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A fundamental question in the field of molecular computation is what computational tasks a biochemical system can carry out. In this work, we focus on the problem of finding the maximum likelihood estimate (MLE) for log-affine models. We revisit a construction due to Gopalkrishnan of a mass-action system with the MLE as its unique positive steady state, which is based on choosing a basis for the kernel of the design matrix of the model. We extend this construction to allow for any finite spanning set of the kernel, and explore how the choice of spanning set influences the dynamics of the resulting network, including the existence of boundary steady states, the deficiency of the network, and the rate of convergence. In particular, we prove that using a Markov basis as the spanning set guarantees global stability of the MLE steady state., Comment: 22 pages, 2 figures. Comments welcome!

The sequential execution of actions and their hierarchical structure consisting of different levels of abstraction, provide features that remain unexplored in the task of action recognition. In this study, we present a novel approach to improve action recognition by exploiting the hierarchical organization of actions and by incorporating contextualized textual information, including location and prior actions to reflect the sequential context. To achieve this goal, we introduce a novel transformer architecture tailored for action recognition that utilizes both visual and textual features. Visual features are obtained from RGB and optical flow data, while text embeddings represent contextual information. Furthermore, we define a joint loss function to simultaneously train the model for both coarse and fine-grained action recognition, thereby exploiting the hierarchical nature of actions. To demonstrate the effectiveness of our method, we extend the Toyota Smarthome Untrimmed (TSU) dataset to introduce action hierarchies, introducing the Hierarchical TSU dataset. We also conduct an ablation study to assess the impact of different methods for integrating contextual and hierarchical data on action recognition performance. Results show that the proposed approach outperforms pre-trained SOTA methods when trained with the same hyperparameters. Moreover, they also show a 17.12% improvement in top-1 accuracy over the equivalent fine-grained RGB version when using ground-truth contextual information, and a 5.33% improvement when contextual information is obtained from actual predictions.

Cognitive decline is a natural part of aging, often resulting in reduced cognitive abilities. In some cases, however, this decline is more pronounced, typically due to disorders such as Alzheimer's disease. Early detection of anomalous cognitive decline is crucial, as it can facilitate timely professional intervention. While medical data can help in this detection, it often involves invasive procedures. An alternative approach is to employ non-intrusive techniques such as speech or handwriting analysis, which do not necessarily affect daily activities. This survey reviews the most relevant methodologies that use deep learning techniques to automate the cognitive decline estimation task, including audio, text, and visual processing. We discuss the key features and advantages of each modality and methodology, including state-of-the-art approaches like Transformer architecture and foundation models. In addition, we present works that integrate different modalities to develop multimodal models. We also highlight the most significant datasets and the quantitative results from studies using these resources. From this review, several conclusions emerge. In most cases, the textual modality achieves the best results and is the most relevant for detecting cognitive decline. Moreover, combining various approaches from individual modalities into a multimodal model consistently enhances performance across nearly all scenarios.

In recent years, nanosatellites have revolutionized the space sector due to their significant economic and time-saving advantages. As a result, they have fostered the testing of advanced instruments intended for larger space science missions. The case of MELISA is presented in this work. MELISA is a magnetic measurement instrument which aims at demonstrating the in-orbit performance of AMR sensors featuring dedicated noise reduction techniques at sub-millihertz frequencies. Such low frequency ranges are relevant for future space-borne gravitational wave detectors, where the local magnetic environment of the satellite might yield a significant contribution to the overall noise budget of the observatory. The demanding magnetic noise levels required for this bandwidth, down to 0.1 mHz, make measurements arduous. To explore sensing solutions within the H2020 European Commission Programme with the involvement of ESA, the functional performance of MELISA-III will be validated in-orbit. During operations, there is the possibility to measure the low-frequency magnetic contribution stemming from orbiting the Earth's magnetic field, impeding the characterization of the intrinsic performance of the sensor. With the objective of minimizing excess noise during the in-flight operations, the present research aims to simulate the environmental magnetic conditions in LEO to identify and subtract undesired contributions to the measurements. The in-orbit long-term magnetic fluctuations are replicated using a Helmholtz coil system. A fluxgate magnetometer allows the correlation of the generated field with the payload measurements, leading to the subsequent subtraction. Proving the effect of this approach will facilitate the noise characterization of magnetic sensors in LEO, paving the way for the in-orbit validation of MELISA-III for use in magnetically demanding missions with long integration times.

