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Which surfaces can be realized with two-dimensional faces of the five-dimensional cube (the penteract)? How can we visualize them? In recent work, Aveni, Govc, and Roldan, show that there exist 2690 connected closed cubical surfaces up to isomorphism in the 5-cube. They give a classification in terms of their genus $g$ for closed orientable cubical surfaces and their demigenus $k$ for a closed non-orientable cubical surface. In this paper, we explain the main idea behind the exhaustive search and we visualize the projection to $\mathbb{R}^3$ of a torus, a genus two torus, the projective plane, and the Klein bottle. We use reinforcement learning techniques to obtain configurations optimized for 3D printing., Comment: 5 pages, 3 Figures

We study topological and geometric properties of a cell growth process in the Euclidean plane, where the cells are regular pentagons. To explore the aesthetic aspects of this model, we employ a laser cutter on various materials to create physical representations for some simulations of the model., Comment: 4 pages, 6 figures

The discrepancies in different measurements of the lifetime of isolated neutrons could be resolved by considering an extra neutron decay channel into dark matter, with a branching ratio of the order of $O(1$\%). Although the decay channel into a dark fermion $\chi$ plus visible matter has been already experimentally excluded, a dark decay with either a scalar or dark photon remains still a possibility. In particular, a model with a fermion mass $m_\chi\approx 1$ GeV and a scalar $m_\phi \approx O(\rm{MeV})$ could provide not only the required branching ratio to explain the anomaly but also a good dark matter (DM) candidate with the right thermal abundance today. Although the interaction DM-neutron will affect the formation of neutron stars, the combined effect of the dark matter self-interactions mediated by the light scalar and an effective repulsive interaction with the neutrons induced by the scalar-Higgs coupling would allow heavy enough neutron stars. The combined constraints from neutron lifetime, dark matter abundance, neutron star and Higgs physics, and Big Bang Nucleosynthesis, restrict the light scalar mass to the range $2 m_e < m_\phi < 2 m_e + 0.0375$ MeV., Comment: version accepted in PRD; improved discussion on DM abundance; comments on SN cooloing bounds and SIDM contraints added; new Fig. 4 added

Fullerenes have been observed in several astronomical objects since the discovery of C$_{60}$ in the mid-infrared (mid-IR) spectrum of the planetary nebula (PN) Tc 1. It has been suggested that the carriers of the broad unidentified infrared (UIR) plateau features, such as the 9$-$13$\mu$m emission feature (12$\mu$m hereafter), may be related to the formation of fullerenes. In particular, their carriers have been suggested to be mixed aromatic or aliphatic hydrocarbons such as hydrogenated amorphous carbon (HAC-like hereafter) grains. For this study, we modeled the mid-IR emission of the C$_{60}$-PN Tc 1 with a photoionization code, including for the first time the laboratory optical constants ($n$ and $k$ indices) of HAC-like dust at 300 K. Interestingly, we find that the broad 12$\mu$m plateau feature in Tc 1 is well reproduced by using a distribution of canonical HAC grains, while at the same time they provide an important fraction of the IR dust continuum emission and are consistent with the other UIR features observed (e.g., the broad 6$-$9$\mu$m plateau feature). This finding suggests that HAC-like grains may be possible carriers of the 12$\mu$m plateau feature, being likely related to the fullerene formation mechanism in PNe. More laboratory experiments, to obtain the optical constants of HAC-like dust with several structures or a composition at different physical conditions, are strongly encouraged -- that is, in order to extend this pilot study to more fullerene PNe, and to unveil the details of fullerene formation and of the potential carriers of the elusive UIR plateau features., Comment: Published in Astronomy and Astrophysics Letters. 7 pages, 3 figures

In this paper, we address the limitations of traditional constant false alarm rate (CFAR) target detectors in automotive radars, particularly in complex urban environments with multiple objects that appear as extended targets. We propose a data-driven radar target detector exploiting a highly efficient 2D CNN backbone inspired by the computer vision domain. Our approach is distinguished by a unique cross sensor supervision pipeline, enabling it to learn exclusively from unlabeled synchronized radar and lidar data, thus eliminating the need for costly manual object annotations. Using a novel large-scale, real-life multi-sensor dataset recorded in various driving scenarios, we demonstrate that the proposed detector generates dense, lidar-like point clouds, achieving a lower Chamfer distance to the reference lidar point clouds than CFAR detectors. Overall, it significantly outperforms CFAR baselines detection accuracy., Comment: Accepted for lecture presentation at IEEE RadarConf'24, Denver, USA

