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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.

In this paper we analyze and solve eigenvalue programs, which consist of the task of minimizing a function subject to constraints on the "eigenvalues" of the decision variable. Here, by making use of the FTvN systems framework introduced by Gowda, we interpret "eigenvalues" in a broad fashion going beyond the usual eigenvalues of matrices. This allows us to shed new light on classical problems such as inverse eigenvalue problems and also leads to new applications. In particular, after analyzing and developing a simple projected gradient algorithm for general eigenvalue programs, we show that eigenvalue programs can be used to express what we call vanishing quadratic constraints. A vanishing quadratic constraint requires that a given system of convex quadratic inequalities be satisfied and at least a certain number of those inequalities must be tight. As a particular case, this includes the problem of finding a point $x$ in the intersection of $m$ ellipsoids in such a way that $x$ is also in the boundary of at least $\ell$ of the ellipsoids, for some fixed $\ell > 0$. At the end, we also present some numerical experiments., Comment: 19 pages, 2 figures. A few minor changes and new experiments with multiple SDP blocks

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

In semidefinite programming the dual may fail to attain its optimal value and there could be a duality gap, i.e., the primal and dual optimal values may differ. In a striking paper, Ramana proposed a polynomial size extended dual that does not have these deficiencies and yields a number of fundamental results in complexity theory. In this work we walk the reader through a concise and self-contained derivation of Ramana's dual, relying mostly on elementary linear algebra., Comment: To appear, Optimization Letters

We use angle-resolved photoemission to map the Fermi surface and quasiparticle dispersion of bulk-like thin films of SrMoO$_3$ grown by pulsed laser deposition. The electronic self-energy deduced from our data reveals weak to moderate correlations in SrMoO$_3$, consistent with our observation of well-defined electronic states over the entire occupied band width. We further introduce spectral function calculations that combine dynamical mean-field theory with an unfolding procedure of density functional calculations and demonstrate good agreement of this approach with our experiments.

We prove tight H\"olderian error bounds for all $p$-cones. Surprisingly, the exponents differ in several ways from those that have been previously conjectured; moreover, they illuminate $p$-cones as a curious example of a class of objects that possess properties in 3 dimensions that they do not in 4 or more. Using our error bounds, we analyse least squares problems with $p$-norm regularization, where our results enable us to compute the corresponding KL exponents for previously inaccessible values of $p$. Another application is a (relatively) simple proof that most $p$-cones are neither self-dual nor homogeneous. Our error bounds are obtained under the framework of facial residual functions, and we expand it by establishing for general cones an optimality criterion under which the resulting error bound must be tight., Comment: 37 pages, comments welcome. To appear at Mathematics of Operations Research

Amenability is a notion of facial exposedness for convex cones that is stronger than being facially dual complete (or "nice") which is, in turn, stronger than merely being facially exposed. Hyperbolicity cones are a family of algebraically structured closed convex cones that contain all spectrahedral cones (linear sections of positive semidefinite cones) as special cases. It is known that all spectrahedral cones are amenable. We establish that all hyperbolicity cones are amenable. As part of the argument, we show that any face of a hyperbolicity cone is a hyperbolicity cone. As a corollary, we show that the intersection of two hyperbolicity cones, not necessarily sharing a common relative interior point, is a hyperbolicity cone., Comment: 11 pages. v2: added Section 3.2 giving an explicit description of the span of a face and Section 3.3 giving concrete examples. Minor edits throughout

Amenability is a geometric property of convex cones that is stronger than facial exposedness and assists in the study of error bounds for conic feasibility problems. In this paper we establish numerous properties of amenable cones, and investigate the relationships between amenability and other properties of convex cones, such as niceness and projectional exposure. We show that the amenability of a compact slice of a closed convex cone is equivalent to the amenability of the cone, and prove several results on the preservation of amenability under intersections and other convex operations. It then follows that homogeneous, doubly nonnegative and other cones that can be represented as slices of the cone of positive semidefinite matrices, are amenable. It is known that projectionally exposed cones are amenable and that amenable cones are nice, however the converse statements have been open questions. We construct an example of a four-dimensional cone that is nice but not amenable. We also show that amenable cones are projectionally exposed in dimensions up to and including four. We conclude with a discussion on open problems related to facial structure of convex sets that we came across in the course of this work, but were not able to fully resolve., Comment: 30 pages, 4 figures, comments welcome. To appear in SIAM Journal on Optimization

We construct a general framework for deriving error bounds for conic feasibility problems. In particular, our approach allows one to work with cones that fail to be amenable or even to have computable projections, two previously challenging barriers. For the purpose, we first show how error bounds may be constructed using objects called one-step facial residual functions. Then, we develop several tools to compute these facial residual functions even in the absence of closed form expressions for the projections onto the cones. We demonstrate the use and power of our results by computing tight error bounds for the exponential cone feasibility problem. Interestingly, we discover a natural example for which the tightest error bound is related to the Boltzmann-Shannon entropy. We were also able to produce an example of sets for which a H\"{o}lderian error bound holds but the supremum of the set of admissible exponents is not itself an admissible exponent., Comment: 39 pages, comments welcome. In this version, we simplified the error bound framework and also obtained a better error bound result for products of exponential cones

