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We apply the phenomenological renormalization group to resting-state fMRI time series of brain activity in a large population. By recursively coarse-graining the data, we compute scaling exponents for the series variance, log probability of silence, and largest covariance eigenvalue. The exponents clearly exhibit linear interdependencies, which we derive analytically in a mean-field approach. We find a significant correlation of exponent values with the gray matter volume and cognitive performance. Akin to scaling relations near critical points in thermodynamics, our findings suggest scaling interdependencies are intrinsic to brain organization and may also exist in other complex systems.

The critical brain hypothesis posits that neural systems operate near a phase transition, optimising the transmission, storage, and processing of information. While scale invariance and non-Gaussian dynamics - hallmarks of criticality - have been observed in brain activity, a direct link between criticality and behavioural performance remains unexplored. Here, we use a phenomenological renormalisation group (PRG) approach to examine neuronal activity in the primary visual cortex of mice performing a visual recognition task. We show that non-trivial scaling in neuronal activity is associated with enhanced task performance, with pronounced scaling observed during successful task completion. When rewards were removed or non-natural stimuli presented, these scaling signatures diminished. These results suggest that critical dynamics in the brain may be crucial for optimising behavioural outcomes, offering new insights into the functional role of criticality in cortical processing.

In this article, we propose novel boundary treatment algorithms to avoid order reduction when implicit-explicit Runge-Kutta time discretization is used for solving convection-diffusion-reaction problems with time-dependent Di\-richlet boundary conditions. We consider Cartesian meshes and PDEs with stiff terms coming from the diffusive parts of the PDE. The algorithms treat boundary values at the implicit-explicit internal stages in the same way as the interior points. The boundary treatment strategy is designed to work with multidimensional problems with possible nonlinear advection and source terms. The proposed methods recover the designed order of convergence by numerical verification. For the spatial discretization, in this work, we consider Local Discontinuous Galerkin methods, although the developed boundary treatment algorithms can operate with other discretization schemes in space, such as Finite Differences, Finite Elements or Finite Volumes.

Hypothesis tests calibrated by (re)sampling methods (such as permutation, rank and bootstrap tests) are useful tools for statistical analysis, at the computational cost of requiring Monte-Carlo sampling for calibration. It is common and almost universal practice to execute such tests with predetermined and large number of Monte-Carlo samples, and disregard any randomness from this sampling at the time of drawing and reporting inference. At best, this approach leads to computational inefficiency, and at worst to invalid inference. That being said, a number of approaches in the literature have been proposed to adaptively guide analysts in choosing the number of Monte-Carlo samples, by sequentially deciding when to stop collecting samples and draw inference. These works introduce varying competing notions of what constitutes "valid" inference, complicating the landscape for analysts seeking suitable methodology. Furthermore, the majority of these approaches solely guarantee a meaningful estimate of the testing outcome, not the $p$-value itself $\unicode{x2014}$ which is insufficient for many practical applications. In this paper, we survey the relevant literature, and build bridges between the scattered validity notions, highlighting some of their complementary roles. We also introduce a new practical methodology that provides an estimate of the $p$-value of the Monte-Carlo test, endowed with practically relevant validity guarantees. Moreover, our methodology is sequential, updating the $p$-value estimate after each new Monte-Carlo sample has been drawn, while retaining important validity guarantees regardless of the selected stopping time. We conclude this paper with a set of recommendations for the practitioner, both in terms of selection of methodology and manner of reporting results.

The "time-and-band limiting" commutative property was found and exploited by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960's, and independently by M. Mehta and later by C. Tracy and H. Widom in Random matrix theory. The property in question is the existence of local operators with simple spectrum that commute with naturally appearing global ones. Here we give a general result that insures the existence of a commuting differential operator for a given family of exceptional orthogonal polynomials satisfying the "bispectral property". As a main tool we go beyond bispectrality and make use of the notion of Fourier Algebras associated to the given sequence of exceptional polynomials. We illustrate this result with two examples, of Hermite and Laguerre type, exhibiting also a nice Perline's form for the commuting differential operator.

