The recent work arXiv:2407.17373 proposes a derivative-free consensus-based particle method that computes global solutions to nonconvex-nonconcave min-max problems and establishes global exponential convergence in the sense of the mean-field law. This paper aims to address the theoretical gaps in arXiv:2407.17373, specifically by providing a quantitative estimate of the mean-field limit with respect to the number of particles, as well as establishing the well-posedness of both the finite particle model and the corresponding mean-field dynamics.

In this paper, we prove that, for a residual set of $C^{k}$ connections defined on a smooth vector bundle $E \to M$, all eigenvalues of the connection Laplacian operator $\mathscr{L}$, acting on the space of sections of $E$, are simple. As an application, we prove that all eigenvalues of the Laplace-Beltrami operator on a compact $G$-principal bundle $P \to M$ are $G$-simple.

Atomic interactions play an important role in the properties of ultracold atomic gases. In single component bosonic systems, its effect is already present at the critical point for the Bose-Einstein condensate phase transition by shifting it to lower temperatures as a consequence of effective repulsion between the atoms. When considering atomic bosonic mixtures, interesting effects arise from the competition between intra- and interspecies interactions such as the miscible-immiscible phase transition and the particular case of self-bounded quantum droplets. In such a scenario, it is natural to expect that these interactions will also affect the critical point of each species composing the mixture. In this paper, we obtain analytical expressions for the critical temperature shift of the phase transition to a Bose-Einstein condensate in the presence of a second species. We treat differently the cases in with the second species is above or below its own critical temperature and apply the obtained relations to the case of a $^{23}$Na-$^{39}$K bosonic mixture which can be realized in current running experimental setups. Our findings can be easily extended to other atomic mixtures trapped by arbitrary conservative traps.

We consider subleading contributions to the three-nucleon force from tree-level diagrams involving a single-pion exchange and a contact interaction between two nucleons, which appear at fifth order in the chiral expansion. We show that the corresponding D-like three-nucleon potential depends on 16 low-energy constants, which need to be determined from few-body data. Assuming that their numerical values are governed by the intermediate Δ(1232) excitation mechanism, the considered three-nucleon force can be approximated using 4 low-energy constants that parametrize the short-range nucleon-nucleon to nucleon-Δ transition amplitude.

In this work we investigate the sociocultural values learned by large language models (LLMs). We introduce a novel open-access dataset, Sociocultural Statements, constructed from natural debate statements using a multi-step methodology. The dataset is synthetically labeled to enable the quantization of sociocultural norms and beliefs that LLMs exhibit in their responses to these statements, according to the Hofstede cultural dimensions. We verify the accuracy of synthetic labels using human quality control on a representative sample. We conduct a comparative analysis between two groups of LLMs developed in different countries (U.S. and China), and use as a comparative baseline patterns observed in human measurements. Using this new dataset and the analysis above, we found that culturally-distinct LLMs reflect the values and norms of the countries in which they were developed, highlighting their inability to adapt to the sociocultural backgrounds of their users.

Unimodal univariate distributions can be characterized as piecewise convex-concave cumulative distribution functions. In this note we transfer this shape constraint characterization to the quantile function. We show that this characterization comes with the upside that the quantile function of a unimodal distribution is always absolutely continuous and consequently unimodality is equivalent to the quasi-convexity of its Radon-Nikodym derivative, i.e., the quantile density. Our analysis is based on the theory of generalized inverses of non-decreasing functions and relies on a version of the inverse function rule for non-decreasing functions.

Numerical solution of partial differential equations (PDEs) plays a vital role in various fields of science and engineering. In recent years, deep neural networks (DNNs) have emerged as a powerful tool for solving PDEs, leveraging their approximation capabilities to handle complex domains and high-dimensional problems. Among these, operator learning has gained increasing attention by learning mappings between function spaces using DNNs. This paper proposes a novel approach, termed the Neural Evolutionary Kernel Method (NEKM), for solving a class of time-dependent partial differential equations (PDEs) via deep neural network (DNN)-based kernel representations. By integrating boundary integral techniques with operator learning, prior mathematical information of time-dependent partial differential equations (PDEs) is embedded into the design of neural network architectures for predicting their solutions, enhancing both computational efficiency and solution accuracy. Numerical experiments on the heat, wave, and Schrödinger equations demonstrate that the Neural Evolutionary Kernel Method (NEKM) achieves high accuracy and favorable computational efficiency. Furthermore, the operator learning framework inherently supports the simultaneous prediction of solutions to multiple PDEs with different coefficients, rendering its capability for solving random PDEs.