VSG control has emerged as a crucial technology for integrating renewable energy sources. However, renewable energy have limited tolerance to overcurrent, necessitating the implementation of current limiting (CL)strategies to mitigate the overcurrent. The introduction of different CL strategies can have varying impacts on the system. While previous studies have discussed the effects of different CL strategies on the system, but they lack intuitive and explicit explanations. Meanwhile, previous CL strategy have failed to effectively ensure the stability of the system. In this paper, the Equal Proportional Area Criterion (EPAC) method is employed to intuitively explain how different CL strategies affect transient stability. Based on this, an effective current limiting strategy is proposed. Simulations are conducted in MATLAB/Simulink to validate the proposed strategy. The simulation results demonstrate that, the proposed effective CL strategy exhibits superior stability., Comment: 2024 IEEE Energy Conversion Congress and Exposition (ECCE)

The generalized SU(2) Proca theory is a vector-tensor modified gravity theory characterized by an action that remains invariant under both diffeomorphisms and global internal transformations of the SU(2) group. This study aims to further explore the physical properties of the theory within astrophysical contexts. Previous investigations have unveiled intriguing astrophysical solutions, including particle-like configurations and black holes. The purpose of this work is to constrain the theory's free parameters by modeling realistic neutron stars. To that end, we have assumed solutions that are static, spherically symmetric, and have adopted the t'Hooft-Polyakov magnetic monopole configuration for the vector fields. Employing both analytical techniques, such as asymptotic expansions, and numerical methods involving solving boundary value problems, we have obtained neutron star solutions whose baryonic matter is described by realistic equations of state for nuclear matter. Furthermore, we have constructed mass-radius relations which reveal that neutron stars exhibit greater compactness in comparison with general relativity predictions for most of the solutions we have found and for the employed equations of state. Finally, we have found out solutions where the mass of the star is greater than $\sim$ 2.5 $M_\odot$; this result poses an alternative in the exploration of the mass gap of compact stellar objects., Comment: LaTeX file in RevTeX 4.1 style, 14 pages, 9 figures

Polynomial neural networks have been implemented in a range of applications and present an advantageous framework for theoretical machine learning. A polynomial neural network of fixed architecture and activation degree gives an algebraic map from the network's weights to a set of polynomials. The image of this map is the space of functions representable by the network. Its Zariski closure is an affine variety known as a neurovariety. The dimension of a polynomial neural network's neurovariety provides a measure of its expressivity. In this work, we introduce the notion of the activation threshold of a network architecture which expresses when the dimension of a neurovariety achieves its theoretical maximum. In addition, we prove expressiveness results for polynomial neural networks with equi-width~architectures., Comment: 13 pages

In the Seat Arrangement problem the goal is to allocate agents to vertices in a graph such that the resulting arrangement is optimal or fair in some way. Examples include an arrangement that maximises utility or one where no agent envies another. We introduce two new ways of calculating the utility that each agent derives from a given arrangement, one in which agents care only about their most preferred neighbour under a given arrangement, and another in which they only care about their least preferred neighbour. We also present a new restriction on agent's preferences, namely 1-dimensional preferences. We give algorithms, hardness results, and impossibility results for these new types of utilities and agents' preferences. Additionally, we refine previous complexity results, by showing that they hold in more restricted settings., Comment: 18 pages

Cognitive decline is a natural process that occurs as individuals age. Early diagnosis of anomalous decline is crucial for initiating professional treatment that can enhance the quality of life of those affected. To address this issue, we propose a multimodal model capable of predicting Mild Cognitive Impairment and cognitive scores. The TAUKADIAL dataset is used to conduct the evaluation, which comprises audio recordings of clinical interviews. The proposed model demonstrates the ability to transcribe and differentiate between languages used in the interviews. Subsequently, the model extracts audio and text features, combining them into a multimodal architecture to achieve robust and generalized results. Our approach involves in-depth research to implement various features obtained from the proposed modalities., Comment: GitHub repository: https://github.com/davidorp/taukadial

