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We classify the faces of copositive and completely positive cones over a second-order cone and investigate their dimension and exposedness properties. Then we compute two parameters related to chains of faces of both cones. At the end, we discuss some possible extensions of the results with a view toward analyzing the facial structure of general copositive and completely positive cones.

A convex cone is said to be projectionally exposed (p-exposed) if every face arises as a projection of the original cone. It is known that, in dimension at most four, the intersection of two p-exposed cones is again p-exposed. In this paper we construct two p-exposed cones in dimension $5$ whose intersection is not p-exposed. This construction also leads to the first example of an amenable cone that is not projectionally exposed, showing that these properties, which coincide in dimension at most $4$, are distinct in dimension $5$. In order to achieve these goals, we develop a new technique for constructing arbitrarily tight inner convex approximations of compact convex sets with desired facial structure. These inner approximations have the property that all proper faces are extreme points, with the exception of a specific exposed face of the original set., Comment: 21 pages, 2 figures

A convex cone $\mathcal{K}$ is said to be homogeneous if its group of automorphisms acts transitively on its relative interior. Important examples of homogeneous cones include symmetric cones and cones of positive semidefinite (PSD) matrices that follow a sparsity pattern given by a homogeneous chordal graph. Our goal in this paper is to elucidate the facial structure of homogeneous cones and make it as transparent as the faces of the PSD matrices. We prove that each face of a homogeneous cone $\mathcal{K}$ is mapped by an automorphism of $\mathcal{K}$ to one of its finitely many so-called principal faces. Furthermore, constructing such an automorphism can be done algorithmically by making use of a generalized Cholesky decomposition. Among other consequences, we give a proof that homogeneous cones are projectionally exposed, which strengthens the previous best result that they are amenable. Using our results, we will carefully analyze the facial structure of cones of PSD matrices satisfying homogeneous chordality and discuss consequences for the corresponding family of PSD completion problems., Comment: 29 pages. Comments welcome

The fate of the Fermi surface in bulk electron-doped Sr$_{2}$IrO$_{4}$ remains elusive, as does the origin and extension of its pseudogap phase. Here, we use high-resolution angle-resolved photoelectron spectroscopy (ARPES) to investigate the electronic structure of Sr$_{2-x}$La$_{x}$IrO$_{4}$ up to $x=0.2$, a factor of two higher than in previous work. Our findings reveal that the Fermi surface evolves smoothly with doping. Notably, the antinodal pseudogap persists up to the highest doping level, while nodal quasiparticle coherence increases monotonously. This demonstrates that the sharp increase in Hall carrier density recently observed above $x^{*}=0.16$ [Y.-T. Hsu et al., Nature Physics 20, 1596 (2024)] cannot be attributed to the closure of the pseudogap. Further, we determine a temperature boundary of the pseudogap of $T^{*}\simeq~200~\textrm{K}$ for $x=0.2$, comparable to cuprates. Our results suggest that pseudogaps are a generic feature of doped quasi-2D antiferromagnetic Mott insulators, likely related to short range magnetic correlations., Comment: 8 pages, 3 figures. Supplementary Information: 3 pages, 3 figures

In this article, we study the FitzHugh-Nagumo $(1,1)$--fast-slow system where the vector fields associated to the slow/fast equations come from the reduction of the Hodgin-Huxley model for the nerve impulse. After deriving dynamical properties of the singular and regular cases, we perform a bifurcation analysis and we investigate how the parameters (of the affine slow equation) impact the dynamics of the system. The study of codimension one bifurcations and the numerical locus of canards concludes this case-study. All theoretical results are numerically illustrated.

The two-dimensional electron gas (2DEG) found in KTaO3-based interfaces has garnered attention due to its remarkable electronic properties. In this study, we investigated the conducting system embedded at the Si3N4/Al//KTO(110) heterostructure. We demonstrate that the Al/KTO interface supports a conducting system, with the Si3N4 passivation layer acting as a barrier to oxygen diffusion, enabling ex-situ characterization. Our findings reveal that the mobility and carrier density of the system can be tuned by varying the Al layer thickness. Using scanning transmission electron microscopy, electron energy-loss spectroscopy, X-ray photoemission spectroscopy, and time-of-flight secondary ion mass spectrometry, we characterized the structural and chemical composition of the interface. We found that the Al layer fully oxidizes into AlOx, drawing oxygen from the KTaO3 substrate. The oxygen depletion zone extends 3-5 nm into the substrate and correlates to the Al thickness. Heterostructures with thicker Al layers exhibit higher carrier densities but lower mobilities, likely due to interactions with the oxygen vacancies that act as scattering centers. These findings highlight the importance of considering the effect and extent of the oxygen depletion zone when designing and modeling two-dimensional electron systems in complex oxides.

