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For a group $\Gamma$, a $\Gamma$-labelled graph is an undirected graph $G$ where every orientation of an edge is assigned an element of $\Gamma$ so that opposite orientations of the same edge are assigned inverse elements. A path in $G$ is non-null if the product of the labels along the path is not the neutral element of $\Gamma$. We prove that for every finite group $\Gamma$, non-null $S$-$T$ paths in $\Gamma$-labelled graphs exhibit the half-integral Erd\H{o}s-P\'osa property. More precisely, there is a function $f$, depending on $\Gamma$, such that for every $\Gamma$-labelled graph $G$, subsets of vertices $S$ and $T$, and integer $k$, one of the following objects exists: a family $\cal F$ consisting of $k$ non-null $S$-$T$ paths in $G$ such that every vertex of $G$ participates in at most two paths of $\cal F$; or a set $X$ consisting of at most $f(k)$ vertices that meets every non-null $S$-$T$ path in $G$. This in particular proves that in undirected graphs $S$-$T$ paths of odd length have the half-integral Erd\H{o}s-P\'osa property., Comment: 12 pages, 1 figure

We propose an algorithm to identify numerically periodic solutions of high-dimensional dynamical systems and their local stability properties. One of the most popular approaches is the Harmonic Balance Method (HBM), which expresses the cycle as a sum of Fourier modes and analyses its stability using the Hill's method. A drawback of Hill's method is that the relevant Floquet exponents have to be chosen from all the computed exponents. To overcome this problem the current work discusses the application of Chebyshev polynomials to the description of the time dependence of the periodic dynamics. The stability characteristics of the periodic orbit are directly extracted from the linearisation around the periodic orbit. The method is compared with the HBM with examples from Lorenz and Langford systems. The main advantage of the present method is that, unlike HBM, it allows for an unambiguous determination of the Floquet exponents. The method is applied to natural convection in a differentially heated cavity which demonstrates its potential for large scale problems arising from the discretisation of the incompressible Navier-Stokes equations.

While fields like Artificial Life have made huge strides in quantifying the mechanisms that distinguish living systems from non-living ones, particular mechanisms remain difficult to reproduce in silico. Known as open-endedness, we've been successful in finding mechanisms that generate new states, but have been less successful in finding mechanisms that generate new rules. Here, we weigh whether or not analyzing the effects of internal and external system constraints on a system's dynamics would be a fruitful avenue to understanding open-endedness. We discuss the connection between physical constraints and the ways that the system can physically reach possible states while those constraints are present. It seems that the physical constraints that define biological objects (and dynamics) are maintained by dynamics that occur from within the system. This is in opposition to current modeling approaches where system constraints are maintained externally. We suggest that constraints can be characterized as variables whose values are either completely conserved, quasi-conserved, or conditionally conserved. Regardless of whether or not a constrained variable is a part of the biological object or present in the object's environment, we discuss how the accessible system states under that constraint can lead to local, emergent conservation laws (rules), with examples. Finally, we discuss the possible benefits of formally understanding how system constraints that emerge from within a system lead to system dynamics that can be characterized as new, emergent rules -- particularly for artificial intelligence, hybrid life, embodiment, astrobiology, and more. Understanding how new, local rules might emerge from within the system is crucial for understanding how open-ended systems continually discover new update rules, in addition to continually discovering new states., Comment: 8 pages, 2 figures, Accepted for oral presentation at IEEE WCCI 2024

Artificial Life (ALife) as an interdisciplinary field draws inspiration and influence from a variety of perspectives. Scientific progress crucially depends, then, on concerted efforts to invite cross-disciplinary dialogue. The goal of this paper is to revitalize discussions of potential connections between the fields of Computational Creativity (CC) and ALife, focusing specifically on the concept of Open-Endedness (OE); the primary goal of CC is to endow artificial systems with creativity, and ALife has dedicated much research effort into studying and synthesizing OE and artificial innovation. However, despite the close proximity of these concepts, their use so far remains confined to their respective communities, and their relationship is largely unclear. We provide historical context for research in both domains, and review the limited work connecting research on creativity and OE explicitly. We then highlight specific questions to be considered, with the eventual goals of (i) decreasing conceptual ambiguity by highlighting similarities and differences between the concepts of OE and creativity, (ii) identifying synergy effects of a research agenda that encompasses both concepts, and (iii) establishing a dialogue between ALife and CC research., Comment: 11 pages, accepted for publication in the proceedings of the 2024 International Conference for Artificial Life, Copenhagen, Denmark