Let $Z$ and $X$ be Banach spaces. Suppose that $X$ is Asplund. Let $\mathcal{M}$ be a bounded set of operators from $Z$ to $X$ with the following property: a bounded sequence $(z_n)_{n\in \mathbb{N}}$ in $Z$ is weakly null if, for each $M \in \mathcal{M}$, the sequence $(M(z_n))_{n\in \mathbb{N}}$ is weakly null. Let $(z_n)_{n\in \mathbb{N}}$ be a sequence in $Z$ such that: (a) for each $n\in \mathbb{N}$, the set $\{M(z_n):M\in \mathcal{M}\}$ is relatively norm compact; (b) for each sequence $(M_n)_{n\in \mathbb{N}}$ in $\mathcal{M}$, the series $\sum_{n=1}^\infty M_n(z_n)$ is weakly unconditionally Cauchy. We prove that if $T\in \mathcal{M}$ is Dunford-Pettis and $\inf_{n\in \mathbb{N}}\|T(z_n)\|\|z_n\|^{-1}>0$, then the series $\sum_{n=1}^\infty T(z_n)$ is absolutely convergent. As an application, we provide another proof of the fact that a countably additive vector measure taking values in an Asplund Banach space has finite variation whenever its integration operator is Dunford-Pettis.

Every electron crystallography experiment is fundamentally limited by radiation damage. Nevertheless, little is known about the onset and progression of radiolysis in beam-sensitive molecular crystals. Here we apply ambient-temperature scanning nanobeam electron diffraction to record simultaneous dual-space snapshots of organic and organometallic nanocrystals at sequential stages of beam-induced radiolytic decay. We show that the underlying mosaic of coherently diffracting zones (CDZs) continuously undergoes spatial reorientation as a function of accumulating electron exposure, causing the intensities of many Bragg reflections to fade nonmonotonically. Furthermore, we demonstrate that repeated irradiation at a single probe position leads to the concentric propagation of delocalized radiolytic damage well beyond the initial point of impact. These results sharpen our understanding of molecular crystals as conglomerates of CDZs whose complex lattice structure deteriorates through a series of dynamic internal changes during exposure to ionizing radiation., Comment: Download TeX Source to see supplementary movies. Associated 4D-STEM data available in Zenodo repository 10387146

Generating human-human motion interactions conditioned on textual descriptions is a very useful application in many areas such as robotics, gaming, animation, and the metaverse. Alongside this utility also comes a great difficulty in modeling the highly dimensional inter-personal dynamics. In addition, properly capturing the intra-personal diversity of interactions has a lot of challenges. Current methods generate interactions with limited diversity of intra-person dynamics due to the limitations of the available datasets and conditioning strategies. For this, we introduce in2IN, a novel diffusion model for human-human motion generation which is conditioned not only on the textual description of the overall interaction but also on the individual descriptions of the actions performed by each person involved in the interaction. To train this model, we use a large language model to extend the InterHuman dataset with individual descriptions. As a result, in2IN achieves state-of-the-art performance in the InterHuman dataset. Furthermore, in order to increase the intra-personal diversity on the existing interaction datasets, we propose DualMDM, a model composition technique that combines the motions generated with in2IN and the motions generated by a single-person motion prior pre-trained on HumanML3D. As a result, DualMDM generates motions with higher individual diversity and improves control over the intra-person dynamics while maintaining inter-personal coherence., Comment: Project page: https://pabloruizponce.github.io/in2IN/

Let $\nu$ be a countably additive vector measure defined on a $\sigma$-algebra and taking values in a Banach space. In this paper we deal with the following three properties for the Banach lattice $L_1(\nu)$ of all $\nu$-integrable real-valued functions: the Dunford-Pettis property, the positive Schur property and being lattice-isomorphic to an AL-space. We give new results and we also provide alternative proofs of some already known ones.

