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We study upward pointset embeddings (UPSEs) of planar $st$-graphs. Let $G$ be a planar $st$-graph and let $S \subset \mathbb{R}^2$ be a pointset with $|S|= |V(G)|$. An UPSE of $G$ on $S$ is an upward planar straight-line drawing of $G$ that maps the vertices of $G$ to the points of $S$. We consider both the problem of testing the existence of an UPSE of $G$ on $S$ (UPSE Testing) and the problem of enumerating all UPSEs of $G$ on $S$. We prove that UPSE Testing is NP-complete even for $st$-graphs that consist of a set of directed $st$-paths sharing only $s$ and $t$. On the other hand, for $n$-vertex planar $st$-graphs whose maximum $st$-cutset has size $k$, we prove that it is possible to solve UPSE Testing in $O(n^{4k})$ time with $O(n^{3k})$ space, and to enumerate all UPSEs of $G$ on $S$ with $O(n)$ worst-case delay, using $O(k n^{4k} \log n)$ space, after $O(k n^{4k} \log n)$ set-up time. Moreover, for an $n$-vertex $st$-graph whose underlying graph is a cycle, we provide a necessary and sufficient condition for the existence of an UPSE on a given poinset, which can be tested in $O(n \log n)$ time. Related to this result, we give an algorithm that, for a set $S$ of $n$ points, enumerates all the non-crossing monotone Hamiltonian cycles on $S$ with $O(n)$ worst-case delay, using $O(n^2)$ space, after $O(n^2)$ set-up time., Comment: This is the long version of a paper to appear at the 32nd International Symposium on Graph Drawing and Network Visualization (GD '24)

This article presents a neural network approach for estimating the covariance function of spatial Gaussian random fields defined in a portion of the Euclidean plane. Our proposal builds upon recent contributions, expanding from the purely isotropic setting to encompass geometrically anisotropic correlation structures, i.e., random fields with correlation ranges that vary across different directions. We conduct experiments with both simulated and real data to assess the performance of the methodology and to provide guidelines to practitioners.

The ESO public survey VISTA Variables in the V\'ia L\'actea (VVV) surveyed the inner Galactic bulge and the adjacent southern Galactic disk from $2009-2015$. Upon its conclusion, the complementary VVV eXtended (VVVX) survey has expanded both the temporal as well as spatial coverage of the original VVV area, widening it from $562$ to $1700$ sq. deg., as well as providing additional epochs in $JHK_{\rm s}$ filters from $2016-2023$. With the completion of VVVX observations during the first semester of 2023, we present here the observing strategy, a description of data quality and access, and the legacy of VVVX. VVVX took $\sim 2000$ hours, covering about 4% of the sky in the bulge and southern disk. VVVX covered most of the gaps left between the VVV and the VISTA Hemisphere Survey (VHS) areas and extended the VVV time baseline in the obscured regions affected by high extinction and hence hidden from optical observations. VVVX provides a deep $JHK_{\rm s}$ catalogue of $\gtrsim 1.5\times10^9$ point sources, as well as a $K_{\rm s}$ band catalogue of $\sim 10^7$ variable sources. Within the existing VVV area, we produced a $5D$ map of the surveyed region by combining positions, distances, and proper motions of well-understood distance indicators such as red clump stars, RR Lyrae, and Cepheid variables. In March 2023 we successfully finished the VVVX survey observations that started in 2016, an accomplishment for ESO Paranal Observatory upon 4200 hours of observations for VVV+VVVX. The VVV+VVVX catalogues complement those from the Gaia mission at low Galactic latitudes and provide spectroscopic targets for the forthcoming ESO high-multiplex spectrographs MOONS and 4MOST., Comment: 17 pages, 11 figures (+ appendix). Accepted for publication in Astronomy and Astrophysics in section 14: Catalogs and data