Rotor-stator flows are known to exhibit instabilities in the form of circular and spiral rolls. While the spirals are known to emanate from a supercritical Hopf bifurcation, the origin of the circular rolls is still unclear. In the present work we suggest a quantitative scenario for the circular rolls as a response of the system to external forcing. We consider two types of axisymmetric forcing: bulk forcing (based on the resolvent analysis) and boundary forcing using direct numerical simulation. Using the singular value decomposition of the resolvent operator the optimal response is shown to take the form of circular rolls. The linear gain curve shows strong amplification at non-zero frequencies following a pseudo-resonance mechanism. The optimal energy gain is found to grow rapidly with the Reynolds number (based on the rotation rate and interdisc spacing $H$) in connection with huge levels of non-normality. The results for both types of forcing are compared with former experimental works and previous numerical studies. Our findings suggest that the circular rolls observed experimentally are the combined effect of the high forcing gain and the roll-like form of the leading response of the linearised operator. For high enough Reynolds number it is possible to delineate between linear and nonlinear response. For sufficiently strong forcing amplitudes, the nonlinear response is consistent with the self-sustained states found recently for the unforced problem. The onset of such non-trivial dynamics is shown to correspond in state space to a deterministic leaky attractor, as in other subcritical wall-bounded shear flows.

Reflectance Confocal Microscopy (RCM) is a non-invasive imaging technique used in biomedical research and clinical dermatology. It provides virtual high-resolution images of the skin and superficial tissues, reducing the need for physical biopsies. RCM employs a laser light source to illuminate the tissue, capturing the reflected light to generate detailed images of microscopic structures at various depths. Recent studies explored AI and machine learning, particularly CNNs, for analyzing RCM images. Our study proposes a segmentation strategy based on textural features to identify clinically significant regions, empowering dermatologists in effective image interpretation and boosting diagnostic confidence. This approach promises to advance dermatological diagnosis and treatment.

Highly-doped graphene samples show the conductance reduced and the shot-noise power enhanced compared to standard ballistic systems in two-dimensional electron gas. These features can be understood within a model assuming incoherent scattering of Dirac electrons between two interfaces separating the sample and the leads. Here we find, by adopting the above-mentioned model for the edge-free (Corbino) geometry and by means of the computer simulation of quantum transport, that another graphene-specific feature should be observable when the current flow through a doped disk is blocked by high magnetic field. In case the conductance drops to zero, the Fano factor approaches the value of $F\approx{}0.56$, with a very weak dependence on the disk radii ratio. The role of finite source-drain voltages and the system behavior upon tuning the electrostatic potential barrier from a rectangular to parabolic shape are also discussed., Comment: RevTeX, 15 pages, 7 figures

A recently formulated thermal model for hadron production in heavy-ion collisions in the few-GeV energy regime is combined with the idea that some part of protons and neutrons present in the original thermal system forms deuterons via the coalescence mechanism. Using realistic parametrizations of the freeze-out conditions, which reproduce well the spectra of protons and pions, we make predictions for deuteron transverse-momentum and rapidity spectra. The best agreement with the experimentally known deuteron yield is obtained if the freeze-out temperature is relatively high and, accordingly, the system size at freeze-out is rather small. In addition, the standard Gaussian distribution of the relative distance between nucleons is replaced by the distribution resulting from their independent and approximately uniform production inside the initial thermal system., Comment: 23 pages, 7 figures

Rotor-stator cavity flows are known to exhibit unsteady flow structures in the form of circular and spiral rolls. While the origin of the spirals is well understood, that of the circular rolls is not. In the present study the axisymmetric flow in an aspect ratio $R/H=10$ cavity is revisited {numerically using recent concepts and tools from bifurcation theory}. It is confirmed that a linear instability takes place at a finite critical Reynolds number $Re=Re_c$, and that there exists a subcritical branch of large amplitude chaotic solutions. This motivates the search for subcritical finite-amplitude solutions. The branch of periodic states born in a Hopf bifurcation at $Re=Re_c$, identified using a Self-Consistent Method (SCM) and arclength continuation, is found to be supercritical. The associated solutions only exist, however, in a very narrow range of $Re$ and do not explain the subcritical chaotic rolls. Another subcritical branch of periodic solutions is found using the Harmonic Balance Method with an initial guess obtained by SCM. In addition, edge states separating the steady laminar and chaotic regimes are identified using a bisection algorithm. These edge states are bi-periodic in time for most values of $Re$, {where} their dynamics is {analysed in detail}. Both solution branches fold around at approximately the same value of $Re$, which is lower than $Re_c$ yet still larger than the values reported in experiments. This suggests that, at least in the absence of external forcing, sustained chaotic rolls have their origin in the bifurcations from these unstable solutions.