We report optical brain imaging using a semi-transparent organic light-emitting diode (OLED) based on the orange light-emitting polymer (LEP) Livilux PDO-124. The OLED serves as a compact, extended light source which is capable of uniformly illuminating the cortical surface when placed across a burr hole in the skull. Since all layers of the OLED are substantially transparent to photons with energies below the optical gap of the LEP, light emitted or reflected by the cortical surface may be efficiently transmitted through the OLED and into the objective lens of a low magnification microscope ('macroscope'). The OLED may be placed close to the cortical surface, providing efficient coupling of incident light into the brain cavity; furthermore, the macroscope may be placed close to the upper surface of the OLED, enabling efficient collection of reflected/emitted light from the cortical surface. Hence the use of a semi-transparent OLED simplifies the optical setup, while at the same time maintaining high sensitivity. The OLED is applied here to one of the most demanding forms of optical brain imaging, namely extrinsic optical imaging involving a voltage sensitive dye (VSD). Specifically, we carry out functional imaging of the primary visual cortex (V1) of a rat, using the voltage sensitive dye RH-1691 as a reporter. Imaging through the OLED light-source, we are able to resolve small (~ 0.1 %) changes in the fluorescence intensity of the dye due to changes in the neuronal membrane potential following a visual stimulus. Results are obtained on a single trial basis -- i.e. without averaging over multiple measurements -- with a time-resolution of ten milliseconds., Comment: Main article plus supporting information

The Johnson-Lindenstrauss Lemma states that there exist linear maps that project a set of points of a vector space into a space of much lower dimension such that the Euclidean distance between these points is approximately preserved. This lemma has been previously used to prove that we can randomly aggregate, using a random matrix whose entries are drawn from a zero-mean sub-Gaussian distribution, the equality constraints of an Linear Program (LP) while preserving approximately the value of the problem. In this paper we extend these results to the inequality case by introducing a random matrix with non-negative entries that allows to randomly aggregate inequality constraints of an LP while preserving approximately the value of the problem. By duality, the approach we propose allows to reduce both the number of constraints and the dimension of the problem while obtaining some theoretical guarantees on the optimal value. We will also show an extension of our results to certain semidefinite programming instances.

We consider primal-dual pairs of semidefinite programs and assume that they are ill-posed, i.e., both primal and dual are either weakly feasible or weakly infeasible. Under such circumstances, strong duality may break down and the primal and dual might have a nonzero duality gap. Nevertheless, there are arbitrary small perturbations to the problem data which makes the perturbed primal-dual pair strongly feasible thus zeroing the duality gap. In this paper, we conduct an asymptotic analysis of the optimal value as the perturbation is driven to zero. Specifically, we fix two positive definite matrices (typically the identity matrices), and shift the associated affine spaces of the primal and dual slightly in the direction of the two positive definite matrices possibly in a different proportion so that the perturbed problems have interior feasible solutions, and analyze the behavior of the optimal value of the perturbed problem when the perturbation is reduced to zero keeping the proportion. A key feature of our analysis is that no further assumptions such as compactness or constraint qualifications are ever made. It will be shown that the optimal value of the perturbed problem converges to a value between the primal and dual optimal values of the original problem. Finally, the analysis leads us to the relatively surprising consequence that the infeasible interior-point algorithms for SDP generates a sequence converging to a number between the primal and dual optimal values, even in the presence of a nonzero duality gap. We expect that this property might be particularly useful in solving mixed integer SDPs with infeasible interior-point methods., Comment: This is a thoroughly revised version to improve readability. A detailed analysis on interior-point algorithms is added, though the main results are unchanged

We report high-resolution angle resolved photoemission measurements on single crystals of Pt2HgSe3 grown by high-pressure synthesis. Our data reveal a gapped Dirac nodal line whose (001)-projection separates the surface Brillouin zone in topological and trivial areas. In the non-trivial $k$-space range we find surface states with multiple saddle-points in the dispersion resulting in two van Hove singularities in the surface density of states. Based on density functional theory calculations, we identify these surface states as signatures of a topological crystalline state which coexists with a weak topological phase.

Two-dimensional electron gases (2DEGs) in oxides show great potential for discovering new physical phenomena and at the same time hold promise for electronic applications. In this work we use angle resolved photoemission to determine the electronic structure of a 2DEG stabilized in the (111)-oriented surface of the strong spin orbit coupling material KTaO3. Our measurements reveal multiple sub-bands that emerge as a consequence of quantum confinement and form a six-fold symmetric Fermi surface. This electronic structure is well reproduced by self-consistent tight-binding supercell calculations. Based on these calculations we determine the spin and orbital texture of the 2DEG. We show that the 2DEG Fermi surface is derived from bulk J = 3/2 states and exhibits an unconventional anisotropic Rashba-like lifting of the spin-degeneracy. Spin-momentum locking holds only for high symmetry directions and a strong out-of-plane spin component renders the spin-texture three-fold symmetric. We find that the average spin-splitting on the Fermi surface is an order of magnitude larger than in SrTiO3, which should translate into an enhancement in the spin-orbitronic response of (111)-KTaO3 2DEG based devices., Comment: This is the submitted version of the published manuscript before peer-review