Separating C6 cyclic hydrocarbons, specifically benzene and cyclohexane, presents a significant industrial challenge due to their similar physicochemical properties. We conducted Monte Carlo simulations in the Grand-Canonical ensemble to acquire adsorption properties and separation performance data for benzene and cyclohexane in three metal-organic frameworks featuring coordinatively unsaturated metal sites (Ni-MOF-74, Ni-ClBBTA, and Ni-ClBTDD). The separation performance of these MOFs was analyzed and compared with literature data for adsorbents of different natures, demonstrating superior performance. Additionally, we explored the molecular origins of this effective separation, examining the pore-filling mechanism, interaction of guest molecules with metal centers, and mutual interactions of each adsorbate. Our results highlight that the selected adsorbents, with remarkable loading capacity, can efficiently separate both compounds in a mixture with exceptional effectiveness.

Detecting anomalies in large sets of observations is crucial in various applications, such as epidemiological studies, gene expression studies, and systems monitoring. We consider settings where the units of interest result in multiple independent observations from potentially distinct referentials. Scan statistics and related methods are commonly used in such settings, but rely on stringent modeling assumptions for proper calibration. We instead propose a rank-based variant of the higher criticism statistic that only requires independent observations originating from ordered spaces. We show under what conditions the resulting methodology is able to detect the presence of anomalies. These conditions are stated in a general, non-parametric manner, and depend solely on the probabilities of anomalous observations exceeding nominal observations. The analysis requires a refined understanding of the distribution of the ranks under the presence of anomalies, and in particular of the rank-induced dependencies. The methodology is robust against heavy-tailed distributions through the use of ranks. Within the exponential family and a family of convolutional models, we analytically quantify the asymptotic performance of our methodology and the performance of the oracle, and show the difference is small for many common models. Simulations confirm these results. We show the applicability of the methodology through an analysis of quality control data of a pharmaceutical manufacturing process.

Motivated by the problem of detecting a change in the evolution of a network, we consider the preferential attachment random graph model with a time-dependent attachment function. Our goal is to detect whether the attachment mechanism changed over time, based on a single snapshot of the network and without directly observable information about the dynamics. We cast this question as a hypothesis testing problem, where the null hypothesis is a preferential attachment model with a constant affine attachment parameter $\delta_0$, and the alternative hypothesis is a preferential attachment model where the affine attachment parameter changes from $\delta_0$ to $\delta_1$ at an unknown changepoint time $\tau_n$. For our analysis we focus on the regime where $\delta_0$ and $\delta_1$ are fixed, and the changepoint occurs close to the observation time of the network (i.e., $\tau_n = n - c n^\gamma$ with $c>0$ and $\gamma \in (0, 1)$). This corresponds to the relevant scenario where we aim to detect the changepoint shortly after it has happened. We present two tests based on the number of vertices with minimal degree, and show that these are asymptotically powerful when $\tfrac{1}{2}<\gamma<1$. We conjecture that there is no powerful test based on the final network snapshot when $\gamma < \tfrac{1}{2}$. The first test we propose requires knowledge of $\delta_0$. The second test is significantly more involved, and does not require the knowledge of $\delta_0$ while still achieving the same performance guarantees. Furthermore, we prove that the test statistics for both tests are asymptotically normal, allowing for accurate calibration of the tests. This is demonstrated by numerical experiments, that also illustrate the finite sample test properties.

The building climate industry and its influence on energy consumption have consequences on the environment due to the emission of greenhouse gasses. Improving the efficiency of this sector is essential to reduce the effect on climate change. In recent years, the interest in porous materials in applications such as heat pumps has increased for their promising potential. To assess the performance of adsorption heat pumps and cooling systems, here we discuss a multistep approach based on the processing of adsorption data combined with a thermodynamic model. The process provides properties of interest, such as the coefficient of performance, the working capacity, the specific heat or cooling effect, or the released heat upon adsorption and desorption cycles, and it also has the advantage of identifying the optimal conditions for each adsorbent-fluid pair. To test this method, we select several metal-organic frameworks that differ in topology, chemical composition, and pore size, which we validate with available experiments. Adsorption equilibrium curves were calculated using molecular simulations to describe the adsorption mechanisms of methanol and ethanol as working fluids in the selected adsorbents. Then, using a thermodynamic model we calculate the energetic properties combined with iterative algorithms that simultaneously vary all the required working conditions. We discuss the strong influence of operating temperatures on the performance of heat pump devices. Our findings point to the highly hydrophobic metal azolate framework MAF-6 as a very good candidate for heating and cooling applications for its high working capacity and excellent energy efficiency.

