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We study the fundamental properties of pointwise semi-Lipschitz functions between asymmetric spaces, which are the natural asymmetric counterpart of pointwise Lipschitz functions. We also study the influence that partial symmetries of a given space may have on the behavior of pointwise semi-Lipschitz functions defined on it. Furthermore, we are interested in characterizing the pointwise semi-Lipschitz structure of an asymmetric space in terms of real-valued pointwise semi-Lipschitz functions defined on it. By using two algebras of functions naturally associated to our spaces of pointwise real-valued semi-Lipschitz functions, we are able to provide two Banach-Stone type results in this context. In fact, these results are obtained as consequences of a general Banach-Stone type theorem of topological nature, stated for abstract functional spaces, which is quite flexible and can be applied to many spaces of continuous functions over metric and asymmetric spaces., Comment: No additional comments

In this work we investigate the presence of integrable hidden structures in the dynamics of perturbed non-rotating black holes (BHs). This can also be considered as a first step in a wider program of an effective identification of ``slow'' and ``fast'' degrees of freedom (DoFs) in the (binary) BH dynamics, following a wave-mean flow perspective. The slow DoFs would be associated with a nonlinear integrable dynamics, on which the fast ones propagate following an effective linear dynamics. BH perturbation theory offers a natural ground to test these properties. Indeed, the decoupling of Einstein equations into wave master equations with a potential provides an instance of such splitting into (frozen) slow DoFs (background potential) over which the linear dynamics of the fast ones (perturbation master functions) evolve. It has been recently shown that these wave equations possess an infinite number of symmetries that correspond to the flow of the infinite hierarchy of Korteweg-de Vries (KdV) equations. Starting from these results, we systematically investigate the presence of integrable structures in BH perturbation theory. We first study them in Cauchy slices and then extend the analysis to hyperboloidal foliations. This second step introduces a splitting of the master equation into bulk and boundary contributions, unveiling an underlying structural relation with the slow and fast DoFs. This insight represents a first step to establish the integrable structures associated to the slow DoFs as bulk symmetries of the dynamics of perturbed BHs., Comment: 23 pages, comments are welcome

We construct and explore the complex structures of boson stars, drawing inspiration from similar configurations of non-topological solitons in Minkowski space. These "molecular states" of boson stars have a multipolar structure and both positive and negative Noether charges within one star, and the opposite charges swap with time. Thanks to the gravitational attraction, they exist even in the case of a free scalar field. We also explore the effects of scalar self-interactions on these complex structures. We propose to use galactic-scale charge-swapping boson stars as a potential solution to the problem of the observed anisotropic distribution of satellite galaxies., Comment: 25 pages, 23 figures

Curry-Howard correspondences between Linear Logic (LL) and session types provide a firm foundation for concurrent processes. As the correspondences hold for intuitionistic and classic versions of LL (ILL and CLL), we obtain two different families of type systems for concurrency. An open question remains: how do these two families exactly relate to each other? Based upon a translation from CLL to ILL due to Laurent (2018), we provide two complementary answers, in the form of full abstraction results based on a typed observational equivalence due to Atkey (2017). Our results elucidate hitherto missing formal links between seemingly related yet different type systems for concurrency., Comment: Full version, 19 pages + appendices