From classical knot theory we know that every knot in $S^3$ is the boundary of an oriented, embedded surface. A standard demonstration of this fact achieved by elementary technique comes from taking a regular projection of any knot and employing Seifert's constructive algorithm. In this note we give a natural generalization of Seifert's algorithm to any closed integral homology 3-sphere. The starting point of our algorithm is presenting the handle structure of a Heegaard splitting of a given integral homology sphere as a planar diagram on the boundary of a $3$-ball. (For a well known example of such a planar presentation, see the Poincar\'e homology sphere planar presentation in {\em Knots and Links} by D. Rolfsen \cite{Rolfsen}.) An oriented link can then be represented by the regular projection of an oriented $k$-strand tangle. From there we give a natural way to find a ``Seifert circle" and associated half-twisted bands., Comment: 16 pages, 12 figures

Tantalum films incorporated into superconducting circuits have exhibited low surface losses, resulting in long-lived qubit states. Remaining loss pathways originate in microscopic defects which manifest as two level systems (TLS) at low temperature. These defects limit performance, so careful attention to tantalum film structures is critical for optimal use in quantum devices. In this work, we investigate the growth of tantalum using magnetron sputtering on sapphire, Si, and photoresist substrates. In the case of sapphire, we present procedures for growth of fully-oriented films with alpha-Ta [1 1 1] // Al2O3 [0 0 1] and alpha-Ta [1 -1 0] // Al2O3 [1 0 0] orientational relationships, and having residual resistivity ratios (RRR) ~ 60 for 220 nm thick films. On Si, we find a complex grain texturing with Ta [1 1 0] normal to the substrate and RRR ~ 30. We further demonstrate airbridge fabrication using Nb to nucleate alpha-Ta on photoresist surfaces. Superconducting resonators patterned from films on sapphire show TLS-limited quality factors of 1.4 +/- 0.3 x 10^6 at 10 mK. Structural characterization using scanning electron microscopy, X-ray diffraction, low temperature transport, secondary ion mass spectrometry, and transmission electron microscopy reveal the dependence of residual impurities and screw dislocation density on processing conditions. The results provide practical insights for fabrication of high-performing technological devices including qubit arrays, and guide future work on crystallographically deterministic qubit fabrication.

We consider the Kadomtsev-Petviashvili II (KP) model placed in $\mathbb R_t \times \mathbb R_{x,y}^2$, in the case of smooth data that are not necessarily in a Sobolev space. In this paper, the subclass of smooth solutions we study is of ``soliton type'', characterized by a phase $\Theta=\Theta(t,x,y)$ and a unidimensional profile $F$. In particular, every classical KP soliton and multi-soliton falls into this category with suitable $\Theta$ and $F$. We establish concrete characterizations of KP solitons by means of a natural set of nonlinear differential equations and inclusions of functionals of Wronskian, Airy and Heat types, among others. These functional equations only depend on the new variables $\Theta$ and $F$. A distinct characteristic of this set of functionals is its special and rigid structure tailored to the considered soliton. By analyzing $\Theta$ and $F$, we establish the uniqueness of line-solitons, multi-solitons, and other degenerate solutions among a large class of KP solutions. Our results are also valid for other 2D dispersive models such as the quadratic and cubic Zakharov-Kuznetsov equations., Comment: 46 pp, 1 fig

Large intelligent surface (LIS) has gained momentum as a potential 6G-enabling technology that expands the benefits of massive multiple-input multiple-output (MIMO). On the other hand, orthogonal space-division multiplexing (OSDM) may give a promising direction for efficient exploitation of the spatial resources, analogous as what is achieved with orthogonal frequency-division multiplexing (OFDM) in the frequency domain. To this end, we study how to enforce channels orthogonality in a panel-based LIS scenario. Our proposed method consists of having a subset of active LIS-panels coherently serving a set of users, and another subset of LIS-panels operating in semi-passive mode by implementing a receive and re-transmit (RRTx) process. This results in an inter-symbol interference (ISI) channel, where we characterize the semi-passive processing required to achieve simultaneous orthogonality in time and space. We then employ the remaining degrees of freedom (DoFs) from the orthogonality constraint to minimize the semi-passive processing power, where we derive a closed-form global minimizer, allowing for efficient implementation of the proposed scheme., Comment: 6 pages, 3 figures. This work has been submitted to the IEEE for possible publication, copyright information may be affected upon publication

This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three general algorithms that allow to reconstruct a wide spectrum of random fields having a covariance function that depends on a specific metric, called resistance metric, and proposed in recent literature. The algorithms are applied to a synthetic case study consisting of a street network. They prove to be fast and accurate in that they reproduce the target covariance function and provide random fields whose finite-dimensional distributions are approximately Gaussian.