Let $\nu$ be a vector measure defined on a $\sigma$-algebra $\Sigma$ and taking values in a Banach space. We prove that if $\nu$ is homogeneous and $L_1(\nu)$ is non-separable, then there is a vector measure $\tilde{\nu}:\Sigma \to c_0(\kappa)$ such that $L_1(\nu)=L_1(\tilde{\nu})$ with equal norms, where $\kappa$ is the density character of $L_1(\nu)$. This is a non-separable version of a result of [G.P. Curbera, Pacific J. Math. 162 (1994), no. 2, 287--303].

In the last quarter of a century, algebraic statistics has established itself as an expanding field which uses multilinear algebra, commutative algebra, computational algebra, geometry, and combinatorics to tackle problems in mathematical statistics. These developments have found applications in a growing number of areas, including biology, neuroscience, economics, and social sciences. Naturally, new connections continue to be made with other areas of mathematics and statistics. This paper outlines three such connections: to statistical models used in educational testing, to a classification problem for a family of nonparametric regression models, and to phase transition phenomena under uniform sampling of contingency tables. We illustrate the motivating problems, each of which is for algebraic statistics a new direction, and demonstrate an enhancement of related methodologies., Comment: This research was performed while the authors were visiting the Institute for Mathematical and Statistical Innovation (IMSI), which is supported by the National Science Foundation (Grant No. DMS-1929348). We participated in the long program "Algebraic Statistics and Our Changing World"

The differences on the thermal behavior (DTA-TG) of mica samples measured before and after sonication have been studied. Sonication treatment produces important modifications in the thermal behavior of muscovite and biotite samples. For muscovite, it produces a broadening and decrease in temperature of the dehydroxylation and crystallization effects, reaching a steady stage after 40 h treatment time. For biotite, the original single peak profile for the dehydroxylation of the untreated sample is converted into a two peaks profile after sonication, the intensity of the low temperature peak increases with sonication time, while the intensity of the high temperature peak decreases. The modification of the thermal behavior for sonicated samples has been correlated to the particle size distribution effect produced by the sonication treatment. It has been also observed that the cup tip of the sonication equipment contaminates the samples releasing titanium of its composition

In recent years many novel applications have appeared that promote the provision of services and activities in a collaborative manner. The key idea behind such systems is to take advantage of idle or underused capacities of existing resources, in order to provide improved services that assist people in their daily tasks, with additional functionality, enhanced efficiency, and/or reduced cost. Particularly in the domain of urban transportation, many researchers have put forward novel ideas, which are then implemented and evaluated through prototypes that usually draw upon AI methods and tools. However, such proposals also bring up multiple non-technical issues that need to be identified and addressed adequately if such systems are ever meant to be applied to the real world. While, in practice, legal and ethical aspects related to such AI-based systems are seldomly considered in the beginning of the research and development process, we argue that they not only restrict design decisions, but can also help guiding them. In this manuscript, we set out from a prototype of a taxi coordination service that mediates between individual (and autonomous) taxis and potential customers. After representing key aspects of its operation in a semi-structured manner, we analyse its viability from the viewpoint of current legal restrictions and constraints, so as to identify additional non-functional requirements as well as options to address them. Then, we go one step ahead, and actually modify the existing prototype to incorporate the previously identified recommendations. Performing experiments with this improved system helps us identify the most adequate option among several legally admissible alternatives.

Object pose estimation is a core perception task that enables, for example, object grasping and scene understanding. The widely available, inexpensive and high-resolution RGB sensors and CNNs that allow for fast inference based on this modality make monocular approaches especially well suited for robotics applications. We observe that previous surveys on object pose estimation establish the state of the art for varying modalities, single- and multi-view settings, and datasets and metrics that consider a multitude of applications. We argue, however, that those works' broad scope hinders the identification of open challenges that are specific to monocular approaches and the derivation of promising future challenges for their application in robotics. By providing a unified view on recent publications from both robotics and computer vision, we find that occlusion handling, novel pose representations, and formalizing and improving category-level pose estimation are still fundamental challenges that are highly relevant for robotics. Moreover, to further improve robotic performance, large object sets, novel objects, refractive materials, and uncertainty estimates are central, largely unsolved open challenges. In order to address them, ontological reasoning, deformability handling, scene-level reasoning, realistic datasets, and the ecological footprint of algorithms need to be improved., Comment: Accepted for publication in Transactions on Robotics: https://ieeexplore.ieee.org/document/10609560 arXiv admin note: substantial text overlap with arXiv:2302.11827