In this manuscript, we undertake an examination of a classical plasma deployed on two finite co-planar surfaces: a circular region $\Omega_{in}$ into an annular region $\Omega_{out}$ with a gap in between. It is studied both from the point of view of statistical mechanics and the electrostatics of continua media. We employ a dual perspective: the first one is by using Molecular Dynamics (MD) simulations to find the system's positional correlation functions and velocity distributions. That by modeling the system as a classical two-dimensional Coulomb plasma of point-like charged particles $q_1$ and $q_2$ on the layers $\Omega_{in}$ and $\Omega_{out}$ respectively with no background density. The second one corresponds to a finite surface electrode composed of planar metallic layers displayed on the regions $\Omega_{in}$, $\Omega_{out}$ at constant voltages $V_{in}$, $V_{out}$ considering axial symmetry. The surface charge density is calculated by the Method of Moments (MoM) under the electrostatic approximation. Point-like and differential charges elements interact via a $1/r$ - electric potential in both cases. The thermodynamic averages of the number density, and electric potential due to the plasma depend on the coupling and the charge ratio $\xi=q_1/q_2$ once the geometry of the layers is fixed. On the other hand, the fields due to the SE depend on the layer's geometry and their voltage. In the document, is defined a protocol to properly compare the systems. We show that there are values of the coupling parameter, where the thermodynamic averages computed via MD agree with the results of MoM for attractive $\xi=-1$ and repulsive layers $\xi=1$. Keywords: molecular dynamics, method of moments, Coulomb systems, long-range interaction., Comment: 32 pages, 16 Figures

Neutron-Transformer Reflectometry and Advanced Computation Engine (N-TRACE ), a neural network model using transformer architecture, is introduced for neutron reflectometry data analysis. It offers fast, accurate initial parameter estimations and efficient refinements, improving efficiency and precision for real-time data analysis of lithium-mediated nitrogen reduction for electrochemical ammonia synthesis, with relevance to other chemical transformations and batteries. Despite limitations in generalizing across systems, it shows promises for the use of transformers as the basis for models that could replace trial-and-error approaches to modeling reflectometry data., Comment: 11 pages, 7 figures

In this radiation tolerance study, Low Gain Avalanche Detectors (LGADs) with a carbon-enriched broad and shallow multiplication layer were examined in comparison to identical non-carbonated LGADs. Manufactured at IMB-CNM, the sensors underwent neutron irradiation at the TRIGA reactor in Ljubljana, reaching a fluence of $1.5e^{15} {n_{eq}} cm^{-2}$. The results revealed a smaller deactivation of boron and improved resistance to radiation in carbonated LGADs. The study demonstrated the potential benefits of carbon enrichment in mitigating radiation damage effects, particularly the acceptor removal mechanism, reducing the acceptor removal constant by more than a factor of two. Additionally, time resolution and collected charge degradation due to irradiation were observed, with carbonated samples exhibiting better radiation tolerance. A noise analysis focused on baseline noise and spurious pulses showed the presence of thermal-generated dark counts attributed to a too narrow distance between the gain layer end and the p-stop implant at the periphery of the pad for the characterized LGAD design; however, without significant impact of operation performance.

Nanomechanical resonators can serve as ultrasensitive, miniaturized force probes. While vertical structures like nanopillars are ideal for this purpose, transducing their motion is challenging. Pillar-based photonic crystals (PhCs) offer a potential solution by integrating optical transduction within the pillars. However, achieving high-quality PhCs is hindered by inefficient vertical light confinement. Here, we present a full-silicon 1D photonic crystal cavity based on nanopillars as a new platform with great potential for applications in force sensing and biosensing areas. Its unit cell consists of a silicon pillar with larger diameter at its top portion than at the bottom, which allows vertical light confinement and an energy bandgap in the near infrared range for transverse-magnetic (TM) polarization. We experimentally demonstrate optical cavities with Q-factors exceeding 1e3 constructed by inserting a defect within a periodic arrangement of this type of pillars. Given the fact that that each nanopillar naturally behaves as a nanomechanical cantilever, the fabricated geometries are excellent optomechanical (OM) photonic crystal cavities in which the mechanical motion of each nanopillar composing the cavity can be optically transduced. These novel geometries display enhanced mechanical properties, cost-effectiveness, integration possibilities, and scalability, and opens and new path in front of the widely used suspended Si beam OM cavities made on silicon-on-insulator., Comment: Main text: 15 pages, 5 figures Supplementary Information: 8 pages, 6 figures

There is an action of $\mathbb{Z}/2$ on the category of Soergel Bimodules of type $A_1 \times A_1$ induced by the nontrivial automorphism of its Dynkin diagram. We give an isotopy presentation by local generators and relations of the equivariantization of the category of Soergel Bimodules of type $A_1 \times A_1$ under this action. This is the first step in a program to describe and study the categories of equivariant Soergel Bimodules.