Offline policy learning aims to discover decision-making policies from previously-collected datasets without additional online interactions with the environment. As the training dataset is fixed, its quality becomes a crucial determining factor in the performance of the learned policy. This paper studies a dataset characteristic that we refer to as multi-behavior, indicating that the dataset is collected using multiple policies that exhibit distinct behaviors. In contrast, a uni-behavior dataset would be collected solely using one policy. We observed that policies learned from a uni-behavior dataset typically outperform those learned from multi-behavior datasets, despite the uni-behavior dataset having fewer examples and less diversity. Therefore, we propose a behavior-aware deep clustering approach that partitions multi-behavior datasets into several uni-behavior subsets, thereby benefiting downstream policy learning. Our approach is flexible and effective; it can adaptively estimate the number of clusters while demonstrating high clustering accuracy, achieving an average Adjusted Rand Index of 0.987 across various continuous control task datasets. Finally, we present improved policy learning examples using dataset clustering and discuss several potential scenarios where our approach might benefit the offline policy learning community.

Resistive Random Access Memories (RRAMs) are being studied by the industry and academia because it is widely accepted that they are promising candidates for the next generation of high density nonvolatile memories. Taking into account the stochastic nature of mechanisms behind resistive switching, a new technique based on the use of functional data analysis has been developed to accurately model resistive memory device characteristics. Functional principal component analysis (FPCA) based on Karhunen-Loeve expansion is applied to obtain an orthogonal decomposition of the reset process in terms of uncorrelated scalar random variables. Then, the device current has been accurately described making use of just one variable presenting a modeling approach that can be very attractive from the circuit simulation viewpoint. The new method allows a comprehensive description of the stochastic variability of these devices by introducing a probability distribution that allows the simulation of the main parameter that is employed for the model implementation. A rigorous description of the mathematical theory behind the technique is given and its application for a broad set of experimental measurements is explained.

Functional principal component analysis based on Karhunen Loeve expansion allows to describe the stochastic evolution of the main characteristics associated to multiple systems and devices. Identifying the probability distribution of the principal component scores is fundamental to characterize the whole process. The aim of this work is to consider a family of statistical distributions that could be accurately adjusted to a previous transformation. Then, a new class of distributions, the linear-phase-type, is introduced to model the principal components. This class is studied in detail in order to prove, through the KL expansion, that certain linear transformations of the process at each time point are phase-type distributed. This way, the one-dimensional distributions of the process are in the same linear-phase-type class. Finally, an application to model the reset process associated with resistive memories is developed and explained.

A powerful time series analysis modeling technique is presented to describe cycle-to-cycle variability in memristors. These devices show variability linked to the inherent stochasticity of device operation and it needs to be accurately modeled to build compact models for circuit simulation and design purposes. A new multivariate approach is proposed for the reset and set voltages that accurately describes the statistical data structure of a resistive switching series. Experimental data were measured from advanced hafnium oxide based devices. The models reproduce the experiments correctly and a comparison of the multivariate and univariate approaches is shown for comparison.

A new statistical approach has been developed to analyze Resistive Random Access Memory (RRAM) variability. The stochastic nature of the physical processes behind the operation of resistive memories makes variability one of the key issues to solve from the industrial viewpoint of these new devices. The statistical features of variability have been usually studied making use of Weibull distribution. However, this probability distribution does not work correctly for some resistive memories, in particular for those based on the Ni/HfO2/Si structure that has been employed in this work. A completely new approach based on phase-type modeling is proposed in this paper to characterize the randomness of resistive memories operation. An in-depth comparison with experimental results shows that the fitted phase-type distribution works better than the Weibull distribution and also helps to understand the physics of the resistive memories.