With the increasing diversity of use cases of large language models, a more informative treatment of texts seems necessary. An argumentative analysis could foster a more reasoned usage of chatbots, text completion mechanisms or other applications. However, it is unclear which aspects of argumentation can be reliably identified and integrated in language models. In this paper, we present an empirical assessment of the reliability with which different argumentative aspects can be automatically identified in hate speech in social media. We have enriched the Hateval corpus (Basile et al. 2019) with a manual annotation of some argumentative components, adapted from Wagemans (2016)'s Periodic Table of Arguments. We show that some components can be identified with reasonable reliability. For those that present a high error ratio, we analyze the patterns of disagreement between expert annotators and errors in automatic procedures, and we propose adaptations of those categories that can be more reliably reproduced., Comment: 9 Pages plus reference and appendix

We make use of multiplicative degree-based topological indices $X_\Pi(G)$ to perform a detailed analytical and statistical study of random networks $G=(V(G),E(G))$. We consider two classes of indices: $X_\Pi(G) = \prod_{u \in V(G)} F_V(d_u)$ and $X_\Pi(G) = \prod_{uv \in E(G)} F_E(d_u,d_v)$, where $uv$ denotes the edge of $G$ connecting the vertices $u$ and $v$, $d_u$ is the degree of the vertex $u$, and $F_V(x)$ and $F_E(x,y)$ are functions of the vertex degrees. Specifically, we find analytical inequalities involving these multiplicative indices. Also, we apply $X_\Pi(G)$ on three models of random networks: Erd\"os-R\'enyi networks, random geometric graphs, and bipartite random networks. We show that $\left< \ln X_\Pi(G) \right>$, normalized to the order of the network, scale with the corresponding average degree; here $\left< \cdot \right>$ denotes the average over an ensemble of random networks., Comment: 19 pages, 7 figures

We survey recent applications of topology and singularity theory in the study of the algebraic complexity of concrete optimization problems in applied algebraic geometry and algebraic statistics., Comment: comments are very welcome!

Object pose estimation is important for object manipulation and scene understanding. In order to improve the general applicability of pose estimators, recent research focuses on providing estimates for novel objects, that is objects unseen during training. Such works use deep template matching strategies to retrieve the closest template connected to a query image. This template retrieval implicitly provides object class and pose. Despite the recent success and improvements of Vision Transformers over CNNs for many vision tasks, the state of the art uses CNN-based approaches for novel object pose estimation. This work evaluates and demonstrates the differences between self-supervised CNNs and Vision Transformers for deep template matching. In detail, both types of approaches are trained using contrastive learning to match training images against rendered templates of isolated objects. At test time, such templates are matched against query images of known and novel objects under challenging settings, such as clutter, occlusion and object symmetries, using masked cosine similarity. The presented results not only demonstrate that Vision Transformers improve in matching accuracy over CNNs, but also that for some cases pre-trained Vision Transformers do not need fine-tuning to do so. Furthermore, we highlight the differences in optimization and network architecture when comparing these two types of network for deep template matching.