In this article, we study a two-parameter family of rotating rank-one maps defined on $\textbf{S}^1\times [1, 1+b]\times \textbf{S}^1$, with $b\gtrsim 0$, whose dynamics is characterised by a coupling of a family of planar maps exhibiting rank-one strange attractors and an Arnold family of circle maps. The main result is about the dynamics on the skew-product, which is governed by the existence and prevalence of strange attractors in the corresponding resonance tongues of the Arnold family. The strange attractors carry the unique physical measure of the system, which determines the behaviour of Lebesgue-almost all initial conditions. This phenomenon can be considered as the transition dynamics from a strange attractor with one positive Lyapunov exponent to hyperchaos. Besides an analytical rigorous proof, we illustrate the main results with numerical simulations. We also conjecture how persistent hyperchaos can be obtained., Comment: 28 pages

We introduce the notion of Karamata regular operators, which is a notion of regularity that is suitable for obtaining concrete convergence rates for common fixed point problems. This provides a broad framework that includes, but goes beyond, H\"olderian error bounds and H\"older regular operators. By concrete, we mean that the rates we obtain are explicitly expressed in terms of a function of the iteration number $k$ instead, of say, a function of the iterate $x^k$. While it is well-known that under H\"olderian-like assumptions many algorithms converge linearly/sublinearly (depending on the exponent), little it is known when the underlying problem data does not satisfy H\"olderian assumptions, which may happen if a problem involves exponentials and logarithms. Our main innovation is the usage of the theory of regularly varying functions which we showcase by obtaining concrete convergence rates for quasi-cylic algorithms in non-H\"olderian settings. This includes certain rates that are neither sublinear nor linear but sit somewhere in-between, including a case where the rate is expressed via the Lambert W function. Finally, we connect our discussion to o-minimal geometry and show that definable operators in any o-minimal structure are always Karamata regular., Comment: 44 pages, comments welcome

We discuss the problem of projecting a point onto an arbitrary hyperbolicity cone from both theoretical and numerical perspectives. While hyperbolicity cones are furnished with a generalization of the notion of eigenvalues, obtaining closed form expressions for the projection operator as in the case of semidefinite matrices is an elusive endeavour. To address that we propose a Frank-Wolfe method to handle this task and, more generally, strongly convex optimization over closed convex cones. One of our innovations is that the Frank-Wolfe method is actually applied to the dual problem and, by doing so, subproblems can be solved in closed-form using minimum eigenvalue functions and conjugate vectors. To test the validity of our proposed approach, we present numerical experiments where we check the performance of alternative approaches including interior point methods and an earlier accelerated gradient method proposed by Renegar. We also show numerical examples where the hyperbolic polynomial has millions of monomials. Finally, we also discuss the problem of projecting onto p-cones which, although not hyperbolicity cones in general, are still amenable to our techniques., Comment: 41 pages, some typo fixes. Comments welcome

The spread of microbial infections is governed by the self-organization of bacteria on surfaces. Limitations of live imaging techniques make collective behaviors in clinically relevant systems challenging to quantify. Here, novel experimental and image analysis techniques for high-fidelity single-cell segmentation of bacterial colonies are developed. Machine learning-based segmentation models are trained solely using synthetic microscopy images that are processed to look realistic using state-of-the-art image-to-image translation methods, requiring no biophysical modeling. Accurate single-cell segmentation is achieved for densely packed single-species colonies and multi-species colonies of common pathogenic bacteria, even under suboptimal imaging conditions and for both brightfield and confocal laser scanning microscopy. The resulting data provide quantitative insights into the self-organization of bacteria on soft surfaces. Thanks to their high adaptability and relatively simple implementation, these methods promise to greatly facilitate quantitative descriptions of bacterial infections in varied environments., Comment: 12 pages, 5 figures