Electronic health record (EHR) data are increasingly used to support real-world evidence (RWE) studies. Yet its ability to generate reliable RWE is limited by the lack of readily available precise information on the timing of clinical events such as the onset time of heart failure. We propose a LAbel-efficienT incidenT phEnotyping (LATTE) algorithm to accurately annotate the timing of clinical events from longitudinal EHR data. By leveraging the pre-trained semantic embedding vectors from large-scale EHR data as prior knowledge, LATTE selects predictive EHR features in a concept re-weighting module by mining their relationship to the target event and compresses their information into longitudinal visit embeddings through a visit attention learning network. LATTE employs a recurrent neural network to capture the sequential dependency between the target event and visit embeddings before/after it. To improve label efficiency, LATTE constructs highly informative longitudinal silver-standard labels from large-scale unlabeled patients to perform unsupervised pre-training and semi-supervised joint training. Finally, LATTE enhances cross-site portability via contrastive representation learning. LATTE is evaluated on three analyses: the onset of type-2 diabetes, heart failure, and the onset and relapses of multiple sclerosis. We use various evaluation metrics present in the literature including the $ABC_{gain}$, the proportion of reduction in the area between the observed event indicator and the predicted cumulative incidences in reference to the prediction per incident prevalence. LATTE consistently achieves substantial improvement over benchmark methods such as SAMGEP and RETAIN in all settings., Comment: ERHs data

Let $P$ be a set of $n\geq 2$ points in general position in $R^2$. The edge disjointness graph $D(P)$ of $P$ is the graph whose vertices are all the closed straight line segments with endpoints in $P$, two of which are adjacent in $D(P)$ if and only if they are disjoint. In this note, we give a full characterization of all those edge disjointness graphs that are hamiltonian. More precisely, we shall show that (up to order type isomorphism) there are exactly 8 instances of P for which $D(P)$ is not hamiltonian. Additionally, from one of these 8 instances, we derive a counterexample to a criterion for the existence of hamiltonian cycles due to A. D. Plotnikov in 1998.

In this paper, we study the random dynamical system $f_\omega^n$ generated by a family of maps $\{f_{\omega_0}: \mathbb{S}^1 \to \mathbb{S}^1\}_{\omega_0 \in [-\varepsilon,\varepsilon]},$ $f_{\omega_0}(x) = \alpha \xi (x+\omega_0) +a\ (\mathrm{mod }\ 1),$ where $\xi: \mathbb S^1 \to \mathbb R$ is a non-degenerated map, $a\in [0,1)$, and $\alpha,\varepsilon>0$. Fixing a constant $c\in (0,1)$, we show that for $\alpha$ sufficiently large and for $\varepsilon > \alpha^{-1+c},$ the random dynamical system $f_\omega^n$ presents a random Young tower structure and quenched decay of correlations., Comment: 38 pages, 0 figures

Software Architecture, from definition to maintenance and evolution, is a complex aspect of software development and, consequently, a challenging subject when it comes to teaching it, and learning it. Many research efforts have been devoted to designing teaching approaches, strategies and tools. Most of them, however, focus on the knowledge itself and the ways to convey it to students, rather than on the different learning styles of students themselves. Teaching methods which predominantly rely on verbal and written communication, are very well aligned with some learning styles. However, students with learning styles that benefit more from physical activity or first-hand experience, need to defer to cognitive processes that are less natural to them. In this work, we propose an innovative use of role-playing as teaching strategy for architecture models of reference (i.e. layered, pipe and filter, client-server, etc.). This role-playing of different software architectures, in which students play the part of specific components in the system, intends to complement other classical teaching materials, such as in-person or recorded lectures, lab assignments, or development projects. Addressing all learning styles within a classroom is key to ensure that we favour and foster the students' different learning processes, and give everyone an even playfield in which to best develop their capabilities as Software Architects., Comment: Accepted at 20th IEEE International Conference on Software Architecture (ICSA'23)