Genetic Algorithms (GA) are a powerful tool for stochastic optimisation and non-parametric symbolic regression, already widely used in cosmology. They are capable of reconstructing analytical functions directly from data points without introducing new physical models. A limitation of this approach is that while the reconstructed function is very efficient at reproducing the behaviour of the data points, non-observable quantities involving derivatives are particularly sensitive to stochasticity, hyperparameters, and to the choice of the best-fit function obtained by the GA, which implies the risk of the algorithm getting stuck in a local minimum. In this work we propose an update to the GA methodology for the reconstruction of analytical functions that involves computing a weighted average of an ensemble of GA configurations (\texttt{GAME}). We define the weights via a quantity that accounts for both the goodness-of-fit of the points and the smoothness of the resulting function. We also present a practical method to analytically estimate and correct the errors on the averaged function by combining a path-integral approach with an ensemble variance. We demonstrate the improvement offered by \texttt{GAME} methodology on a generic test function. We then apply the new methodology to a non-parametric reconstruction of the Hubble rate $H(z)$ using Cosmic Chronometers data and, assuming a flat Friedmann-Lemaître-Robertson-Walker background and General Relativity, we infer the corresponding dark energy equation of state $w(z)$. Through consistency tests, we show that current data produces results compatible with $Λ$CDM, and that Stage IV cosmology surveys will allow GA reinforced with \texttt{GAME} methodology to become an even more competitive tool for discriminating between different models.

We investigate a complex analogue of Spencer's Six Standard Deviations Theorem. Specifically, we propose the following conjecture: for any dimension $n \geq 2$, given vectors $a_1, \ldots, a_n \in \mathbb{C}^n$ satisfying $\|a_i\|_{\infty} \leq 1$ for each $i=1, \ldots, n$, there exists a vector $x \in \mathbb{C}^n$ with all coordinates of modulus one such that $|\langle x, a_i \rangle| \leq \sqrt{n}$ for every $i=1, \ldots, n$. The bound of $\sqrt{n}$ is sharp, as demonstrated by the row vectors of any complex $n \times n$ Hadamard matrix. Furthermore, if the conjecture holds in dimension $n$, it implies that the Banach--Mazur distance between the complex $\ell_1^n$ and $\ell_{\infty}^n$ spaces is equal to $\sqrt{n}$. We prove the conjecture for $n =2, 3$, thereby establishing also that $d_{BM}(\ell_1^n, \ell_{\infty}^n) = \sqrt{n}$ for these dimensions. Additionally, we propose a conjecture about the Banach--Mazur distances between complex $\ell_p^n$ spaces and we verify it for $n=2$. This leads to a complete determination of all possible Banach--Mazur distances between complex $\ell_p^2$ spaces.

We consider parametric linear programming problems with multiple objective functions depending linearly on some parameter. Both parametric (single-objective) linear programming and (non-parametric) multi-objective linear programming are well-researched topics. However, literature on the combination of both, parametric linear programming with multiple objectives, is scarce. This research gap encourages our work in this field. Our main focus is on biobjective linear programs with a single parameter. We establish a connection of this problem to non-parametric multi-objective problems. Using the so-called weight set decomposition, we are able to explain the behavior of parametric biobjective linear programs when the parameter value is variated. We investigate two special cases of parametric biobjective linear programs: In the first, there is only one parametric objective and, in the second, the parametric dependency is the same for both objectives. We prove that there is a one-to-one correspondence between the solution of the parametric program and the solution of the triobjective program using the weighted sum scalarization. We provide structural insights to the solution of the parametric biobjective linear program with respect to extreme weights of the weight set of the triobjective linear program and develop solution strategies for the parametric program.