Recognizing symmetries in data allows for significant boosts in neural network training. In many cases, however, the underlying symmetry is present only in an idealized dataset, and is broken in the training data, due to effects such as arbitrary and/or non-uniform detector bin edges. Standard approaches, such as data augmentation or equivariant networks fail to represent the nature of the full, broken symmetry. We introduce a novel data-augmentation scheme that respects the true underlying symmetry and avoids artifacts by augmenting the training set with transformed pre-detector examples whose detector response is then resimulated. In addition, we encourage the network to treat the augmented copies identically, allowing it to learn the broken symmetry. While the technique can be extended to other symmetries, we demonstrate its application on rotational symmetry in particle physics calorimeter images. We find that neural networks trained with pre-detector rotations converge to a solution more quickly than networks trained with standard post-detector augmentation, and that networks modified to encourage similar internal treatment of augmentations of the same input converge even faster.

Acknowledging the reality of streaming languages and platforms overlapping with SQL and database systems, in 2019 INCTIS Data Management established an Expert Group with the focused mission to initiate the process of standardizing streaming support in SQL. Over time, the roster included companies like Actian, Alibaba, Amazon Web Services, Confluent, dbt Labs, Google, Hazelcast, IBM, Materialize, Microsoft, Oracle, Snowflake, SQLstream and Timeplus. For the span of more than one year, representatives of each company have presented key features of their streaming product or, in some cases, multiple streaming products. These were live technical Q&A sessions accompanied by summary or position papers, which are unquestionably valuable. As expected, substantial time was spent in clarifying what common terms meant in each system and setting up a glossary. These sessions were followed by clarification notes and debates, and decisions that appeared mandatory to allow further progress. This first phase was followed by the next phase, which consisted of the group meetings, in which the expert group (EG) agreed on main exit criteria topics that a streaming solution in SQL must address, and position papers and follow-ups were written and discussed. This paper summarizes these group efforts, up to the summer of 2023.

This paper describes the joint effort of Brno University of Technology (BUT), AGH University of Krakow and University of Buenos Aires on the development of Automatic Speech Recognition systems for the CHiME-7 Challenge. We train and evaluate various end-to-end models with several toolkits. We heavily relied on Guided Source Separation (GSS) to convert multi-channel audio to single channel. The ASR is leveraging speech representations from models pre-trained by self-supervised learning, and we do a fusion of several ASR systems. In addition, we modified external data from the LibriSpeech corpus to become a close domain and added it to the training. Our efforts were focused on the far-field acoustic robustness sub-track of Task 1 - Distant Automatic Speech Recognition (DASR), our systems use oracle segmentation., Comment: 6 pages, Chime-7 challenge 2023

Prompt engineering is crucial for deploying LLMs but is poorly understood mathematically. We formalize LLM systems as a class of discrete stochastic dynamical systems to explore prompt engineering through the lens of control theory. We offer a mathematical analysis of the limitations on the controllability of self-attention as a function of the singular values of the parameter matrices. We present complementary empirical results on the controllability of a panel of LLMs, including Falcon-7b, Llama-7b, and Falcon-40b. Given initial state $\mathbf x_0$ from Wikitext and prompts of length $k \leq 10$ tokens, we find that the "correct" next token is reachable at least 97% of the time, and that the top 75 most likely next tokens are reachable at least 85% of the time. Intriguingly, short prompt sequences can dramatically alter the likelihood of specific outputs, even making the least likely tokens become the most likely ones. This control-theoretic analysis of LLMs demonstrates the significant and poorly understood role of input sequences in steering output probabilities, offering a foundational perspective for enhancing language model system capabilities., Comment: 28 pages, 10 figures

We present the application of the physics-informed neural network (PINN) approach in Bayesian formulation. We have adopted the Bayesian neural network framework to obtain posterior densities from Laplace approximation. For each model or fit, the evidence is computed, which is a measure that classifies the hypothesis. The optimal solution is the one with the highest value of evidence. We have proposed a modification of the Bayesian algorithm to obtain hyperparameters of the model. We have shown that within the Bayesian framework, one can obtain the relative weights between the boundary and equation contributions to the total loss. Presented method leads to predictions comparable to those obtained by sampling from the posterior distribution within the Hybrid Monte Carlo algorithm (HMC). We have solved heat, wave, and Burger's equations, and the results obtained are in agreement with the exact solutions, demonstrating the effectiveness of our approach. In Burger's equation problem, we have demonstrated that the framework can combine information from differential equations and potential measurements. All solutions are provided with uncertainties (induced by the model's parameter dependence) computed within the Bayesian framework., Comment: 22 pages, 12 figures, the description of the method extended, one more example added, improved the numerical analysis