We apply an algebraic double copy construction of gravity from gauge theory to three-dimensional (3D) Chern-Simons theory. The kinematic algebra ${\cal K}$ is the 3D de Rham complex of forms equipped, for a choice of metric, with a graded Lie algebra that is equivalent to the Schouten-Nijenhuis bracket on polyvector fields. The double copied gravity is defined on a subspace of ${\cal K}\otimes \bar{\cal K}$ and yields a topological double field theory for a generalized metric perturbation and two 2-forms. This local and gauge invariant theory is non-Lagrangian but can be rendered Lagrangian by abandoning locality. Upon fixing a gauge this reduces to the double copy of Chern-Simons theory previously proposed by Ben-Shahar and Johansson. Furthermore, using complex coordinates in $\mathbb{C}^3$ this theory is related to six-dimensional (6D) Kodaira-Spencer gravity in that truncating the two 2-forms and one equation yields the Kodaira-Spencer equations on a 3D real slice of $\mathbb{C}^3$. The full 6D Kodaira-Spencer theory can instead be obtained as a consistent truncation of a chiral double copy., Comment: 20 pages, second version with added references

Given a hypergraph $\mathcal{H}$, we introduce a new class of evaluation toric codes called edge codes derived from $\mathcal{H}$. We analyze these codes, focusing on determining their basic parameters. We provide estimations for the minimum distance, particularly in scenarios involving $d$-uniform clutters. Additionally, we demonstrate that these codes exhibit self-orthogonality. Furthermore, we compute the minimum distances of edge codes for all graphs with five vertices., Comment: Comments are welcome!

We combine Kirchheim's metric differentials with Cheeger charts in order to establish a non-embeddability principle for any collection $\mathcal C$ of Banach (or metric) spaces: if a metric measure space $X$ bi-Lipschitz embeds in some element in $\mathcal C$, and if every Lipschitz map $X\to Y\in \mathcal C$ is differentiable, then $X$ is rectifiable. This gives a simple proof of the rectifiability of Lipschitz differentiability spaces that are bi-Lipschitz embeddable in Euclidean space, due to Kell--Mondino. Our principle also implies a converse to Kirchheim's theorem: if all Lipschitz maps from a domain space to arbitrary targets are metrically differentiable, the domain is rectifiable. We moreover establish the compatibility of metric and w$^*$-differentials of maps from metric spaces in the spirit of Ambrosio--Kirchheim.

We prove an analog of the wall crossing formula for Welschinger invariants relating the difference of signed curve counting of real curves passing through configurations that differ by a pair of complex conjugated points, and a correspondence Welschinger invariant of the blow up. We prove this analogue for the motivic count of rational curves of fixed degree passing through a generic configuration of points, counted with a motivic multiplicity in the Grothendieck-Witt ring of a base field, extending the notions in the correspondence theorem between motivic invariants for $k$-rational point conditions and tropical curves. We use this formula to compute the degree 4 motivic enumerative invariants of the projective plane counting curves passing through configurations of points defined over quadratic extensions of a base field., Comment: 16 pages, 6 figures; Corrected typos

We demonstrate synthesis of BaZr(S,Se)3 chalcogenide perovskite alloys by selenization of BaZrS3 thin films. The anion-exchange process produces films with tunable composition and band gap without changing the orthorhombic perovskite crystal structure or the film microstructure. The direct band gap is tunable between 1.5 and 1.9 eV. The alloy films made in this way feature 100x stronger photoconductive response and a lower density of extended defects, compared to alloy films made by direct growth. The perovskite structure is stable in high-selenium-content thin films with and without epitaxy. The manufacturing-compatible process of selenization in H2Se gas may spur the development of chalcogenide perovskite solar cell technology.