Quench experiments where the flow passes from a fully turbulent state to a laminar state by an abrupt decrease in the flow Reynolds number ($Re$) have been extensively studied in the literature to quantify the turbulent-laminar transition process in wall-bounded flows. Measurements have been classically made using rheoscopic fluid visualisations, which make turbulent coherent structures easily identifiable, allowing for quantification of the evolution of a turbulent fraction -- the percentage of a given observation window where turbulence is deemed active by the presence of coherent structures, such as streamwise vortices called rolls, and modulations of the streamwise velocity fluctuations called streaks. Decay characteristic times of these structures have therefore been extensively measured. However, owing to the nature of visualization based techniques, only a single decay time is typically extracted, whereas measurements of the velocity field can reveal distinct decay times associated with different velocity or kinetic energy components. As a result, the physical meaning of the decay time inferred from visualization alone is not straightforward. The goal of the present paper is to perform such a comparison quantitatively, using particle image velocimetry (PIV) measurements and rheoscopic fluid visualisations in the same setup: a Couette-Poiseuille experiment. We observe via PIV different characteristic times of decay for streamwise (streaks) and spanwise (rolls) velocity fluctuations. We show that the characteristic time of decay of the turbulent fraction observed by visualisation is close to the decay of the streaks.

We presented the first high-precision, detailed photometric analysis of four W Ursae Majoris (W UMa)-type contact binaries, Linear 10772300, Linear 11150338, Linear 20372537 and DM Cir. In addition to ground-based multiband photometric observations, data from the Transiting Exoplanet Survey Satellite (TESS) were employed for the analysis of the DM Cir system. New ephemeris and linear fit to the O-C diagrams were derived using extracted times of minima and additional literature. The light curve modeling was performed using the PHysics Of Eclipsing BinariEs (PHOEBE) Python code and the BSN application, employing a Markov Chain Monte Carlo approach. In each systems, the two stellar components exhibited minimal temperature differences ($ΔT<150$ K), confirming efficient energy exchange within their common convective envelopes. Absolute parameters were estimated using the Gaia Data Release 3 (Gaia DR3) parallax and astrophysical equations. Based on effective temperatures and component masses, two systems were classified as W-subtype systems, while others belonged to the A-subtype. We computed the initial masses of the primary ($M_{1i}$) and secondary ($M_{2i}$) components for four target systems using a method based on the observational properties of overluminous secondary components. We found initial primary masses in the range 0.6-1.0$M_\odot$ and initial secondary masses in the range 0.9-1.7$M_\odot$ with mass loss $<1.0M_{\odot}$. We investigated the relative energy transfer rates ($U_{1}$ and $U_{2}$) and nuclear luminosities ($L_{10}$ and $L_{20}$) based on the physical parameters of 411 W UMa-type contact binaries, including the four systems analyzed in this study, through wide range of mass ratios. The results for all systems provided a comprehensive view of energy transfer behavior throughout different evolutionary stages of contact binaries.

We present new constraints on ultralight axion-like particles (ALPs) through multi-epoch measurements of differential birefringence induced due to a coupling ($g_{aγ}$) between the ALP and electromagnetic fields. Broadband polarimetric observations in the 2-8 GHz range of the gravitationally lensed system CLASS B1152+199 were carried out over five epochs spanning three months with a cadence of roughly 20 days, and the differential birefringence angle ($Δ\,θ_{a,{\rm lens}}$) between the lensed images were estimated. We also combined an archival observation that effectively increases the span to 9.5 yr to probe the effect of an oscillating ALP field imprinted as oscillating ${Δ\,θ_{a,{\rm lens}}}$ over time. Here we present a new technique for combining multi-epoch measurements of ${Δ\,θ_{a,{\rm lens}}}$ by considering the coherence of the ALP field, such that, ${Δ\,θ_{a,{\rm lens}}}$ over these observations are related. The time scale of coherence depends on the mass of the ALP field ($m_a$). With these new observations, we constrain $g_{aγ} \leq 9.0\times 10^{-12} \,\left( {ρ_{a,\text{em}}}/{20 \text{ GeV cm}^{-3}} \right)^{-1/2}\;\mathrm{GeV}^{-1}$ to $\leq 3.5\times 10^{-8} \,\left( {ρ_{a,\text{em}}}/{20 \text{ GeV cm}^{-3}} \right)^{-1/2}\;\mathrm{GeV}^{-1}$ for $m_a$ between $1.6\times 10^{-22}\;\mathrm{eV}$ and $3.8\times 10^{-18}\;\mathrm{eV}$, where $ρ_{a,{\rm em}}$ is the density of the ALP field at emission. This improves over the constraint provided by the CERN Axion Solar Telescope by up to an order of magnitude in the $m_a$ range $1.6\times 10^{-22}\;\mathrm{eV}$ to $3\times 10^{-21}$ eV.