The homogeneity problem for testing if more than two different samples come from the same population is considered for the case of functional data. The methodological results are motivated by the study of homogeneity of electronic devices fabricated by different materials and active layer thicknesses. In the case of normality distribution of the stochastic processes associated with each sample, this problem is known as Functional ANOVA problem and is reduced to test the equality of the mean group functions (FANOVA). The problem is that the current/voltage curves associated with Resistive Random Access Memories (RRAM) are not generated by a Gaussian process so that a different approach is necessary for testing homogeneity. To solve this problem two different parametric and nonparametric approaches based on basis expansion of the sample curves are proposed. The first consists of testing multivariate homogeneity tests on a vector of basis coefficients of the sample curves. The second is based on dimension reduction by using functional principal component analysis of the sample curves (FPCA) and testing multivariate homogeneity on a vector of principal components scores. Different approximation numerical techniques are employed to adapt the experimental data for the statistical study. An extensive simulation study is developed for analyzing the performance of both approaches in the parametric and non-parametric cases. Finally, the proposed methodologies are applied on three samples of experimental reset curves measured in three different RRAM technologies.

The microscopic structure of several amorphous substances often reveals complex patterns such as medium- or long-range order, spatial heterogeneity, and even local polycrystallinity. To capture all these features, models usually incorporate a refined description of the particle interaction that includes an ad hoc design of the inside of the system constituents, and use temperature as a control parameter. We show that all these features can emerge from a minimal athermal two-dimensional model where particles interact isotropically by a double-well potential, which includes an excluded volume and a maximum coordination number. The rich variety of structural patterns shown by this simple geometrical model apply to a wide range of real systems including water, silicon, and different amorphous materials., Comment: 6 pages, 5 figures

In recent years the need for DC distribution buses has increased considerably. As it can be noticed in the transport for example the distribution systems of the more electric aircrafts, ships, or electric cars. Given the complexities of the systems presented above, the need to use more and more switched power converters has arisen. The main problem of the connection of multiple controlled switched converters acting as source and load is the degradation of stability that occurs on the DC distribution bus due to the converter interactions. To study the stability in the distribution bus there are some wellestablished criteria. These criteria require knowledge of the input impedance of the converters that act as load and the output impedance of the equipment that acts as source. In order to reduce the complexity of obtaining the input impedance a model based on a controlled converter acting as a constant power load (CPL) is commonly used. This article studies the accuracy of this model for a commonly used topology in distribution systems nowadays, Two Level Voltage Source Converter (2L-VSC), studying different scenarios that make the model become inaccurate.

The study of neutrino oscillation at accelerators is limited by systematic uncertainties, in particular on the neutrino flux, cross-section, and energy estimates. These systematic uncertainties could be eliminated by a novel experimental technique: neutrino tagging. This technique relies on a new type of neutrino beamline and its associated instrumentation which would enable the kinematical reconstruction of the neutrinos produced in $\pi^{\pm} \to \mu^{\pm} \nu_\mu$ and $K^{\pm} \to \mu^{\pm} \nu_\mu$ decays. This article presents a proof-of-concept study for such a tagged beamline, aiming to serve a long baseline neutrino experiment exploiting a megaton scale natural water Cherenkov detector. After optimizing the target and the beamline optics to first order, a complete Monte Carlo simulation of the beamline has been performed. The results show that the beamline provides a meson beam compatible with the operation of the spectrometer, and delivers a neutrino flux sufficient to collect neutrino samples with a size comparable with similar experiments and with other un-tagged long-baseline neutrino experimental proposals.

Every non-solvable and non-semisimple quadratic Lie algebra can be obtained as a double extension of a solvable quadratic Lie algebra. Thanks to a partial classification of nilpotent Lie algebras and this result, we can design different techniques to obtain any quadratic Lie algebra whose (solvable) radical ideal is nilpotent. To achieve this, we propose two alternative methods, both involving the use of quotients. In addition to their mathematical description, both approaches introduced in this paper have been computationally implemented and are publicly available to use for generating these algebras., Comment: 20 pages