We report a comparative study of temperature-dependent photoluminescence and structural dynamics of two perovskite semiconductors, the chalcogenide BaZrS$_3$ (BZS) and the halide CsPbBr$_3$ (CPB). These materials have similar crystal structures and direct band gaps, but we find that they have quite distinct optoelectronic and vibrational properties. Both materials exhibit thermally-activated non-radiative recombination, but the non-radiative recombination rate in BZS is between two and four orders of magnitude faster than in CPB. Raman spectroscopy reveals that the effects of phonon anharmonicity are far more pronounced in CPB than in BZS. Further, although both materials feature a large dielectric response due to low-energy polar optical phonons, the phonons in CPB are substantially lower in energy than in BZS. Our results suggest that electron-phonon coupling in BZS is more effective at non-radiative recombination than in CPB, and that BZS may also have a substantially higher concentration of non-radiative recombination centers than CPB. The low defect concentration in CPB may be related to the ease of lattice reconfiguration, typified by anharmonic bonding. It remains to be seen to what extent these differences are inherent to the chalcogenide and halide perovskites and to what extent they can be affected by materials processing; comparing BZS single-crystals and thin films provides reason for optimism., Comment: Main text - 12 pages with 5 figures and 1 table. Supplemental text - 16 pages with 6 figures and 5 tables

We explore the idea of restoring the full diffeomorphism (Diff) invariance in theories with only transverse diffeomorphisms (TDiff) by the introduction of additional fields. In particular, we consider in detail the case of a TDiff invariant scalar field and how Diff symmetry can be restored preserving locality by introducing an additional vector field. We reobtain the corresponding dynamics and energy-momentum tensor from the covariantized action and analyze the potential and kinetic domination regimes. For the former, the theory describes a cosmological constant-type behaviour, while for the latter we show that the theory can describe an adiabatic perfect fluid whose equation of state and speed of sound is obtained in a straightforward way. Furthermore, the reformulation with the full symmetry allows us to analyze the gravitational properties of the theory beyond those particular regimes. In particular, we find the general expression for the effective speed of sound of the non-adiabatic perfect fluid, which provides us with physically reasonable conditions that should be satisfied by the coupling functions. Finally, we investigate the particular models leading to an adiabatic fluid., Comment: V2: 24 pages, new section V, new appendix, new applications, conclusions unchanged, version accepted for publication in PRD. V1: 9 pages, 1 Appendix

6-dimensional superconformal field theories are exotic and fascinating. They emerge from compactifications of F-theory on Calabi-Yau elliptic fibrations, which grants them a rich array of dualities with various other formulations of string and M-theory. In this thesis, we consider extended families of elliptic fibrations, giving rise to 6d theories connected by Higgs transitions. These families not only encompass the moduli space of a specific manifold but also include other manifolds with different topologies. Our investigation focuses on rank 1 6D superconformal field theories from two distinct angles. In Chapter 4, we employ modularity, which arises from the holomorphic anomaly equations, to compute the topological string partition function in terms of Jacobi modular forms. We also provide a prescription for obtaining the topological partition function of a Higgsed theory from its parent. Through this approach, we can explain numerous symmetry enhancements that we observed in our study. On the other hand, in Chapter 5, we explore the 2D soliton of the 6D theory, the non-critical string. The elliptic genus of this non-critical string coincides with a part of the topological string partition function. By carefully studying this non-critical string, we propose an ansatz for the elliptic genera expressed in terms of characters of the associated current algebras. We present compelling evidence supporting the validity of this ansatz and unveil novel closed form expressions for the elliptic genera of these non-critical strings. Through these investigations, we hope to shed light on the intriguing world of 6D superconformal field theories and uncover new insights into their remarkable properties and connections., Comment: Doctoral thesis

