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Estimating means on Riemannian manifolds is generally computationally expensive because the Riemannian distance function is not known in closed-form for most manifolds. To overcome this, we show that Riemannian diffusion means can be efficiently estimated using score matching with the gradient of Brownian motion transition densities using the same principle as in Riemannian diffusion models. Empirically, we show that this is more efficient than Monte Carlo simulation while retaining accuracy and is also applicable to learned manifolds. Our method, furthermore, extends to computing the Fr\'echet mean and the logarithmic map for general Riemannian manifolds. We illustrate the applicability of the estimation of diffusion mean by efficiently extending Euclidean algorithms to general Riemannian manifolds with a Riemannian $k$-means algorithm and maximum likelihood Riemannian regression.

For $X$ a finite category and $F$ a finite field, we study the additive image of the functor $\operatorname{H}_0(-,F) \colon \operatorname{rep}(X, \mathbf{Top}) \to \operatorname{rep}(X, \mathbf{Vect}_F)$, or equivalently, of the free functor $\operatorname{rep}(X, \mathbf{Set}) \to \operatorname{rep}(X, \mathbf{Vect}_F)$. We characterize all finite categories $X$ for which the indecomposables in the additive image coincide with the indecomposable indicator representations and provide examples of quivers of wild representation type where the additive image contains only finitely many indecomposables. Motivated by questions in topological data analysis, we conduct a detailed analysis of the additive image for finite grids. In particular, we show that for grids of infinite representation type, there exist infinitely many indecomposables both within and outside the additive image. We develop an algorithm for determining if a representation of a finite category is in the additive image. In addition, we investigate conditions for realizability and the effect of modifications of the source category and the underlying field. The paper concludes with a discussion of the additive image of $\operatorname{H}_n(-,F)$ for an arbitrary field $F$, extending previous work for prime fields., Comment: Added a new section on edge contractions and polished the manuscript

With the goal of increasing the speed and efficiency in robotic manipulation, a control approach is presented that aims to utilize intentional simultaneous impacts to its advantage. This approach exploits the concept of the time-invariant reference spreading framework, in which partly-overlapping ante- and post-impact reference vector fields are used. These vector fields are coupled via an impact model in proximity of the expected impact area, minimizing the otherwise large impact-induced velocity errors and control efforts. We show how a nonsmooth physics engine can be used to construct this impact model for complex scenarios, which warrants applicability to a large range of possible impact states without requiring contact stiffness and damping parameters. In addition, a novel interim-impact control mode provides robustness in the execution against the inevitable lack of exact impact simultaneity and the corresponding unreliable velocity error during the time when contact is only partially established. This interim mode uses a position feedback signal that is derived from the ante-impact velocity reference to promote contact completion, and smoothly transitions into the post-impact mode. An experimental validation of time-invariant reference spreading control is presented for the first time through a set of 600 robotic hit-and-push and dual-arm grabbing experiments., Comment: 15 pages, 10 figures. Submitted to IEEE Transactions on Robotics (T-RO)

Impact-aware robotic manipulation benefits from an accurate map from ante-impact to post-impact velocity signals to support, e.g., motion planning and control. This work proposes an approach to generate and experimentally validate such impact maps from simulations with a physics engine, allowing to model impact scenarios of arbitrarily large complexity. This impact map captures the velocity jump assuming an instantaneous contact transition between rigid objects, neglecting the nearly instantaneous contact transition and impact-induced vibrations. Feedback control, which is required for complex impact scenarios, will affect velocity signals when these vibrations are still active, making an evaluation solely based on velocity signals as in previous works unreliable. Instead, the proposed validation approach uses the reference spreading control framework, which aims to reduce peaks and jumps in the control feedback signals by using a reference consistent with the rigid impact map together with a suitable control scheme. Based on the key idea that selecting the correct rigid impact map in this reference spreading framework will minimize the net feedback signal, the rigid impact map is experimentally determined and compared with the impact map obtained from simulation, resulting in a 3.1% average error between the post-impact velocity identified from simulations and from experiments., Comment: 13 pages, 9 figures. Submitted to IEEE Transactions on Robotics

This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system matrices of the discounted LQ-OCPs into systems of differential equations. Subsequently, we derive the discrete-time equivalent of the discounted LQ-OCP by solving these systems. This paper presents three numerical methods for solving the proposed differential equations systems: the fixed-time-step ordinary differential equation (ODE) method, the step-doubling method, and the matrix exponential method. Our numerical experiment demonstrates that all three methods accurately solve the differential equation systems. Interestingly, the step-doubling method emerges as the fastest among them while maintaining the same level of accuracy as the fixed-time-step ODE method.