We give a sufficient condition for a pair of Banach spaces $(X,Y)$ to have the following property: whenever $W_1 \subseteq X$ and $W_2 \subseteq Y$ are sets such that $\{x\otimes y: \, x\in W_1, \, y\in W_2\}$ is weakly precompact in the projective tensor product $X \widehat{\otimes}_\pi Y$, then either $W_1$ or $W_2$ is relatively norm compact. For instance, such a property holds for the pair $(\ell_p,\ell_q)$ if $1

We prove some results on weakly almost square Banach spaces and their relatives. On the one hand, we discuss weak almost squareness in the setting of Banach function spaces. More precisely, let $(\Omega,\Sigma)$ be a measurable space, let $E$ be a Banach lattice and let $\nu:\Sigma \to E^+$ be a non-atomic countably additive measure having relatively norm compact range. Then the space $L_1(\nu)$ is weakly almost square. This result applies to some abstract Ces\`{a}ro function spaces. Similar arguments show that the Lebesgue-Bochner space $L_1(\mu,Y)$ is weakly almost square for any Banach space~$Y$ and for any non-atomic finite measure~$\mu$. On the other hand, we make some progress on the open question of whether there exists a locally almost square Banach space which fails the diameter two property. In this line we prove that if $X$ is any Banach space containing a complemented isomorphic copy of~$c_0$, then for every $0<\varepsilon<1$ there exists an equivalent norm $|\cdot|$ on~$X$ satisfying: (i)~every slice of the unit ball $B_{(X,|\cdot|)}$ has diameter~$2$; (ii) $B_{(X,|\cdot|)}$ contains non-empty relatively weakly open subsets of arbitrarily small diameter; and (iii)~$(X,|\cdot|)$ is $(r,s)$-SQ for all $0

The Generalized SU(2) Proca theory is a vector-tensor theory of gravity whose action is invariant under global transformations of the SU(2) group and includes second-order derivative self-interactions of the vector field beyond the massive Yang-Mills theory. We find that the presence of two Lagrangian pieces consisting of four gauge fields minimally coupled to gravity gives rise to an exact Reissner-Nordstr\"{o}m black hole solution endowed with two different non-Abelian effective charges that depend on the specific combination, $\chi = 2\chi_1 + \chi_2$, of the respective coupling constants. After studying the spacetime structure of the black hole, some astrophysical implications of the black hole solutions are investigated. First, joint analysis of observations of the EHT's first images of Sagittarius A$^{\star}$ of our Galaxy set the first serious constraint on the free parameters of the theory beyond the theoretical bounds found. Second, we investigate the accretion properties of spherical steady flows around this class of non-Abelian Reissner-Nordstr\"{o}m black hole. Specifically, we examine the general conditions under which transonic flow is allowed. Analytical solution for critical accretion is found in terms of the coupling constant. In addition, we explore numerically the effect of changing $\chi$ on the radial velocity and mass density, and show how the extremal Reissner-Nordstr\"{o}m and the standard Schwarzschild solutions as limit cases are achieved. Finally, working in the fully relativistic regime, an analytical expression for the critical mass accretion rate of a polytropic fluid onto a black hole is derived. As a main result, we find that the critical accretion rate efficiency can be noticeably improved compared to the Schwarzschild case for a specific region of the parameter space where the non-Abelian charge becomes imaginary., Comment: 18 pages, 8 figures. Typos fixed, introduction extended to match published version

The generalized SU(2) Proca theory is a vector-tensor modified gravity theory where the action is invariant under both diffeomorphisms and global internal transformations of the SU(2) group. This work constitutes the first approach to investigate the physical properties of the theory at astrophysical scales. We have found solutions that naturally generalize the particle-like solutions of the Einstein-Yang-Mills equations, also known as gauge boson stars. Under the requirement that the solutions must be static, asymptotically flat, and globally regular, the t'Hooft-Polyakov magnetic monopole configuration for the vector field rises as one viable possibility. The solutions have been obtained analytically through asymptotic expansions and numerically by solving the boundary value problem. We have found new features in the solutions such as regions with negative effective energy density and imaginary effective charge. We have also obtained a new kind of globally charged solutions for some region in the parameter space of the theory. Furthermore, we have constructed equilibrium sequences and found turning points in some cases. These results hint towards the existence of stable solutions which are absent in the Einstein-Yang-Mills case., Comment: LaTeX file in RevTeX 4.1 style, 21 pages, 13 figures. v2: Minor clarifications added. Conclusions unchanged. v3: Some other clarifications, an appendix, and two figures added. Conclusions unchanged. Version published in Journal of Cosmology and Astroparticle Physics