We show that, whenever the perturbations of some field are excited during inflation by a physical process on sub-horizon scales, they unavoidably generate, even through gravitational interactions alone, a significant resonant IR cascade of power down to scales that are of the order of the horizon at that time (we denote these scales as near IR). We provide general analytic one-loop results for the enhancement of the IR power of the curvature perturbation generated by this effect, highlighting the role played by the resonance. We then study a number of examples in which the excited state is: (i) an isocurvature field, (ii) the curvature perturbation itself, (iii) a mixture of curvature and isocurvature fluctuations driven to an excited state by their coupled dynamics. In the cases shown, the cascade significantly modifies the near IR part of the power spectrum of the curvature perturbation with respect to the linear theory, indicating that this effect can impact the phenomenology associated with a variety of mechanisms considered in the literature, notably concerning primordial black holes and gravitational waves., Comment: 37 pages, 5 figures

Thermopower and the Lorentz number for an edge-free (Corbino) graphene disk in the quantum Hall regime is calculated within the Landauer-B\"{u}ttiker formalism. We find, by varying the electrochemical potential, that amplitude of the Seebeck coefficient follows a modified Goldsmid-Sharp relation, in which energy gap is identified with the interval between zero-th and first Landau level in bulk graphene. Analogous relation for the Lorentz number is also determined. Therefore, these thermoelectric properties are solely defined by the magnetic field, temperature, the Fermi velocity in graphene, and fundamental constants including the electrons charge, the Planck and Boltzmann constants, being independent on the system geometric dimensions. This suggests that the Corbino disk in graphene may operate as a thermoelectric thermometer, allowing to determine small temperature difference between two reservoirs, if mean temperature and magnetic field are known., Comment: Minor revisions; Refs. added. Sec.II revised and extended. RevTeX; 11 pages, 7 figures

Computation, if treated as a set of physical processes that act on information represented by states of matter, encompasses biological systems, digital systems, and other constructs, and may be a fundamental measure of living systems. The opportunity for biological computation, represented in the propagation and selection-driven evolution of information-carrying organic molecular structures, has been partially characterized in terms of planetary habitable zones based on primary conditions such as temperature and the presence of liquid water. A generalization of this concept to computational zones is proposed, with constraints set by three principal characteristics: capacity (including computation rates), energy, and instantiation (or substrate, including spatial extent). Computational zones naturally combine traditional habitability factors, including those associated with biological function that incorporate the chemical milieu, constraints on nutrients and free energy, as well as element availability. Two example applications are presented by examining the fundamental thermodynamic work efficiency and Landauer limit of photon-driven biological computation on planetary surfaces and of generalized computation in stellar energy capture structures (a.k.a. Dyson structures). It is suggested that computational zones involving nested structures or substellar objects could manifest unique observational signatures as cool far-infrared emitters. While these latter scenarios are entirely hypothetical, they offer a useful, complementary, introduction to the potential universality of computational zones., Comment: 49 pages, 3 figures, published in The Astrobiology Journal June 2024

Unlike other II-VI semiconductors, CdO-based transparent oxide has great potential application for the fabrication of many optoelectronic devices. In this work, we study the growth of CdxMg1-xO alloys on m- and on c-plane sapphire substrates in Cd-rich to Mg-rich conditions using the plasma-assisted molecular beam epitaxy method. A structural and morphological study of CdMgO random alloys was carried out using X-ray diffraction and Atomic Force Microscope (AFM) techniques whereas composition analysis was done by Energy-dispersive X-ray (EDX) spectroscopy method. The optical properties of thin films were investigated by UV-Vis spectroscopy at room temperature. X-ray analysis confirmed the presence of cubic rock salt structure with <111> CdMgO crystallographic orientation on c-plane sapphire and <110> CdMgO preferential orientation on m-plane sapphire. The surface roughness was measured by the AFM. From the absorption curve, the optical bandgaps were determined using Tauc relation and it was found that the bandgap of films is influenced by the incorporation of Mg2+ ions into the CdO lattice. Bowing parameter was calculated both for samples on m- and c- sapphires., Comment: 19 pages, 11 figures

Here, we report on the characterization of {CdO/ZnO}m superlattice structures (SLs) grown by plasma assisted molecular beam epitaxy. The properties of as-grown and annealed SLs deposited on m-oriented sapphire were investigated by secondary ion mass spectrometry (SIMS) and scanning electron microscopy (SEM) in cathodoluminescence (CL) and energy dispersive X-ray modes. The deformation of the crystallographic structure of SLs was observed after rapid thermal annealing at 900{\deg}C in oxygen flow due to migration and segregation of Cd atoms. SIMS measurements revealed that the distributions of cadmium in the annealed samples depend on the thicknesses of the CdO and ZnO sublayers in the as grown superlattice structures. Depth-resolved CL measurements showed that shifting of the near band edge emission peaks is closely related to the Cd profiles measured with SIMS., Comment: 14 pages, 6 figures