Several planetary nebulae (PNe) have been found to contain both polycyclic aromatic hydrocarbon (PAH-like) species and fullerenes (C$_{60}$) distinguished by their mid-infrared emission. Previous laboratory and astronomical studies suggest that the formation of both species could be related to the decomposition, by photochemical processing, of hydrogenated amorphous carbon (HAC) grains. Then, HACs and, seemingly, big-fullerene related species (e.g., carbon onions) have been suggested as potential carriers of the UV bump at 2175{\AA} and the far-UV rise common to interstellar extinction curves. Our goal is to investigate the UV bump with the possible presence of a HAC extinction component in the International Ultraviolet Explorer (IUE) spectra of C-rich PNe; both with detected and non-detected fullerenes. The considered sample includes three C$_{60}$-PNe (Tc 1, IC 418, and IC 2501) and the non-C$_{60}$-PN Hen 2-5. Independently of the presence of C$_{60}$ in their circumstellar envelopes, we found that the UV bump in all sample PNe is well explained by interstellar extinction, suggesting that species different from those of the foreground insterstellar medium, e.g., large fullerene-related species like carbon onions, are not the carrier. Interestingly, we found that PNe Tc 1 and Hen 2-5 show an absorption in the FUV rise. Their IUE continuum spectra may be very well reproduced by including the extinction curve of HAC-like very small grains (VSG). The possible presence of both species, HAC-like grains and fullerenes (C$_{60}$), in Tc 1 could support the HAC photochemical processing scenario for the formation of fullerenes in the complex circumstellar envelopes of PNe., Comment: 9 pages, 8 figures. Accepted for publication in MNRAS

Based on bibliometric information from Scopus for the period 1996-2019, this document characterizes the evolution of Uruguayan scientific production and establishes the areas in which the country has a revealed comparative advantage (RCA). Methodologically, it is proposed that there is a RCA in an area if this area has a greater share in national scientific production than the share of the area in world scientific production. The evidence presented considers two measurements of scientific production (published articles and citations) and three levels of aggregation in the areas (a minor one with 5 large areas, a more detailed one with 27 disciplines and another even more granular with more than 300 disaggregations). Within Health Sciences there is a RCA in Veterinary, Nursing and Medicine. Within Life Sciences there is a RCA in Agricultural and Biological Sciences, Immunology and Microbiology and Biochemistry, Genetics and Molecular Biology. In Physical Sciences there is only a RCA in Environmental Science and in Social Sciences only in Economics, Econometrics and Finance., Comment: Pages 48, in Spanish language, 2 tables, 20 figure

Knowledge generated in a given scientific domain may spill over into other close scientific disciplines, thereby improving performance. Using bibliometric data from the SCImago database drawn from a sample of 174 countries, we implement a measure of proximity based on revealed comparative advantage (RCA). Our estimates show that proximity between disciplines positively and significantly affects the RCA growth rate. This impact is larger on disciplines that currently do not have RCA., Comment: Pages 32, 11 tables, 3 figure

The procedure of double extension of vector spaces endowed with non-degenerate bilinear forms allows us to introduce the class of generalized $\mbK$-oscillator algebras over any arbitrary field $\mbK$. Starting from basic structural properties of such algebras and the canonical forms of skew-adjoint endomorphisms, we will proceed to classify the subclass of quadratic nilpotent algebras and characterize those algebras in the class with quadratic dimension 2. This will enable us to recover the well-known classification of real oscillator algebras, also known as Lorentzian algebras, given by Alberto Medina in 1985., Comment: 24 pages

Using martingale theory, we compute, in very few lines, exact analytical expressions for various first-exit-time statistics associated with one-dimensional biased diffusion. Examples include the distribution for the first-exit time from an interval, moments for the first-exit site, and functionals of the position, which involve memory and time integration. As a key example, we compute analytically the mean area swept by a biased diffusion until it escapes an interval that may be asymmetric and have arbitrary length. The mean area allows us to derive the hitherto unexplored cross-correlation function between the first-exit time and the first-exit site, which vanishes only for exit problems from symmetric intervals. As a colophon, we explore connections of our results with gambling, showing that betting on the time-integrated value of a losing game it is possible to design a strategy that leads to a net average win., Comment: 14 pages, 5 figures

Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations research, and numerous areas due to its significance in a wide range of applications. While known to be computationally challenging (NP-hard) several approximation algorithms have been proposed, most with high-order polynomial-time complexity. However, the graph topology of complex networks with heavy-tailed degree distributions present characteristics that can be exploited to yield custom-tailored algorithms. We compare eight algorithms specifically designed for complex networks and evaluate their performance based on accuracy and efficiency for problems of varying sizes and application areas. Rather than relying on a small number of problems, we conduct over 16,000 experiments covering a wide range of network sizes and k-median{} values. While individual results vary, a few methods provide consistently good results. We draw general conclusions about how algorithms perform in practice and provide general guidelines for solutions.