To understand its evolution and the effects of its eruptive events, the Sun is permanently monitored by multiple satellite missions. The optically-thin emission of the solar plasma and the limited number of viewpoints make it challenging to reconstruct the geometry and structure of the solar atmosphere; however, this information is the missing link to understand the Sun as it is: a three-dimensional evolving star. We present a method that enables a complete 3D representation of the uppermost solar layer (corona) observed in extreme ultraviolet (EUV) light. We use a deep learning approach for 3D scene representation that accounts for radiative transfer, to map the entire solar atmosphere from three simultaneous observations. We demonstrate that our approach provides unprecedented reconstructions of the solar poles, and directly enables height estimates of coronal structures, solar filaments, coronal hole profiles, and coronal mass ejections. We validate the approach using model-generated synthetic EUV images, finding that our method accurately captures the 3D geometry of the Sun even from a limited number of 32 ecliptic viewpoints ($|\text{latitude}| \leq 7^\circ$). We quantify uncertainties of our model using an ensemble approach that allows us to estimate the model performance in absence of a ground-truth. Our method enables a novel view of our closest star, and is a breakthrough technology for the efficient use of multi-instrument datasets, which paves the way for future cluster missions.

We prove existence of spiral waves in oscillatory media with nonlocal coupling. Our starting point is a nonlocal complex Ginzburg-Landau (cGL) equation, rigorously derived as an amplitude equation for integro-differential equations undergoing a Hopf bifurcation. Because this reduced equation includes higher order terms that are usually ignored in a formal derivation of the cGL, the solutions we find also correspond to solutions of the original nonlocal system. To prove existence of these patterns we use perturbation methods together with the implicit function theorem. Within appropriate parameter regions, we find that spiral wave patterns have wavenumbers, $\kappa$, with expansion $\kappa \sim C e^{-a/\varepsilon}$, where $a$ is a positive constant, $\varepsilon$ is the small bifurcation parameter, and the positive constant $C$ depends on the strength and spread of the nonlocal coupling. The main difficulty we face comes from the linear operators appearing in our system of equations. Due to the symmetries present in the system, and because the equations are posed on the plane, these maps have a zero eigenvalue embedded in their essential spectrum. Therefore, they are not invertible when defined between standard Sobolev spaces and a straightforward application of the implicit function theorem is not possible. We surpass this difficulty by redefining the domain of these operators using doubly weighted Sobolev spaces. These spaces encode algebraic decay/growth properties of functions, near the origin and in the far field, and allow us to recover Fredholm properties for these maps., Comment: 57 pages, 4 figures

The response of any open system is closely related to the complex frequencies of the quasinormal modes (QNMs) of the system. While QNM-based expansion theories in electromagnetism have successfully elucidated the modal physics within resonator boundaries, their application beyond these confines into the surrounding open space has been limited. This limitation stems from the exponential spatial growth, or divergence, of QNM fields beyond resonator boundaries, posing challenges to the completeness of QNM expansions and often leading to misconceptions about modal physics in the open space. We address these challenges by investigating fundamentals, such as first-order perturbation theory and dissipative coupling between distant bodies, shedding light on the implications of the divergence. Our analysis reveals that QNMs are increasingly influenced by perturbers as they move farther away from the resonator body in open space. Furthermore, we demonstrate that the coupling coefficients between QNMs of distant resonators amplify with separation distance, indicating entanglement between their QNMs and challenging our intuition that remote resonators behave independently. These insights, easily understandable, hold significant implications for contemporary developments in QNM electromagnetic theory. They aid in discerning between questionable and promising trends and suggest innovative avenues for QNM expansions across near, intermediate, and far-field zones.

In a modern DBMS, working memory is frequently the limiting factor when processing in-memory analytic query operations such as joins, sorting, and aggregation. Existing resource estimation approaches for a DBMS estimate the resource consumption of a query by computing an estimate of each individual database operator in the query execution plan. Such an approach is slow and error-prone as it relies upon simplifying assumptions, such as uniformity and independence of the underlying data. Additionally, the existing approach focuses on individual queries separately and does not factor in other queries in the workload that may be executed concurrently. In this research, we are interested in query performance optimization under concurrent execution of a batch of queries (a workload). Specifically, we focus on predicting the memory demand for a workload rather than providing separate estimates for each query within it. We introduce the problem of workload memory prediction and formalize it as a distribution regression problem. We propose Learned Workload Memory Prediction (LearnedWMP) to improve and simplify estimating the working memory demands of workloads. Through a comprehensive experimental evaluation, we show that LearnedWMP reduces the memory estimation error of the state-of-the-practice method by up to 47.6%. Compared to an alternative single-query model, during training and inferencing, the LearnedWMP model and its variants were 3x to 10x faster. Moreover, LearnedWMP-based models were at least 50% smaller in most cases. Overall, the results demonstrate the advantages of the LearnedWMP approach and its potential for a broader impact on query performance optimization.