This study presents the design, discretization and implementation of the continuous-time linear-quadratic model predictive control (CT-LMPC). The control model of the CT-LMPC is parameterized as transfer functions with time delays, and they are separated into deterministic and stochastic parts for relevant control and filtering algorithms. We formulate time-delay, finite-horizon CT linear-quadratic optimal control problems (LQ-OCPs) for the CT-LMPC. By assuming piece-wise constant inputs and constraints, we present the numerical discretization of the proposed LQ-OCPs and show how to convert the discrete-time (DT) equivalent into a standard quadratic program. The performance of the CT-LMPC is compared with the conventional DT-LMPC algorithm. Our numerical experiments show that, under fixed tunning parameters, the CT-LMPC shows better closed-loop performance as the sampling time increases than the conventional DT-LMPC.

A novel method to reconstruct the energy of hadronic showers in the CMS High Granularity Calorimeter (HGCAL) is presented. The HGCAL is a sampling calorimeter with very fine transverse and longitudinal granularity. The active media are silicon sensors and scintillator tiles readout by SiPMs and the absorbers are a combination of lead and Cu/CuW in the electromagnetic section, and steel in the hadronic section. The shower reconstruction method is based on graph neural networks and it makes use of a dynamic reduction network architecture. It is shown that the algorithm is able to capture and mitigate the main effects that normally hinder the reconstruction of hadronic showers using classical reconstruction methods, by compensating for fluctuations in the multiplicity, energy, and spatial distributions of the shower's constituents. The performance of the algorithm is evaluated using test beam data collected in 2018 prototype of the CMS HGCAL accompanied by a section of the CALICE AHCAL prototype. The capability of the method to mitigate the impact of energy leakage from the calorimeter is also demonstrated.

This paper develops a novel mixed-integer linear programming (MILP) model for optimal participation of battery energy storage systems (BESSs) in the Swedish frequency containment reserve (FCR) markets. The developed model aims to maximize the battery owner's potential profit by considering battery degradation and participation in multiple FCR markets, i.e., FCR in normal operation (FCR-N), and FCR in disturbances (FCR-D) for up- and down-regulations. Accordingly, a precise formulation of a detailed battery degradation model and adherence to the technical requirements of the Swedish FCR markets are incorporated into the developed model. To achieve more practical results, simulations are conducted based on one minute time step realistic data for the whole year 2022. The results show a potential profit of 708 thousand Euros for a 1MW/1MWh BESS by participating in multi-FCR market. Analyzing the impact of considering degradation in the optimization problem has shown that the annual battery aging cost could decrease by 5%-29% without a significant effect on profit. The proposed model can be practically used by flexibility asset owners to achieve profitable and sustainable operation strategies that reduce battery degradation., Comment: Submitted to IEEE Transactions on Power Systems

This paper describes the new TPTP format for representing interpretations. It provides a background survey that helped us ensure that the representation format is adequate for different types of interpretations: Tarskian, Herbrand, and Kripke interpretations. The needs of applications that use models are considered. The syntax and semantics of the new format is expounded in detail, with multiple examples. Verification of models is discussed. Some tools that support processing the new format are noted. The properties of interpretations represented in the new format are discussed.

Bayesian evidence is a standard method used for comparing the ability of different models to fit available data and is used extensively in cosmology. However, since the evidence calculation involves performing an integral of the likelihood function over the entire space of model parameters this can be prohibitively expensive in terms of both CPU and time consumption. For example, in the simplest $\Lambda$CDM model and using CMB data from the Planck satellite, the dimensionality of the model space is over 30 (typically 6 cosmological parameters and 28 nuisance parameters). Even the simplest possible model requires $\mathcal{O}(10^6)$ calls to an Einstein--Boltzmann solver such as CLASS or CAMB and takes several days. Here we present calculations of Bayesian evidence using the CONNECT framework to calculate cosmological observables. We demonstrate that we can achieve results comparable to those obtained using Einstein--Boltzmann solvers, but at a minute fraction of the computational cost. As a test case, we then go on to compute Bayesian evidence ratios for a selection of slow-roll inflationary models. In the setup presented here, the total computation time is completely dominated by the likelihood function calculation which now becomes the main bottleneck for increasing computation speed., Comment: 14 pages, 3 figures