Gallium antimonide (GaSb) is a key material for near- and mid-infrared photonics, enabling high-performance laser architectures and detectors. Design and simulation of such devices depend on accurate optical material data, especially the complex refractive index $n^*_{\text{GaSb}} = n_{\text{GaSb}} +ik_{\text{GaSb}}$, consisting of the real part $n_{\text{GaSb}}$ (refractive index) and the imaginary part $k_{\text{GaSb}}$ (extinction coefficient). However, GaSb refractive index values are based either on theoretical models, typically informed by legacy experimental data, or on experimental measurements without quantified uncertainties. This limits their reliability for state-of-the-art devices. Here, we present measurement results of $n^*_{\text{GaSb}}$ in the near- to mid-infrared range from \SIrange{1}{3.1}{\micro \metre} with a relative uncertainty <\num{7.8e-5} for $n_{\text{GaSb}}$, and <\num{2.0e-3} for $k_{\text{GaSb}}$. As a side result of our method, we also report $n_{\text{AlAsSb}}$ for aluminium arsenide antimonide ($\mathrm{AlAs_{0.08}Sb_{0.92}}$) with a relative uncertainty <\num{3.9e-4}. Our results are based on two complementary measurements on a GaSb/AlAsSb-based heteroepitaxial structure under controlled environmental conditions: photometric transmission and layer-thickness analysis by cross-sectional scanning electron microscopy. We simultaneously retrieve the refractive indices of the two materials by fitting a Sellmeier equation and a theoretical dispersion model by Djurišić \textit{et al.}~\cite{djurisic_modeling_2000}. The uncertainties of $n^*_{\text{GaSb}}$ and $n_{\text{AlAsSb}}$ are quantified using a Monte Carlo-based approach. Our results provide accurate complex refractive index values for GaSb, which are vital to advance photonics-related technologies in the near- and mid infrared spectral region.

In this paper, a subclass of bounded distributive lattices, that is, finitely disjunctive distributive lattices (FDD-lattices) have been introduced. Then we apply it to establish a Stone duality for Lawson compact algebraic L-domains. Furthermore, we develop a dual equivalence between the category of FDD-lattices with lattice homomorphisms and that of Lawson compact algebraic L-domains with spectral maps.

The interactions between chemical phase fields and structural defects play a key role in the properties of alloys. We illustrate the importance of these interactions in driven alloys, where defects are continuously being created, with particular focus on systems where radiation-induced segregation occurs. Specifically, we compare the microstructural evolution in undersaturated Ni-Si and Ni-Ge alloys during both 100 keV He and 2 MeV Ti irradiations. While the equilibrium phase diagrams of these systems are similar, and both systems show strong radiation-induced segregation, the evolving defect structures are remarkably different. Ni-Si reveals a high density of Frank loops, while Ni-Ge shows a complex array of dislocations. Moreover, a Ni3Ge precipitate shell is observed to coat He bubbles, while no segregation of Si is observed at such bubbles. We explain these differences in behaviors to solute drag by interstitial fluxes in Ni-Si vs solute drag by vacancy fluxes in Ni-Ge.