Motivated by the result of Dantas et. al. (2023) that there exist metric spaces for which the set of strongly norm-attaining Lipschitz functions does not contain an isometric copy of $c_0$, we introduce and study a weaker notion of norm-attainment for Lipschitz functions called the pointwise norm-attainment. As a main result, we show that for every infinite metric space $M$, there exists a metric space $M_0 \subseteq M$ such that the set of pointwise norm-attaining Lipschitz functions on $M_0$ contains an isometric copy of $c_0$. We also observe that there are countable metric spaces $M$ for which the set of pointwise norm-attaining Lipschitz functions contains an isometric copy of $\ell_\infty$, which is a result that does not hold for the set of strongly norm-attaining Lipschitz functions. Several new results on $c_0$-embedding and $\ell_1$-embedding into the set of strongly norm-attaining Lipschitz functions are presented as well. In particular, we show that if $M$ is a subset of an $\mathbb{R}$-tree containing all the branching points, then the set of strongly norm-attaining Lipschitz functions contains $c_0$ isometrically. As a related result, we provide an example of metric space $M$ for which the set of norm-attaining functionals on the Lipschitz-free space over $M$ cannot contain an isometric copy of $c_0$. Finally, we compare the concept of pointwise norm-attainment with the several different kinds of norm-attainment from the literature., Comment: 40 pages, 2 figures

The relationship between the thermodynamic and computational characteristics of dynamical physical systems has been a major theoretical interest since at least the 19th century, and has been of increasing practical importance as the energetic cost of digital devices has exploded over the last half century. One of the most important thermodynamic features of real-world computers is that they operate very far from thermal equilibrium, in finite time, with many quickly (co-)evolving degrees of freedom. Such computers also must almost always obey multiple physical constraints on how they work. For example, all modern digital computers are periodic processes, governed by a global clock. Another example is that many computers are modular, hierarchical systems, with strong restrictions on the connectivity of their subsystems. This properties hold both for naturally occurring computers, like brains or Eukaryotic cells, as well as digital systems. These features of real-world computers are absent in 20th century analyses of the thermodynamics of computational processes, which focused on quasi-statically slow processes. However, the field of stochastic thermodynamics has been developed in the last few decades - and it provides the formal tools for analyzing systems that have exactly these features of real-world computers. We argue here that these tools, together with other tools currently being developed in stochastic thermodynamics, may help us understand at a far deeper level just how the fundamental physical properties of dynamic systems are related to the computation that they perform., Comment: Updated version

Perceptual decision-making frequently requires making rapid, reliable choices upon encountering noisy sensory inputs. To better define the statistical processes underlying perceptual decision-making, here we characterize the choices of human participants visualizing a system of nonequilibrium stationary physical dynamics and compare such choices to the performance of an optimal agent computing Wald's sequential probability ratio test (SPRT). Participants viewed movies of a particle endowed with drifted Brownian dynamics and had to judge the motion as leftward or rightward. Overall, the results uncovered fundamental performance limits, consistent with recently established thermodynamic trade-offs involving speed, accuracy, and dissipation. Specifically, decision times are sensitive to entropy production rates. Moreover, to achieve a given level of observed accuracy, participants require more time than predicted by SPRT, indicating suboptimal integration of available information. In view of such suboptimality, we develop an alternative account based on evidence integration with a memory time constant. Setting the time constant proportionately to the deviation from equilibrium in the stimuli significantly improved trial-by-trial predictions of decision metrics with respect to SPRT. This study shows that perceptual psychophysics using stimuli rooted in nonequilibrium physical processes provides a robust platform for understanding how the brain takes decisions on stochastic information inputs., Comment: 18 pages, 13 figures