Critical experimental design issues connecting energy transduction and inheritable information within a protocell are explored and elucidated. The protocell design utilizes a photo-driven energy transducer (a ruthenium complex) to turn resource molecules into building blocks, in a manner that is modulated by a combinatorial DNA-based co-factor. This co-factor molecule serves as part of an electron relay for the energy transduction mechanism, where the charge-transport rates depend on the sequence that contains an oxo-guanine. The co-factor also acts as a store of inheritable information due to its ability to replicate non-enzymatically through template-directed ligation. Together, the energy transducer and the co-factor act as a metabolic catalyst that produces co-factor DNA building blocks as well as fatty acids (from picolinium ester and modified DNA oligomers), where the fatty acids self-assemble into vesicles on which exterior surface both the co-factor (DNA) and the energy transducer are anchored with hydrophobic tails. Here we use simulations to study how the co-factor sequence determines its fitness as reflected by charge transfer and replication rates. To estimate the impact on the protocell, we compare these rates with previously measured metabolic rates from a similar system where the charge transfer is directly between the ruthenium complex and the oxo-guanine (without DNA replication and charge transport). Replication and charge transport turn out to have different and often opposing sequence requirements. Functional information of the co-factor molecules is used to probe the feasibility of randomly picking co-factor sequences from a limited population of co-factors molecules, where a good co-factor can enhance both metabolic biomass production and its own replication rate.

Cosmological emulators of observables such as the Cosmic Microwave Background (CMB) spectra and matter power spectra commonly use training data sampled from a Latin hypercube. This method often incurs high computational costs by covering less relevant parts of the parameter space, especially in high dimensions where only a small fraction of the parameter space yields a significant likelihood. In this paper, we introduce hypersphere sampling, which instead concentrates sample points in regions with higher likelihoods, significantly enhancing the efficiency and accuracy of emulators. A novel algorithm for sampling within a high-dimensional hyperellipsoid aligned with axes of correlation in the cosmological parameters is presented. This method focuses the distribution of training data points on areas of the parameter space that are most relevant to the models being tested, thereby avoiding the computational redundancies common in Latin hypercube approaches. Comparative analysis using the \textsc{connect} emulation tool demonstrates that hypersphere sampling can achieve similar or improved emulation precision with more than an order of magnitude fewer data points and thus less computational effort than traditional methods. This was tested for both the $\Lambda$CDM model and a 5-parameter extension including Early Dark Energy, massive neutrinos, and additional ultra-relativistic degrees of freedom. Our results suggest that hypersphere sampling holds potential as a more efficient approach for cosmological emulation, particularly suitable for complex, high-dimensional models., Comment: 22 pages, 10 figures

How do galaxies of different luminosities contribute to the metal absorber populations of varying species and strength? We present our analysis of the predicted metal contributions from galaxies as observed in quasar absorption line spectra during the end of the Epoch of Reionization (EoR; $10 \geq z \geq 5.5$). This was done by implementing on-the-fly particle tracking into the latest \textsc{Technicolor Dawn} simulation and then linking CII, CIV, SiII, SiIV, OI, and MgII absorbers to host galaxies in post-processing. We define the Host Galaxy Luminosity Distribution (HGLD) as the rest-frame ultraviolet luminosity distribution of galaxies contributing ions to an absorber, weighted by the fractional contribution, and compute its dependence on ion and absorber strength. The HGLD shape is predicted to be indistinguishable from the field luminosity function, indicating that there is no relationship between the absorber strength or ion and the luminosity of the dominant contributing galaxy. Switching from galaxy luminosity to stellar mass, the predicted host galaxy mass distributions (HGMD) indicate that more-massive galaxies contribute a higher fraction of metal ions to absorbers of each species, with the HGMD of stronger absorbers extending out to higher masses. We conclude that the fraction of absorbing metal ions contributed by galaxies increases weakly with stellar mass, but the scatter in luminosity at fixed stellar mass obscures this relationship. For the same reason, we predict that observational analyses of the absorber-galaxy relationship will uncover stronger trends with stellar mass than with luminosity., Comment: 18 pages, 9 figures, 6 tables. Accepted to ApJ