We envision a future in which multi-antenna technology effectively exploits the spatial domain as a set of non-interfering orthogonal resources, allowing for flexible resource allocation and efficient modulation/demodulation. Reconfigurable intelligent surface (RIS) has emerged as a promising technology which allows shaping the propagation environment for improved performance. This paper studies the ability of three extended types of reconfigurable surface (RS), including the recently proposed beyond diagonal RIS (BD-RIS), to achieve perfectly orthogonal channels in a general multi-user multiple-input multiple-output (MU-MIMO) scenario. We propose practical implementations for the three types of RS consisting of passive components, and obtain the corresponding restrictions on their reconfigurability. We then use these restrictions to derive closed-form conditions for achieving arbitrary (orthogonal) channels. We also study the problem of optimal orthogonal channel selection for achieving high channel gain without active amplification at the RS, and we propose some methods with satisfying performance. Finally, we provide efficient channel estimation and RS configuration techniques such that all the computation, including the channel selection, may be performed at the base station (BS). The numerical results showcase the potential and practicality of RS channel orthogonalization, thus taking a step towards orthogonal spatial domain multiplexing (OSDM)., Comment: 13 pages, 4 figures. This work has been submitted to the IEEE for possible publication, copyright information may be affected upon publication

In geostatistics, block likelihood offers a balance between statistical accuracy and computational efficiency when estimating covariance functions. This balance is reached by dividing the sample into blocks and computing a weighted sum of (sub) log-likelihoods corresponding to pairs of blocks. Practitioners often choose block sizes ranging from hundreds to a few thousand observations, inherently involving matrix-based implementations. An alternative, residing at the opposite end of this methodological spectrum, treats each observation as a block, resulting in the matrix-free pairwise likelihood method. We propose an additional alternative within this broad methodological landscape, systematically constructing blocks of size two and merging pairs of blocks through conditioning. Importantly, our method strategically avoids large-sized blocks, facilitating explicit calculations that ultimately do not rely on matrix computations. Studies with both simulated and real data validate the effectiveness of our approach, on one hand demonstrating its superiority over pairwise likelihood, and on the other, challenging the intuitive notion that employing matrix-based versions universally lead to better statistical performance.

We propose to train neural networks (NNs) using a novel variant of the ``Additively Preconditioned Trust-region Strategy'' (APTS). The proposed method is based on a parallelizable additive domain decomposition approach applied to the neural network's parameters. Built upon the TR framework, the APTS method ensures global convergence towards a minimizer. Moreover, it eliminates the need for computationally expensive hyper-parameter tuning, as the TR algorithm automatically determines the step size in each iteration. We demonstrate the capabilities, strengths, and limitations of the proposed APTS training method by performing a series of numerical experiments. The presented numerical study includes a comparison with widely used training methods such as SGD, Adam, LBFGS, and the standard TR method.

Graph matching is a fundamental problem in pattern recognition, with many applications such as software analysis and computational biology. One well-known type of graph matching problem is graph isomorphism, which consists of deciding if two graphs are identical. Despite its usefulness, the properties that one may check using graph isomorphism are rather limited, since it only allows strict equality checks between two graphs. For example, it does not allow one to check complex structural properties such as if the target graph is an arbitrary length sequence followed by an arbitrary size loop. We propose a generalization of graph isomorphism that allows one to check such properties through a declarative specification. This specification is given in the form of a Regular Graph Pattern (ReGaP), a special type of graph, inspired by regular expressions, that may contain wildcard nodes that represent arbitrary structures such as variable-sized sequences or subgraphs. We propose a SAT-based algorithm for checking if a target graph matches a given ReGaP. We also propose a preprocessing technique for improving the performance of the algorithm and evaluate it through an extensive experimental evaluation on benchmarks from the CodeSearchNet dataset., Comment: Shorter version accepted for publication at AAAI 2024

