space can be attributed to the Fourier transforms of the various possible time orderings. Finally, we extend our analysis to theories with $\mathcal{N}=1,2$ supersymmetry, where we find that the constraints due to the superconformal ward identities are identical to identities involving hypergeometric functions., Comment: 28+6 pages

For a finite abelian group $G,$ the Davenport Constant, denoted by $D(G)$, is defined to be the least positive integer $k$ such that every sequence of length at least $k$ has a non-trivial zero-sum subsequence. A long-standing conjecture is that the Davenport constant of a finite abelian group $G =C_{n_1}\times\cdots\times C_{n_d}$ of rank $d \in \mathbb{N}$ is $1+\displaystyle\sum_{i=1}^d (n_i-1) $. This conjecture is false in general, but it remains to know for which groups it is true. In this paper, we consider groups of the form $G = (C_p)^{d-1} \times C_{pq},$ where $p$ is a prime and $q\in \mathbb{N}$ and provide sufficient condition when the conjecture holds true., Comment: 11 pages

The deployment of ever-larger machine learning models reflects a growing consensus that the more expressive the model class one optimizes over$\unicode{x2013}$and the more data one has access to$\unicode{x2013}$the more one can improve performance. As models get deployed in a variety of real-world scenarios, they inevitably face strategic environments. In this work, we consider the natural question of how the interplay of models and strategic interactions affects the relationship between performance at equilibrium and the expressivity of model classes. We find that strategic interactions can break the conventional view$\unicode{x2013}$meaning that performance does not necessarily monotonically improve as model classes get larger or more expressive (even with infinite data). We show the implications of this result in several contexts including strategic regression, strategic classification, and multi-agent reinforcement learning. In particular, we show that each of these settings admits a Braess' paradox-like phenomenon in which optimizing over less expressive model classes allows one to achieve strictly better equilibrium outcomes. Motivated by these examples, we then propose a new paradigm for model selection in games wherein an agent seeks to choose amongst different model classes to use as their action set in a game., Comment: Reworded title, fixed typos and changed organization from previous version

In supervised machine learning, feature selection plays a very important role by potentially enhancing explainability and performance as measured by computing time and accuracy-related metrics. In this paper, we investigate a method for feature selection based on the well-known L1 and L2 regularization strategies associated with logistic regression (LR). It is well known that the learned coefficients, which serve as weights, can be used to rank the features. Our approach is to synthesize the findings of L1 and L2 regularization. For our experiment, we chose the CIC-IDS2018 dataset owing partly to its size and also to the existence of two problematic classes that are hard to separate. We report first with the exclusion of one of them and then with its inclusion. We ranked features first with L1 and then with L2, and then compared logistic regression with L1 (LR+L1) against that with L2 (LR+L2) by varying the sizes of the feature sets for each of the two rankings. We found no significant difference in accuracy between the two methods once the feature set is selected. We chose a synthesis, i.e., only those features that were present in both the sets obtained from L1 and that from L2, and experimented with it on more complex models like Decision Tree and Random Forest and observed that the accuracy was very close in spite of the small size of the feature set. Additionally, we also report on the standard metrics: accuracy, precision, recall, and f1-score.

We find the entanglement entropy of a subregion of the vacuum state in scalar quantum electrodynamics, working perturbatively to the 2-loops level. Doing so leads us to derive the Maxwell-Proca propagator in conical Euclidean space. The area law of entanglement entropy is recovered in both the massive and massless limits of the theory, as is expected. These results yield the renormalisation group flow of entanglement entropy, and we find that loop contributions suppress entanglement entropy. We highlight these results in the light of the renormalization group flow of couplings and correlators, which are increased in scalar quantum electrodynamics, so that the potential tension between the increase in correlations between two points of spacetime and the decrease in entanglement entropy between two regions of spacetime with energy is discussed. We indeed show that the vacuum of a subregion of spacetime purifies with energy in scalar quantum electrodynamics, which is related to the concept of screening., Comment: 10 pages, 1 figure

We showcase the digital quantum simulation of the action of a Hamiltonian that governs the interaction between a quantum mechanical oscillator and an optical field, generating quantum entanglement between them via gravitational effects. This is achieved by making use of a boson-qubit mapping protocol and a digital gate decomposition that allow us to run the simulations in the quantum computers available in the IBM Quantum platform. We present the obtained results for the fidelity of the experiment in two different quantum computers, after applying error mitigation and post-selection techniques. The achieved results correspond to fidelities over 90%, which indicates that we were able to perform a faithful digital quantum simulation of the interaction and therefore of the generation of quantum entanglement by gravitational means in optomechanical systems., Comment: 15 pages, 4 figures, typos corrected, results unaltered