Consider the following simple parking process on $\Lambda_n := \{-n, \ldots, n\}^d,d\ge1$: at each step, a site $i$ is chosen at random in $\Lambda_n$ and if $i$ and all its nearest neighbor sites are empty, $i$ is occupied. Once occupied, a site remains so forever. The process continues until all sites in $\Lambda_n$ are either occupied or have at least one of their nearest neighbors occupied. The final configuration (occupancy) of $\Lambda_n$ is called the jamming limit and is denoted by $X_{\Lambda_n}$. Ritchie (2006) constructed a stationary random field on $\mathbb Z^d$ obtained as a (thermodynamic) limit of the $X_{\Lambda_n}$'s as $n$ tends to infinity. As a consequence of his construction, he proved a strong law of large numbers for the proportion of occupied sites in the box $\Lambda_n$ for the random field $X$. Here we prove the central limit theorem, the law of iterated logarithm, and a gaussian concentration inequality for the same statistics. A particular attention will be given to the case $d=1$, in which we also obtain new asymptotic properties for the sequence $X_{\Lambda_n},n\ge1$ as well as a new proof to the closed-form formula for the occupation density of the parking process., Comment: 19 pages, 1 figure

How can we visualize all the surfaces that can be made from the faces of the tesseract? In recent work, Aveni, Govc, and Rold\'an showed that the torus and the sphere are the only closed surfaces that can be realized by a subset of two-dimensional faces of the tesseract. They also gave an exhaustive list of all the isomorphic types of embeddings of these two surfaces. Here, we generate 3D models of all these surfaces. We also exhibit, with the help of some hyper-ants, the minimum realization of the M\"obius strip on the tesseract., Comment: 4 pages, 6 figures, Bridges 2023 Conference Proceedings

In mathematics, a dissection of a square (or rectangle) into non-congruent rectangles is a Mondrian partition. If all the rectangles have the same area, it is called a perfect Mondrian partition. In this paper, we present a computational result by which we can affirm that there is no perfect Mondrian partition of a length $n$ square for $n\leq 1000$. Using the same algorithm we have been able to establish that there is no perfect Mondrian partition of a $n \times m$ rectangle for $n,m \leq 400$.

In this article, we propose a splitting algorithm to find zeros of the sum of four maximally monotone operators in real Hilbert spaces. In particular, we consider a Lipschitzian operator, a cocoercive operator, and a linear composite term. In the case when the Lipschitzian operator is absent, our method reduces to the Condat-V\~u algorithm. On the other hand, when the linear composite term is absent, the algorithm reduces to the Forward-Backward-Half-Forward algorithm (FBHF). Additionally, in each case, the set of step-sizes that guarantee the weak convergence of those methods are recovered. Therefore, our algorithm can be seen as a generalization of Condat-V\~u and FBHF. Moreover, we propose extensions and applications of our method in multivariate monotone inclusions and saddle point problems. Finally, we present a numerical experiment in image deblurring problems.

Swirling spin textures, including topologically non-trivial states, such as skyrmions, chiral domain walls, and magnetic vortices, have garnered significant attention within the scientific community due to their appeal from both fundamental and applied points of view. However, their creation, controlled manipulation, and stability are typically constrained to certain systems with specific crystallographic symmetries, bulk, or interface interactions, and/or a precise stacking sequence of materials. Here, we make use of the stray field of YBa2Cu3O7-{\delta} superconducting microstructures in ferromagnet/superconductor hybrids to imprint magnetic radial vortices in permalloy at temperatures below the superconducting transition temperature (TC), a method easily extended to other ferromagnets with in-plane magnetic anisotropy. We examine the size dependence and temperature stability of the imprinted magnetic configurations. We show that above TC, magnetic domains retain memory of the imprinted spin texture. Micromagnetic modelling coupled with a SC field model reveals that the stabilization mechanism leading to this memory effect is mediated by microstructural defects. Superconducting control of swirling spin textures below and above the superconducting transition temperature holds promising prospects for shaping spintronics based on magnetic textures.

The distortion of corner-sharing octahedra in isovalent perovskite transition-metal oxide interfaces is proven to be an excellent way to tailor the electronic and magnetic properties of their heterostructures. Combining depth-dependent magnetic characterization technique; (polarized neutron reflectivity, PNR); and theoretical calculation (density functional theory), we report interface-driven magnetic exchange interactions due to a modification in the octahedral rotations at the interfaces in an isovalent La0.67Ca0.33MnO3 (LCMO)/La0.67Sr0.33MnO3 (LSMO) heterostructures. PNR results determined a length scale of ~ 8 unit cells at the interface, which demonstrated a modification in magnetic properties. The results also predicted a low-temperature exchange bias for these ferromagnetic heterostructures with a maximum exchange bias for the heterostructure, which showed an enhanced antiferromagnetic coupling at the interfaces.