Reconfigurable surface (RS) has been shown to be an effective solution for improving wireless communication links in general multi-user multiple-input multiple-output (MU-MIMO) setting. Current research efforts have been largely directed towards the study of reconfigurable intelligent surface (RIS), which corresponds to an RS made of passive reconfigurable elements with only phase shifting capabilities. RIS constitutes a cost- and energy- efficient solution for increased beamforming gain since it allows to generate constructive interference towards desired directions, e.g., towards a base station (BS). However, in many situations, multiplexing gain may have greater impact on the achievable transmission rates and number of simultaneously connected devices, while RIS has only been able to achieve minor improvements in this aspect. Recent work has proposed the use of alternative RS technologies, namely amplitude-reconfigurable intelligent surface (ARIS) and fully-reconfigurable intelligent surface (FRIS), to achieve perfect orthogonalization of MU-MIMO channels, thus allowing for maximum multiplexing gain at reduced complexity. In this work we consider the use of ARIS and FRIS for simultaneously orthogonalizing a MU-MIMO channel, while embedding extra information in the orthogonalized channel. We show that the resulting achievable rates allow for full exploitation of the degrees of freedom in a MU-MIMO system with excess of BS antennas., Comment: 6 pages, 2 figures, accepted at IEEE GLOBECOM 2023

With the increase in the number of antennas at base stations (BSs), centralized multi-antenna architectures have encountered scalability problems from excessive interconnection bandwidth to the central processing unit (CPU), as well as increased processing complexity. Thus, research efforts have been directed towards finding decentralized receiver architectures where a part of the processing is performed at the antenna end (or close to it). A recent paper put forth an information-lossless trade-off between level of decentralization (inputs to CPU) and decentralized processing complexity (multiplications per antenna). This trade-off was obtained by studying a newly defined matrix decomposition--the WAX decomposition--which is directly related to the information-lossless processing that should to be applied in a general framework to exploit the trade-off. {The general framework consists of three stages: a set of decentralized filters, a linear combining module, and a processing matrix applied at the CPU; these three stages are linear transformations which can be identified with the three constituent matrices of the WAX decomposition. The previous work was unable to provide explicit constructions for linear combining modules which are valid for WAX decomposition, while it remarked the importance of these modules being sparse with 1s and 0s so they could be efficiently implemented using hardware accelerators.} In this work we present a number of constructions, as well as possible variations of them, for effectively defining linear combining modules which can be used in the WAX decomposition. Furthermore, we show how these structures facilitate decentralized calculation of the WAX decomposition for applying information-lossless processing in architectures with an arbitrary level of decentralization., Comment: 16 pages, 6 figures, accepted for publication at IEEE Transactions on Signal Processing

Covariance functions are a fundamental tool for modeling the dependence structure of spatial processes. This work investigates novel constructions for covariance functions that enable the integration of anisotropies and hole effects in complex and versatile ways, having the potential to provide more accurate representations of dependence structures arising with real-world data. We show that these constructions extend widely used covariance models, including the Mat\'ern, Cauchy, compactly-supported hypergeometric and cardinal sine models. We apply our results to a geophysical data set from a rock-carbonate aquifer and demonstrate that the proposed models yield more accurate predictions at unsampled locations compared to basic covariance models.

Orthogonal multi-user multiple-input multiple-output (MU-MIMO) channels allow for optimum performance with simplified precoding/equalization, and they achieve maximum multiplexing gain which is shared fairly among users. Reconfigurable intelligent surface (RIS) constitutes a promising cost-efficient solution to improve the wireless channel, since they consist of passive reflecting elements able to adjust the phases of the incoming waves. However, it is still widely unclear how these surfaces can improve spatial-multiplexing. In fact, the common RIS model cannot achieve perfect orthogonalization of MU-MIMO channels with a reasonable number of elements. Furthermore, efficient channel estimation algorithms for RIS, which are key for taking advantage of its benefits, are still a matter of research. We study two types of reconfigurable surfaces (RSs), namely amplitude-reconfigurable intelligent surface (ARIS) and fully-reconfigurable intelligent surface (FRIS), with extended capabilities over RIS. We show how these RSs allow for perfect channel orthogonalization, and, by minimizing the applied power, we show that they can potentially be implemented without the need of amplification. We also present an efficient channel estimation method for each of them that allows the base station (BS) to select the desired propagation channel., Comment: Presented at IEEE GLOBECOM Workshops 2022