The fourth gravitational-wave transient catalog, GWTC-4.0, reports 153 binary black hole mergers with false-alarm rates $<1,\mathrm{yr}^{-1}$. Chirp masses are typically measured well, with the smallest fractional uncertainty being $2%$ at the $90%$ credible level. Spins, on the other hand, are poorly constrained: the median of the best-measured spin component of the population, the effective spin, is $χ_{\rm eff}=0.04$, with a typical $90%$ credible uncertainty of $Δχ_{\rm eff}=0.44$. The large majority -- $90%$ of the observed black holes -- are consistent with spin magnitudes $χ<0.57$ and are weakly aligned with the orbits. At $90%$ credibility, the peaks of the inferred posteriors for spin magnitude are found to lie in the range $0.01$--$0.23$. We show that this ``near-zero spins'' conclusion may be prior-driven, and that uniform-in-magnitude spin priors lead to under-exploration of the moderate-to-high spin region of parameter space. Adopting a physically agnostic prior that is uniform in spin-vector configuration space (i.e., spin states uniform within a unit sphere) yields similar constraints on $χ_{\rm eff}$, but substantially different spin-magnitude inferences than GWTC-4.0. The resulting shift in spins directly impacts tests of general relativity, constraints on near-extremal Kerr remnants, and astrophysical conclusions, including diagnostics of formation channels and hierarchical growth. In short, the data do not require vanishing spins -- the prior does, and accounting for this is essential for robust GR tests and population inferences.

We investigate an interacting Pais-Uhlenbeck oscillator with a Landau-Ginzburg type interaction term and analyse its classical dynamics from a geometric and numerical point of view. We show that the resulting fourth-order equation of motion admits a conformal bi-Hamiltonian formulation, possesses a non-trivial set of Lie symmetries and we demonstrate the existence of bounded and regular trajectories in representative parameter regimes. By establishing an explicit correspondence with an integrable generalised Hénon-Heiles system, we show that the interacting higher-derivative dynamics inherits the integrability properties of the latter. This connection allows us to construct a second conserved Hamiltonian, to clarify the geometric origin of separability, and to obtain explicit classical solutions in terms of elliptic functions. Our results provide a concrete example of an interacting higher-derivative system for which integrability and periodic classical solutions can be established in a fully explicit manner.

In this paper, we study certain properties of $\mathbb{Z}_2^n$-equivariant triangulations of small covers. We show that any $\mathbb{Z}_2^n$-equivariant triangulation of a small cover naturally induces a triangulation of the orbit space. Then, we explicitly construct the minimal $\mathbb{Z}_2^3$-equivariant triangulation of $\mathbb{RP}^3$, which contains $11$ vertices and prove that this is the unique $\mathbb{Z}_2^3$-equivariant triangulation of $\mathbb{RP}^3$ with $11$ vertices. For a finite group $G$, we give a method for constructing some $G$-equivariant triangulations of connected sums of manifolds from their respective $G$-equivariant triangulations. In particular, we construct a $\mathbb{Z}_2^3$-equivariant triangulation of $\mathbb{RP}^3 \# \mathbb{RP}^3$ with $17$ vertices, which is the best known yet. This triangulation of $\mathbb{RP}^3 \# \mathbb{RP}^3$ provides another minimal $g$-vector improving one of the result of Lutz in \cite{LS}. Moreover, we prove that a $\ZZ_2^4$-equivariant triangulation of $\mathbb{RP}^4$ requires at least $18$ vertices.

This study examines the extent to which structural constraints specified in conceptual schemas are represented after transformation to logical schemas. Focusing on the conceptual-to-logical mapping, an Entity-Relationship (ER) model containing binary relationship types is transformed into a Relational Database Schema (RDS). The analysis is conducted under the classical transformation framework in which the logical schema is defined solely by primary key (PK) and foreign key (FK) constraints. Using generalised ER models with variable structural constraint values, the resulting RDS structures are evaluated to determine whether minimum and maximum participation constraints are represented unambiguously. The findings show that, for one-to-one and one-to-many relationships, RDSs do not unambiguously capture minimum participation constraints and do not encode exact maximum participation beyond limited cases. For many-to-many relationships, the schema indicates only that maximum cardinalities exceed one, without preserving exact values. These results clarify the representational limits of standard ER-to-relational transformations and have implications for schema design and constraint enforcement.

These lecture notes develop the theory of learning in deep and recurrent neuronal networks from the point of view of Bayesian inference. The aim is to enable the reader to understand typical computations found in the literature in this field. Initial chapters develop the theoretical tools, such as probabilities, moment and cumulant-generating functions, and some notions of large deviation theory, as far as they are needed to understand collective network behavior with large numbers of parameters. The main part of the notes derives the theory of Bayesian inference for deep and recurrent networks, starting with the neural network Gaussian process (lazy-learning) limit, which is subsequently extended to study feature learning from the point of view of adaptive kernels. The notes also expose the link between the adaptive kernel approach and approaches of kernel rescaling.