Given a finite set of points in $\mathbb{R}^d$, Tverberg's theorem guarantees the existence of partitions of this set into parts whose convex hulls intersect. We introduce a graph structured on the family of Tverberg partitions of a given set of points, whose edges describe closeness between different Tverberg partitions. We prove bounds on the minimum and maximum degree of this graph, the number of vertices of maximal degree, its clique number, and its connectedness.

In this article, we study the convergence of algorithms for solving monotone inclusions in the presence of adjoint mismatch. The adjoint mismatch arises when the adjoint of a linear operator is replaced by an approximation, due to computational or physical issues. This occurs in inverse problems, particularly in computed tomography. In real Hilbert spaces, monotone inclusion problems involving a maximally $\rho$-monotone operator, a cocoercive operator, and a Lipschitzian operator can be solved by the Forward-Backward-Half-Forward and the Forward-Douglas-Rachford-Forward methods. We investigate the case of a mismatched Lipschitzian operator. We propose variants of the two aforementioned methods to cope with the mismatch, and establish conditions under which the weak convergence to a solution is guaranteed for these variants. The proposed algorithms hence enable each iteration to be implemented with a possibly iteration-dependent approximation to the mismatch operator, thus allowing this operator to be modified at each iteration. Finally, we present numerical experiments on a computed tomography example in material science, showing the applicability of our theoretical findings.

Hindsight Experience Replay (HER) is a technique used in reinforcement learning (RL) that has proven to be very efficient for training off-policy RL-based agents to solve goal-based robotic manipulation tasks using sparse rewards. Even though HER improves the sample efficiency of RL-based agents by learning from mistakes made in past experiences, it does not provide any guidance while exploring the environment. This leads to very large training times due to the volume of experience required to train an agent using this replay strategy. In this paper, we propose a method that uses primitive behaviours that have been previously learned to solve simple tasks in order to guide the agent toward more rewarding actions during exploration while learning other more complex tasks. This guidance, however, is not executed by a manually designed curriculum, but rather using a critic network to decide at each timestep whether or not to use the actions proposed by the previously-learned primitive policies. We evaluate our method by comparing its performance against HER and other more efficient variations of this algorithm in several block manipulation tasks. We demonstrate the agents can learn a successful policy faster when using our proposed method, both in terms of sample efficiency and computation time. Code is available at https://github.com/franroldans/qmp-her., Comment: 6 pages, 2 figures, 1 algorithm, 1 table. Version accepted to ICARA 2024

We study the dynamics of an overdamped Brownian particle in a thermal bath that contains a dilute solution of active particles. The particle moves in a harmonic potential and experiences Poisson shot-noise kicks with specified amplitude distribution due to moving active particles in the bath. From the Fokker-Planck equation for the particle dynamics we derive the stationary solution for the displacement distribution along with the moments characterizing mean, variance, skewness, and kurtosis, as well as finite time first and second moments. We also compute an effective temperature through the fluctuation-dissipation theorem and show that equipartition theorem holds for all zero-mean kick distributions, including those leading to non-Gaussian stationary statistics. For the case of Gaussian-distributed active kicks we find a re-entrant behaviour from non-Gaussian to Gaussian stationary states and a heavy-tailed leptokurtic distribution across a wide range of parameters as seen in recent experimental studies. Further analysis reveals statistical signatures of the irreversible dynamics of the particle displacement in terms of the time asymmetry of cross-correlation functions. Fruits of our work is the development of a compact inference scheme that may allow experimentalists to extract the rate and moments of underlying shot-noise solely from the statistics of the particle position., Comment: 22 pages, 5 figures, Annalen der Physik template