The starting point of this paper is the computation of minimal hyperbolic polynomials of duals of cones arising from chordal sparsity patterns. From that, we investigate the relation between ranks of homogeneous cones and their minimal polynomials. Along the way, we answer in the negative a question posed in an earlier paper and show examples of homogeneous cones that cannot be realized as rank-one generated (ROG) hyperbolicity cones., Comment: 20 pages, 1 figure. The proof of Theorem 4.6 was simplified, some extra comments on related works by Nakashima were added and some typos were fixed

In this paper, without requiring any constraint qualifications, we establish tight error bounds for the log-determinant cone, which is the closure of the hypograph of the perspective function of the log-determinant function. This error bound is obtained using the recently developed framework based on one-step facial residual functions., Comment: 32 pages, comments welcome

In this paper, we consider copositive cones over symmetric cones and show that they are never facially exposed when the underlying cone has dimension at least 2. We do so by explicitly exhibiting a non-exposed extreme ray. Our result extends the known fact that the cone of copositive matrices over the nonnegative orthant is not facially exposed in general.

This work focuses on trying to understand how the construction of an airline's network is made. For this purpose, the case of Azul was studied, investigating which and how factors affect the decision of this airline to enter domestic routes, in addition to analyzing how the merger of Azul with the regional airline Trip affected the company's network planning. For this, an academic study was conducted using an econometric model to understand the airline's entry model. The results show that Azul's business model is based on connecting new destinations, not yet served by its competitors, to one of its hubs, and consistently avoiding routes or airports dominated by other airlines. Regarding the effects of the merger, the results suggest that Azul moved away from its original entry model, based on JetBlue, to a model more oriented towards regional aviation, entering shorter routes and regional airports., Comment: This article is written in Portuguese

This study aims to discuss the impacts of a low-cost airline on the air transport market and, especially, to present the most recent findings from specialized literature in the field. To this end, various works on this topic, published since 2015, were selected and analyzed. From this analysis, it was possible to categorize the main topics discussed in the papers into five groups: (i) the impacts of a low-cost airline on competing airlines; (ii) impacts on airports; (iii) general impacts on the demand for air transport; (iv) effects on passengers' choice process; and (v) general effects on a geographical region., Comment: This article is written in Portuguese

The service quality of a passenger transport operator can be measured through face-to-face surveys at the terminals or on board. However, the resulting responses may suffer from the influence of the intrinsic aspects of the respondent's personality and emotional context at the time of the interview. This study proposes a methodology to generate and select control variables for these latent psychosituational traits, thus mitigating the risk of omitted variable bias. We developed an econometric model of the determinants of passenger satisfaction in a survey conducted at the largest airport in Latin America, S\~ao Paulo GRU Airport. Our focus was on the role of flight delays in the perception of quality. The results of this study confirm the existence of a relationship between flight delays and the global satisfaction of passengers with airports. In addition, favorable evaluations regarding airports' food/beverage concessions and Wi-Fi services, but not their retail options, have a relevant moderating effect on that relationship. Furthermore, dissatisfaction arising from passengers' interaction with the airline can have negative spillover effects on their satisfaction with the airport. We also found evidence of blame-attribution behavior, in which only delays of internal origin, such as failures in flight management, are significant, indicating that passengers overlook weather-related flight delays. Finally, the results suggest that an empirical specification that does not consider the latent psychosituational traits of passengers produces a relevant overestimation of the absolute effect of flight delays on passenger satisfaction.

Oxide-based two-dimensional electron gases (2DEGs) have generated significant interest due to their potential for discovering novel physical properties. Among these, 2DEGs formed in KTaO3 stand out due to the recently discovered crystal face-dependent superconductivity and large Rashba splitting, both of which hold potential for future oxide electronics devices. In this work, angle-resolved photoemission spectroscopy is used to study the electronic structure of the 2DEG formed at the (110) surface of KTaO3 after deposition of a thin Al layer. Our experiments revealed a remarkable anisotropy in the orbital character of the electron-like dispersive bands, which form a Fermi surface consisting of two elliptical contours with their major axes perpendicular to each other. The measured electronic structure is used to constrain the modeling parameters of self-consistent tight-binding slab calculations of the band structure. In these calculations, an anisotropic Rashba splitting is found with a value as large as 4 meV at the Fermi level along the [-110] crystallographic direction. This large unconventional and anisotropic Rashba splitting is rationalized based on the orbital angular momentum formulation. These findings provide insights into the interpretation of spin-orbitronics experiments and help to constrain models for superconductivity in the KTO(110)-2DEG system.