We consider online prediction of a binary sequence with expert advice. For this setting, we devise label-efficient forecasting algorithms, which use a selective sampling scheme that enables collecting much fewer labels than standard procedures, while still retaining optimal worst-case regret guarantees. These algorithms are based on exponentially weighted forecasters, suitable for settings with and without a perfect expert. For a scenario where one expert is strictly better than the others in expectation, we show that the label complexity of the label-efficient forecaster scales roughly as the square root of the number of rounds. Finally, we present numerical experiments empirically showing that the normalized regret of the label-efficient forecaster can asymptotically match known minimax rates for pool-based active learning, suggesting it can optimally adapt to benign settings.

We investigate heat transport associated with compositionally-driven convection driven by crystallization at the ocean-crust interface in accreting neutron stars, or growth of the solid core in cooling white dwarfs. We study the effect of thermal diffusion and rapid rotation on the convective heat transport, using both mixing length theory and numerical simulations of Boussinesq convection. We determine the heat flux, composition gradient and P\'eclet number, $\mathrm{Pe}$ (the ratio of thermal diffusion time to convective turnover time) as a function of the composition flux. We find two regimes of convection with a rapid transition between them as the composition flux increases. At small Pe, the ratio between the heat flux and composition flux is independent of Pe,, because the loss of heat from convecting fluid elements due to thermal diffusion is offset by the smaller composition gradient needed to overcome the reduced thermal buoyancy. At large Pe, the temperature gradient approaches the adiabatic gradient, saturating the heat flux. We discuss the implications for neutron star and white dwarf cooling. Convection in neutron stars spans both regimes. We find rapid mixing of neutron star oceans, with a convective turnover time of order weeks to minutes depending on rotation. Except during the early stages of core crystallization, white dwarf convection is in the thermal-diffusion-dominated fingering regime. We find convective velocities much smaller than recent estimates for crystallization-driven dynamos. The small fraction of energy carried as kinetic energy calls into question the effectiveness of crystallization-driven dynamos as an explanation for observed white dwarf magnetic fields., Comment: Accepted for Publication in ApJ (Astrophysical Journal)

Vision Transformers (ViTs) have become a dominant paradigm for visual representation learning with self-attention operators. Although these operators provide flexibility to the model with their adjustable attention kernels, they suffer from inherent limitations: (1) the attention kernel is not discriminative enough, resulting in high redundancy of the ViT layers, and (2) the complexity in computation and memory is quadratic in the sequence length. In this paper, we propose a novel attention operator, called lightweight structure-aware attention (LiSA), which has a better representation power with log-linear complexity. Our operator learns structural patterns by using a set of relative position embeddings (RPEs). To achieve log-linear complexity, the RPEs are approximated with fast Fourier transforms. Our experiments and ablation studies demonstrate that ViTs based on the proposed operator outperform self-attention and other existing operators, achieving state-of-the-art results on ImageNet, and competitive results on other visual understanding benchmarks such as COCO and Something-Something-V2. The source code of our approach will be released online., Comment: 8 pages, 5 figures

We exhibit three examples showing that the "time-and-band limiting" commutative property found and exploited by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960's, and independently by M. Mehta and later by C. Tracy and H. Widom in Random matrix theory, holds for exceptional orthogonal polynomials. The property in question is the existence of local operators with simple spectrum that commute with naturally appearing global ones. We illustrate numerically the advantage of having such a local operator.