We study the Voronoi Diagram of Rotating Rays, a Voronoi structure where the input sites are rays and the distance function between a point and a site/ray, is the counterclockwise angular distance. This novel Voronoi diagram is motivated by illumination or coverage problems, where a domain must be covered by floodlights/wedges of uniform angle, and the goal is to find the minimum angle necessary to cover the domain. We study the diagram in the plane, and we present structural properties, combinatorial complexity bounds, and a construction algorithm. If the rays are induced by a convex polygon, we show how to construct the Voronoi diagram within this polygon in linear time. Using this information, we can find in optimal linear time the Brocard angle, the minimum angle required to illuminate a convex polygon with floodlights of uniform angle.

Identifying causal mechanisms is an essential aspect of disparities research. Rigorous investigations of mechanisms can open the black box and clarify linkages in the causal chain, indicating how effects occur. Studies of mechanisms can also illuminate novel ways to reduce inequality when intervention at the root cause of unequal outcomes is not feasible. Still, research on mechanisms can present challenges for researchers and funders alike. In this essay, the authors summarize the necessary trade-offs and inherent tensions of research on causal mechanisms, and discuss challenges and opportunities for future studies. By explicating the complexities of disparities mechanisms research and exploring ways to address these challenges, the authors hope to help researchers propose work that is both rigorous and novel. The authors also aim to help research funders understand how best to support this work in ways that align with existing interests and resources.

Building usefully coherent superconducting quantum processors depends on reducing losses in their constituent materials. Tantalum, like niobium, has proven utility as the primary superconducting layer within highly coherent qubits. But, unlike Nb, high temperatures are typically used to stabilize the desirable body-centered-cubic phase, alpha-Ta, during thin film deposition. It has long been known that a thin Nb layer permits the room-temperature nucleation of alpha-Ta, although neither an epitaxial process nor few-photon microwave loss measurements have been reported for Nb-nucleated Ta films prior to this study. We compare resonators patterned from Ta films grown at high temperature (500 {\deg}C) and films nucleated at room temperature, in order to understand the impact of crystalline order on quantum coherence. In both cases, films grew with Al2O3 (001) || Ta (110) indicating that the epitaxial orientation is independent of temperature and is preserved across the Nb/Ta interface. We use conventional low-power spectroscopy to measure two level system (TLS) loss, as well as an electric-field bias technique to measure the effective dipole moments of TLS in the surfaces of resonators. In our measurements, Nb-nucleated Ta resonators had greater loss tangent (1.5 +/- 0.1 x 10^-5) than non-nucleated (5 +/- 1 x 10^-6) in approximate proportion to defect densities as characterized by X-ray diffraction (0.27 {\deg} vs 0.18 {\deg} [110] reflection width) and electron microscopy (30 nm vs 70 nm domain size). The dependence of the loss tangent on domain size indicates that the development of more ordered Ta films is likely to lead to improvements in qubit coherence times. Moreover, low-temperature alpha-Ta epitaxy may enable the growth of new, microstate-free heterostructures which would not withstand high temperature processing.

Covariance functions are the core of spatial statistics, stochastic processes, machine learning as well as many other theoretical and applied disciplines. The properties of the covariance function at small and large distances determine the geometric attributes of the associated Gaussian random field. Having covariance functions that allow to specify both local and global properties is certainly on demand. This paper provides a method to find new classes of covariance functions having such properties. We term these models hybrid as they are obtained as scale mixtures of piecewise covariance kernels against measures that are also defined as piecewise linear combination of parametric families of measures. In order to illustrate our methodology, we provide new families of covariance functions that are proved to be richer with respect to other well known families that have been proposed by earlier literature. More precisely, we derive a hybrid Cauchy-Mat\'ern model, which allows us to index both long memory and mean square differentiability of the random field, and a hybrid Hole-Effect-Mat\'ern model, which is capable of attaining negative values (hole effect), while preserving the local attributes of the traditional Mat\'ern model. Our findings are illustrated through numerical studies with both simulated and real data., Comment: 19 pages, 6 figures