Let $({\bf P},{\bf D})$ be a primal-dual pair of SDPs with a nonzero finite duality gap. Under such circumstances, ${\bf P}$ and ${\bf D}$ are weakly feasible and if we perturb the problem data to recover strong feasibility, the (common) optimal value function $v$ as a function of the perturbation is not well-defined at zero (unperturbed data) since there are ``two different optimal values'' $v({\bf P})$ and $v({\bf D})$, where $v({\bf P})$ and $v({\bf D})$ are the optimal values of ${\bf P}$ and ${\bf D}$ respectively. Thus, continuity of $v$ is lost at zero though $v$ is continuous elsewhere. Nevertheless, we show that a limiting version ${v_a}$ of $v$ is a well-defined monotone decreasing continuous bijective function connecting $v({\bf P})$ and $v({\bf D})$ with domain $[0, \pi/2]$ under the assumption that both ${\bf P}$ and ${\bf D}$ have singularity degree one. The domain $[0,\pi/2]$ corresponds to directions of perturbation defined in a certain manner. Thus, ${v_a}$ ``completely fills'' the nonzero duality gap under a mild regularity condition. Our result is tight in that there exists an instance with singularity degree two for which ${v_a}$ is not continuous., Comment: 26 pages. Comments welcome

Error bounds are a requisite for trusting or distrusting solutions in an informed way. Until recently, provable error bounds in the absence of constraint qualifications were unattainable for many classes of cones that do not admit projections with known succinct expressions. We build such error bounds for the generalized power cones, using the recently developed framework of one-step facial residual functions. We also show that our error bounds are tight in the sense of that framework. Besides their utility for understanding solution reliability, the error bounds we discover have additional applications to the algebraic structure of the underlying cone, which we describe. In particular we use the error bounds to compute the dimension of the automorphism group for the generalized power cones, and to identify a set of generalized power cones that are self-dual, irreducible, nonhomogeneous, and perfect, Comment: 24 pages, title change, some minor fixes throughout the paper and removed the appendix. Comments welcome

A hyperbolicity cone is said to be rank-one generated (ROG) if all its extreme rays have rank one, where the rank is computed with respect to the underlying hyperbolic polynomial. This is a natural class of hyperbolicity cones which are strictly more general than the ROG spectrahedral cones. In this work, we present a study of the automorphisms of ROG hyperbolicity cones and their derivative relaxations. One of our main results states that the automorphisms of the derivative relaxations are exactly the automorphisms of the original cone fixing a certain direction. As an application, we completely determine the automorphisms of the derivative relaxations of the nonnegative orthant and of the cone of positive semidefinite matrices. More generally, we also prove relations between the automorphisms of a spectral cone and the underlying permutation-invariant set, which might be of independent interest., Comment: 25 pages. Some minor fixes and changes. To appear at the SIAM Journal on Applied Algebra and Geometry

We analyze self-dual polyhedral cones and prove several properties about their slack matrices. In particular, we show that self-duality is equivalent to the existence of a positive semidefinite (PSD) slack. Beyond that, we show that if the underlying cone is irreducible, then the corresponding PSD slacks are not only doubly nonnegative matrices (DNN) but are extreme rays of the cone of DNN matrices, which correspond to a family of extreme rays not previously described. More surprisingly, we show that, unless the cone is simplicial, PSD slacks not only fail to be completely positive matrices but they also lie outside the cone of completely positive semidefinite matrices. Finally, we show how one can use semidefinite programming to probe the existence of self-dual cones with given combinatorics. Our results are given for polyhedral cones but we also discuss some consequences for negatively self-polar polytopes., Comment: 27 pages, 4 figures. Some minor fixes. To appear at the SIAM Journal on Matrix Analysis