In this paper, we consider absorbing Markov chains $X_n$ admitting a quasi-stationary measure $\mu$ on $M$ where the transition kernel $\mathcal P$ admits an eigenfunction $0\leq \eta\in L^1(M,\mu)$. We find conditions on the transition densities of $\mathcal P$ with respect to $\mu$ which ensure that $\eta(x) \mu(\mathrm d x)$ is a quasi-ergodic measure for $X_n$ and that the Yaglom limit converges to the quasi-stationary measure $\mu$-almost surely. We apply this result to the random logistic map $X_{n+1} = \omega_n X_n (1-X_n)$ absorbed at $\mathbb R \setminus [0,1],$ where $\omega_n$ is an i.i.d sequence of random variables uniformly distributed in $[a,b],$ for $1\leq a <4$ and $b>4.$, Comment: 35 pages, 0 figures

While some works have investigated the particle trajectories and stagnation points beneath solitary waves with constant vorticity, little is known about the pressure beneath such waves. To address this gap, we investigate numerically the pressure beneath solitary waves in flows with constant vorticity. Through a conformal mapping that flats the physical domain, we develop a numerical approach that allows to compute the pressure and the velocity field in the fluid domain. Our experiments indicate that there exists a threshold vorticity such that pressure anomalies and stagnation points occur when the intensity of the vorticity is greater than this threshold. Above this threshold the pressure on the bottom boundary has two points of local maxima and there are three stagnation points in the flow, and below it the pressure has one local maximum and there is no stagnation point., Comment: arXiv admin note: substantial text overlap with arXiv:2205.12313

Reducing carbon dioxide emissions has become a must in society, being crucial to find alternatives to supply the energy demand. Adsorption-based cooling and heating technologies are receiving attention for thermal energy storage applications. In this paper, we study the adsorption of polar working fluids in hydrophobic and hydrophilic zeolites by means of experimental quasi-equilibrated temperature-programmed desorption and adsorption combined with Monte Carlo simulations. We measured and computed water and methanol adsorption isobars in high-silica HS-FAU, NaY, and NaX zeolites. We use the experimental adsorption isobars to develop a set of parameters to model the interaction between methanol and the zeolite and cations. Once having the adsorption of these polar molecules, we use a mathematical model based on the potential theory of adsorption of Dubinin-Polanyi to assess the performance of the adsorbate-working fluids for heat storage applications. We found that the use of molecular simulation is an alternative for investigating energy storage applications since we can reproduce, complement, and extend experimental observations. Our results highlight the importance of controlling the hydrophilic/hydrophobic nature of the zeolites by changing the Al content to maximize the working conditions of the heat storage device.

Technological advances in recent years have promoted the development of virtual reality systems that have a wide variety of hardware and software characteristics, providing varying degrees of immersion. Immersion is an objective property of the virtual reality system that depends on both its hardware and software characteristics. Virtual reality systems are currently attempting to improve immersion as much as possible. However, there is no metric to measure the level of immersion of a virtual reality system based on its characteristics. To date, the influence of these hardware and software variables on immersion has only been considered individually or in small groups. The way these system variables simultaneously affect immersion has not been analyzed either. In this paper, we propose immersion metrics for virtual reality systems based on their hardware and software variables, as well as the development process that led to their formulation. From the conducted experiment and the obtained data, we followed a methodology to find immersion models based on the variables of the system. The immersion metrics presented in this work offer a useful tool in the area of virtual reality and immersive technologies, not only to measure the immersion of any virtual reality system but also to analyze the relationship and importance of the variables of these systems.

The study of the Euler equations in flows with constant vorticity has piqued the curiosity of a considerable number of researchers over the years. Much research has been conducted on this subject under the assumption of steady flow. In this work, we provide a numerical approach that allows us to compute solitary waves in flows with constant vorticity and analyse their stability. Through a conformal mapping technique, we compute solutions of the steady Euler equations, then feed them as initial data for the time-dependent Euler equations. We focus on analysing to what extent the steady solitary waves are stable within the time-dependent framework. Our numerical simulations indicate that although it is possible to compute solitary waves for the steady Euler equations in flows with large values of vorticity, such waves are not numerically stable for vorticities with absolute value much greater than one. Besides, we notice that large waves are unstable even for small values of vorticity.