The accelerated expansion of the Universe is impressively well described by a cosmological constant. However, the observed value of the cosmological constant is much smaller than expected based on quantum field theories. Recent efforts to achieve consistency in these theories have proposed a relationship between Dark Energy and the most compact objects, such as black holes (BH). However, experimental tests are very challenging to devise and perform. In this article, we present a testable model with no cosmological constant, in which the accelerated expansion can be driven by black holes. The model couples the expansion of the Universe (the Friedmann equation) with the mass-function of cosmological haloes (using the Press-Schechter formalism). Through the observed link between halo-masses and BH-masses one thus gets a coupling between the expansion rate of the Universe and the BHs. We compare the predictions of this simple BH model with SN1a data and find a poor agreement with observations. Our method is sufficiently general that it allows us to also test a fundamentally different model, also without a cosmological constant, where the accelerated expansion is driven by a new force proportional to the internal velocity dispersion of galaxies. Surprisingly enough this model cannot be excluded using the SN1a data., Comment: 11 pages, 2 figures, Accepted by Universe, special issue "The Nature of Dark Energy", https://www.mdpi.com/2218-1997/10/5/193

In this study, we introduce numerical methods for discretizing continuous-time linear-quadratic optimal control problems (LQ-OCPs). The discretization of continuous-time LQ-OCPs is formulated into differential equation systems, and we can obtain the discrete equivalent by solving these systems. We present the ordinary differential equation (ODE), matrix exponential, and a novel step-doubling method for the discretization of LQ-OCPs. Utilizing Euler-Maruyama discretization with a fine step, we reformulate the costs of continuous-time stochastic LQ-OCPs into a quadratic form, and show that the stochastic cost follows the $\chi^2$ distribution. In the numerical experiment, we test and compare the proposed numerical methods. The results ensure that the discrete-time LQ-OCP derived using the proposed numerical methods is equivalent to the original problem., Comment: This paper (7 pages) has been accepted by the 22nd European Control Conference (ECC) in Stockholm, Sweden

This paper presents the numerical discretization methods of the continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays. We describe the weight matrices of the LQ-OCPs as differential equations systems, allowing us to derive the discrete equivalent of the continuous-time LQ-OCPs. Three numerical methods are introduced for solving proposed differential equations systems: 1) the ordinary differential equation (ODE) method, 2) the matrix exponential method, and 3) the step-doubling method. We implement a continuous-time model predictive control (CT-MPC) on a simulated cement mill system, and the objective function of the CT-MPC is discretized using the proposed LQ discretization scheme. The closed-loop results indicate that the CT-MPC successfully stabilizes and controls the simulated cement mill system, ensuring the viability and effectiveness of LQ discretization., Comment: This paper (7 pages) has been accepted by the 12th IFAC Symposium on Advanced Control of Chemical Processes (ADCHEM 2024)

White dwarf stars are ubiquitous in the Galaxy, and are essential to understanding stellar evolution. While most white dwarfs are photometrically stable and reliable flux standards, some can be highly variable, which can reveal unique details about the endpoints of low-mass stellar evolution. In this study we characterize a sample of high-confidence white dwarfs with multi-epoch photometry from Gaia Data Release 3. We compare these Gaia light curves with light curves from the Zwicky Transiting Facility and the Transiting Exoplanet Survey Satellite to see when Gaia data independently can accurately measure periods of variability. From this sample, 105 objects have variability periods measured from the Gaia light curves independently, with periods as long as roughly 9.5 d and as short as 256.2 s (roughly 4 min), including seven systems with periods shorter than 1000 s. We discover 86 new objects from the 105 target sample, including pulsating, spotted, and binary white dwarfs, and even a new 68.4 min eclipsing cataclysmic variable. The median amplitude of the absolute photometric variability we confirm from Gaia independently is 1.4%, demonstrating that Gaia epoch photometry is capable of measuring short-term periods even when observations are sparse., Comment: 22 pages, 8 figures, 3 tables, accepted for publication in ApJ; updated headers in table 3 to reflect correct units of amplitude; updated formatting for readability