Motivation: mtDNA distance matrices are standard inputs for distance-based phylogeny, but computing all pairwise alignments is costly. Missing entries can degrade inferred topology and branch lengths, and generic matrix-completion methods may disrupt tree-like (ultrametric) structure. Results: We propose Hyb-Adam-UM, which starts from an alignment-limited Needleman-Wunsch distance backbone and completes the matrix by minimizing a robust triplet ultrametric-violation functional. An Adam-style finite-difference optimizer updates only missing entries while enforcing symmetry, non-negativity, and a zero diagonal. From one complete reference matrix, we generate 20 masked instances at 30%, 50%, 65%, and 85% missingness. Hyb-Adam-UM consistently reduces ultrametric violations and achieves competitive reconstruction error, with improved topological accuracy and branch-length agreement relative to MW*/NJ* projection baselines (which exactly preserve observed distances) and Soft-Impute; gains are most pronounced at 85% missingness. Availability and implementation: https://github.com/mitichya/hyb-adam-um/; Zenodo: https://doi.org/10.5281/zenodo.18609748 Supplementary information: Supplementary data available online.

We propose two easy-to-implement fast algorithms based on moment-matching to compute the nonlocal potential $φ(\textbf{x})=(U\ast ρ)(\textbf{x})$ on bounded domain, where the kernel $U$ is singular at the origin and the density $ρ$ is a fast-decaying smooth function. Each method requires merely minor modifications to commonly-used existing methods, i.e., the sine spectral/Fourier quadrature method, and achieves a much better convergence rate. The key lies in the introduction of a smooth auxiliary function $ρ_1$ whose moments match those of the density up to an integer order $m$. Specifically, $ρ_1$ is constructed using Gaussian function in an explicit way and the associated potential can be calculated analytically. The moments of residual density vanish up to order $m$, and the corresponding residual potential $U \ast (ρ-ρ_1)$ decays much faster than the original potential $φ$ at the far field. As for the residual potential evaluation, for classical kernels (e.g., the Coulomb kernel), we solve a differential/pseudo-differential equation on a rectangular domain with homogeneous Dirichlet boundary conditions via sine pseudospectral method, and achieve an arbitrary high convergence rate. While, for general kernels, the regularity of Fourier integrand increase by $m$ thanks to the moments-vanishing property, therefore, the standard trapezoidal rule/midpoint quadrature also converges much faster. To gain a better numerical performance, we utilize the domain expansion technique to obtain better accuracy, and improve the efficiency by simplifying the quadrature into one discrete convolution and applying Fast Fourier Transform (FFT) to a double-sized vector. Rigorous error estimates and extensive numerical investigations showcase the accuracy and efficiency for different nonlocal potentials.

The proof of the inductive McKay condition has been shown to imply that the character theory above the characters of degree not divisible by $p$ of a normal subgroup is locally determined. In this note, we establish a similar result for the Isaacs' head characters of a normal solvable subgroup of an arbitrary group. In particular, we give a new lower bound of the number of conjugacy classes of a finite group in terms of the Carter subgroups of any of its normal solvable subgroups.

Copper-silver (CuAg) alloys are increasingly explored for applications in high-performance electrical and electronic systems, owing to their unique combination of high electrical and thermal conductivity and enhanced mechanical strength. Nevertheless, a thorough understanding of how these alloys surface characteristics fundamentally influence properties remains largely underdeveloped. Here, we explored the complex interplay between surface texture morphology, layer composition, wetting, and optical properties of Cu, Ag, and CuAg thin films deposited on textured silicon substrates via magnetron sputtering. Employing data mining and machine learning techniques, we identified robust correlations between contact angle and surface fractal dimension across all layer types promoting Cassie-Baxter surface state formation. Our analysis revealed a significant connection between layer thickness and surface topography entropy deficit, suggesting a dynamic evolution of surface order/disorder during metal film growth. Furthermore, we observed that contact angle sensitivity to layer thickness implied a correlation with microstructure evolution. Through K-Means clustering, we successfully categorized the formed surface textures morphology. Finally, a Random Forest regression model was developed to accurately predict water contact angles (Mean Absolute Error around 5 deg) using only texture and optical parameters. The model, along with accompanying Python code, is publicly available. Our findings establish a pathway towards targeted surface texture morphology engineering for tailored material performance.