Here, the synthesis of polyglobalide (PGl) by enzymatic ring-opening polymerization (e-ROP) is investigated, using pressurized carbon dioxide (CO2), pressurized CO2 + dichloromethane (DCM), and pressurized propane as solvents. Particularly, the effects of phase equilibrium on the course of e-ROP and PGl final properties are discussed. The partition coefficients of CO2, DCM, propane, globalide and PGl were calculated with help of thermodynamic models, providing proper understanding of monomer partitioning in the reaction system. Reactions performed in pure CO2 resulted in monomer conversions of 100%. Besides, when only one liquid phase was present inside the reactor, PGl samples presented low polydispersities and high average molecular weights. When carried out in CO2 + DCM, e-ROP resulted in lower monomer conversions and PGl samples with higher polydispersities and lower average molecular weights. Finally, reactions carried out in pressurized propane (200 bar) produced PGl samples with the highest average molecular weights among the analyzed products., Comment: 41 pages, 9 figures, 8 tables

Black holes in anti-de Sitter spacetime provide an important testing ground for both gravitational and field-theoretic phenomena. In particular, the study of perturbations can be useful to further our understanding regarding certain physical processes, such as superradiance, or the dynamics of strongly coupled conformal field theories through the holographic principle. In this work we continue our systematic study of the ultraviolet instabilities of black-hole quasinormal modes, built on the characterization of the latter as eigenvalues of a (spectrally unstable) non-selfadjoint operator and using the pseudospectrum as a main analysis tool, extending our previous studies in the asymptotically flat setting to Anti-de Sitter asymptotics. Very importantly, this step provides a singularly well-suited probe into some of the key structural aspects of the pseudospectrum. This is a consequence of the specific features of the Schwarzschild-anti-de Sitter geometry, together with the existence of a sound characterization by Warnick of quasinormal modes as eigenvalues, that is still absent in asymptotic flatness. This work focuses on such structural aspects, with an emphasis on the convergence issues of the pseudospectrum and, in particular, the comparison between the hyperboloidal and null slicing cases. As a physical by-product of this structural analysis we assess, in particular, the spectral stability of purely imaginary ``hydrodynamic" modes, which appear for axial gravitational perturbations, that become dominant when the black-hole horizon is larger than the anti-de Sitter radius. We find that their spectral stability, under perturbations, depends on how close they are to the real axis, or conversely how distant they are from the first oscillatory overtone., Comment: 20 pages, 8 figures; v2 includes minor changes

We formalize the computation of tree-level scattering amplitudes in terms of the homotopy transfer of homotopy algebras, illustrating it with scalar $\phi^3$ and Yang-Mills theory. The data of a (gauge) field theory with an action is encoded in a cyclic homotopy Lie or $L_{\infty}$ algebra defined on a chain complex including a space of fields. This $L_{\infty}$ structure can be transported, by means of homotopy transfer, to a smaller space that, in the massless case, consists of harmonic fields. The required homotopy maps are well-defined since we work with the space of finite sums of plane-wave solutions. The resulting $L_{\infty}$ brackets encode the tree-level scattering amplitudes and satisfy generalized Jacobi identities that imply the Ward identities. We further present a method to compute color-ordered scattering amplitudes for Yang-Mills theory, using that its $L_{\infty}$ algebra is the tensor product of the color Lie algebra with a homotopy commutative associative or $C_{\infty}$ algebra. The color-ordered scattering amplitudes are then obtained by homotopy transfer of $C_{\infty}$ algebras., Comment: 72 pages, v2: introduction improved, references added