Small metal-containing molecules have been detected and recognized as one of the hybrid species efficiently formed in space; especially in the circumstellar envelopes of evolved stars. It has been predicted also that more complex hybrid species like those formed by metals and fullerenes (metallofullerenes) could be present in such circumstellar environments. Recently, quantum-chemical simulations of metallofullerenes have shown that they are potential emitters contributing to the observed mid-IR spectra in the fullerene-rich circumstellar environments of different types of evolved stars. Here we present the individual simulated mid-IR (~5-50 um) spectra of twenty-eight metallofullerene species; both neutral and charged endo- and exohedral metallofullerenes for seven different metals (Li, Na, K, Ca, Mg, Ti, and Fe) have been considered. The changes induced by the metal-C60 interaction on the intensity and position of the spectral features are highlighted using charge density difference maps and electron density partitioning. Our calculations identify the fundamental IR spectral regions where, depending on the metal binding nature, there should be a major spectral contribution from each of the metallofullerenes. The metallofullerenes IR spectra are made publicly available to the astronomical community, especially James Webb Space Telescope users, for comparisons that could eventually lead to the detection of these species in space., Comment: Accepted for publication in The Astrophysical Journal Supplement Series on 19 September 2023 (in press) (13 pages, 7 figures, and 1 table)

We analyse a nonlinear QW model which can be experimentally implemented using the components of the electric field on an optical nonlinear Kerr medium, which translates into a rotation in the coin operator, with an angle which depends (in a nonlinear fashion) on the state of the walker. This simple dependence makes it easy to consider the space-time continuum limit of the evolution equation, which takes the form of a nonlinear Dirac equation. The analysis of this continuum limit allows us, under some approximations, to gain some insight into the nature of soliton structures, which is illustrated by our numerical calculations. These solitons are stable structures whose trajectories can be modulated by choosing the appropriate initial conditions. We have also studied the stability of solitons when they are subject to an additional phase that simulates an external electric field, and also explored if they are formed in higher dimensional spaces.

We introduce higher-dimensional cubical sliding puzzles that are inspired by the classical 15 Puzzle from the 1880s. In our puzzles, on a $d$-dimensional cube, a labeled token can be slid from one vertex to another if it is topologically free to move on lower-dimensional faces. We analyze the solvability of these puzzles by studying how the puzzle graph changes with the number of labeled tokens vs empty vertices. We give characterizations of the different regimes ranging from being completely stuck (and thus all puzzles unsolvable) to having only one giant component where almost all puzzles can be solved. For the Cube, the Tesseract, and the Penteract ($5$-dimensional cube) we have implemented an algorithm to completely analyze their solvability and we provide specific puzzles for which we know the minimum number of moves needed to solve them., Comment: 21 pages, 5 figures, 6 tables

In this note we study a conjecture by Jer\'onimo-Castro, Magazinov and Sober\'on which generalized a question posed by Dol'nikov. Let $F_1,F_2,\dots,F_n$ be families of translates of a convex compact set $K$ in the plane so that each two sets from distinct families intersect. We show that, for some $j$, $\bigcup_{i\neq j}F_i$ can be pierced by at most $4$ points. To do so, we use previous ideas from Gomez-Navarro and Rold\'an-Pensado together with an approximation result closely tied to the Banach-Mazur distance to the square.

Developing a thermodynamic theory of computation is a challenging task at the interface of non-equilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times, unidirectional (possibly deterministic) transitions, and restricted initial conditions, features common in real-world computers. Here, we present a framework which tackles all such difficulties by extending the martingale theory of non-equilibrium thermodynamics to generic non-stationary Markovian processes, including those with broken detailed balance and/or absolute irreversibility. We derive several universal fluctuation relations and second-law-like inequalities that provide both lower and upper bounds on the intrinsic dissipation (mismatch cost) associated with any periodic process -- in particular the periodic processes underlying all current digital computation. Crucially, these bounds apply even if the process has stochastic stopping times, as it does in many computational machines. We illustrate our results with exhaustive numerical simulations of deterministic finite automata (DFA) processing bit strings, one of the fundamental models of computation from theoretical computer science. We also provide universal equalities and inequalities for the acceptance probability of words of a given length by a deterministic finite automaton in terms of thermodynamic quantities, and outline connections between computer science and stochastic resetting. Our results, while motivated from the computational context, are applicable far more broadly., Comment: 24 + 8 pages, 10 figures; v2: minor changes, references added; v3: presentation improved, extra appendix added, footnotes and references added