Heterogeneous embedded systems, with diverse computing elements and accelerators such as FPGAs, offer a promising platform for fast and flexible ML inference, which is crucial for services such as autonomous driving and augmented reality, where delays can be costly. However, efficiently allocating computational resources for deep learning applications in FPGA-based systems is a challenging task. A Deep Learning Processor Unit (DPU) is a parameterizable FPGA-based accelerator module optimized for ML inference. It supports a wide range of ML models and can be instantiated multiple times within a single FPGA to enable concurrent execution. This paper introduces DPUConfig, a novel runtime management framework, based on a custom Reinforcement Learning (RL) agent, that dynamically selects optimal DPU configurations by leveraging real-time telemetry data monitoring, system utilization, power consumption, and application performance to inform its configuration selection decisions. The experimental evaluation demonstrates that the RL agent achieves energy efficiency 95% (on average) of the optimal attainable energy efficiency for several CNN models on the Xilinx Zynq UltraScale+ MPSoC ZCU102.

Auxiliary information is increasingly available from administrative and other data sources, but it is often incomplete and of non-probability origin. We propose a two-step small area estimation approach in which the first step relies on design-based model calibration and exploits a large non-probability source providing a noisy proxy of the study variable for only part of the population. A unit-level measurement-error working model is fitted on the linked overlap between the probability survey and the external source, and its predictions are incorporated through domain-specific model-calibration constraints to obtain approximately design-unbiased domain totals. These totals and their variance estimates are then used in a Fay-Herriot area-level model with exactly known covariates to produce empirical best linear unbiased predictors. The approach is demonstrated in three enterprise survey settings from official statistics by integrating probability sample data with (i) administrative records, (ii) a cut-off data source, and (iii) web-scraped online information. Empirical comparisons show consistent improvements in domain-level precision over direct estimation and over a Fay-Herriot benchmark that directly incorporates the proxy information as an error-prone covariate. These gains are achieved without modeling the selection mechanism of the non-probability sample.

Many datasets are observed on a finite set of equally spaced directions instead of the exact angles, such as the wind direction data. However, in the statistical literature, bivariate models are only available for continuous circular random variables. This article presents two bivariate circular distributions, namely bivariate wrapped geometric (BWG) and bivariate generalized wrapped geometric (BGWG), for analyzing bivariate discrete circular data. We consider wrapped geometric distributions and a trigonometric function to construct the models. The models are analytically tractable due to the exact closed-form expressions for the trigonometric moments. We thoroughly discuss the distributional properties of the models, including the interpretation of parameters and dependence structure. The estimation methodology based on maximizing the likelihood functions is illustrated for simulated datasets. Finally, the proposed distributions are utilized to analyze pairwise wind direction measurements obtained at different stations in India, and the interpretations for the fitted models are briefly discussed.

Cell-free massive multi-input multi-output (MIMO) promises uniform high performance across the network, but also brings a high energy cost due to joint transmission from distributed radio units (RUs) and centralized processing in the cloud. Leveraging the resource-sharing capabilities of Open Radio Access Network (O-RAN), we propose EARL, an energy-aware adaptive antenna control framework based on reinforcement learning. EARL dynamically configures antenna elements in RUs to minimize radio, optical fronthaul, and cloud processing power consumption while meeting user spectral efficiency demands. Numerical results show power savings of up to 81% and 50% over full-on and heuristic baselines, respectively. The RL-based approach operates within 220 ms, satisfying O-RAN's near-real-time limit, and a greedy refinement further halves power consumption at a 2 s runtime.

This research highlights the potential of quantum annealing in tackling large-scale optimization problems within the airline industry,demonstrating its efficiency for certain problem sizes while also acknowledging its current limitations. The comparative analysis provides valuable insights into the performance of advanced computational techniques, paving the way for further advancements in optimizing fleet assignments in the aviation sector.