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Inferring causal structure from data is a challenging task of fundamental importance in science. Observational data are often insufficient to identify a system's causal structure uniquely. While conducting interventions (i.e., experiments) can improve the identifiability, such samples are usually challenging and expensive to obtain. Hence, experimental design approaches for causal discovery aim to minimize the number of interventions by estimating the most informative intervention target. In this work, we propose a novel Gradient-based Intervention Targeting method, abbreviated GIT, that 'trusts' the gradient estimator of a gradient-based causal discovery framework to provide signals for the intervention acquisition function. We provide extensive experiments in simulated and real-world datasets and demonstrate that GIT performs on par with competitive baselines, surpassing them in the low-data regime., Comment: Accepted to 37th Conference on Neural Information Processing Systems (NeurIPS 2023)

In the intact brain, neural activity can be recorded using sensing electrodes and manipulated using light stimulation. Silicon probes with integrated electrodes and micro-LEDs enable the detection and control of neural activity using a single implanted device. Miniaturized solutions for recordings from small freely moving animals are commercially available, but stimulation is driven by large, stationary current sources. We designed and fabricated a current source chip and integrated it into a headstage PCB that weighs 1.37 g. The proposed system provides 10-bit resolution current control for 32 channels, driving micro-LEDs with up to 4.6 V and sourcing up to 0.9 mA at a refresh rate of 5 kHz per channel. When calibrated against a micro-LED probe, the system allows linear control of light output power, up to 10 micro-W per micro-LED. To demonstrate the capabilities of the system, synthetic sequences of neural spiking activity were produced by driving multiple micro-LEDs implanted in the hippocampal CA1 area of a freely moving mouse. The high spatial, temporal, and amplitude resolution of the system provides a rich variety of stimulation patterns. Combined with commercially available sampling headstages, the system provides an easy to use back-end, fully utilizing the bi-directional potential of integrated opto-electronic arrays., Comment: 11 pages, 9 figures

The interplay between a multitude of electronic, spin, and lattice degrees of freedom underlies the complex phase diagrams of quantum materials. Layer stacking in van der Waals (vdW) heterostructures is responsible for exotic electronic and magnetic properties, which inspires stacking control of two-dimensional magnetism. Beyond the interplay between stacking order and interlayer magnetism, we discover a spin-shear coupling mechanism in which a subtle shear of the atomic layers can have a profound effect on the intralayer magnetic order in a family of vdW antiferromagnets. Using time-resolved x-ray diffraction and optical linear dichroism measurements, interlayer shear is identified as the primary structural degree of freedom that couples with magnetic order. The recovery times of both shear and magnetic order upon optical excitation diverge at the magnetic ordering temperature with the same critical exponent. The time-dependent Ginzburg-Landau theory shows that this concurrent critical slowing down arises from a linear coupling of the interlayer shear to the magnetic order, which is dictated by the broken mirror symmetry intrinsic to the monoclinic stacking. Our results highlight the importance of interlayer shear in ultrafast control of magnetic order via spin-mechanical coupling.

We report optical pumping and X-ray absorption spectroscopy experiments at the PAL free electron laser that directly probe the electron dynamics of a graphene monolayer adsorbed on copper in the femtosecond regime. By analyzing the results with ab-initio theory we infer that the excitation of graphene is dominated by indirect excitation from hot electron-hole pairs created in the copper by the optical laser pulse. However, once the excitation is created in graphene, its decay follows a similar path as in many previous studies of graphene adsorbed on semiconductors, i e. rapid excitation of SCOPS (Strongly Coupled Optical Phonons) and eventual thermalization. It is likely that the lifetime of the hot electron-hole pairs in copper governs the lifetime of the electronic excitation of the graphene., Comment: 22 pages, 8 Figures including Supplementary Material

In recent years, hate speech has gained great relevance in social networks and other virtual media because of its intensity and its relationship with violent acts against members of protected groups. Due to the great amount of content generated by users, great effort has been made in the research and development of automatic tools to aid the analysis and moderation of this speech, at least in its most threatening forms. One of the limitations of current approaches to automatic hate speech detection is the lack of context. Most studies and resources are performed on data without context; that is, isolated messages without any type of conversational context or the topic being discussed. This restricts the available information to define if a post on a social network is hateful or not. In this work, we provide a novel corpus for contextualized hate speech detection based on user responses to news posts from media outlets on Twitter. This corpus was collected in the Rioplatense dialectal variety of Spanish and focuses on hate speech associated with the COVID-19 pandemic. Classification experiments using state-of-the-art techniques show evidence that adding contextual information improves hate speech detection performance for two proposed tasks (binary and multi-label prediction). We make our code, models, and corpus available for further research.

The ability of continual learning systems to transfer knowledge from previously seen tasks in order to maximize performance on new tasks is a significant challenge for the field, limiting the applicability of continual learning solutions to realistic scenarios. Consequently, this study aims to broaden our understanding of transfer and its driving forces in the specific case of continual reinforcement learning. We adopt SAC as the underlying RL algorithm and Continual World as a suite of continuous control tasks. We systematically study how different components of SAC (the actor and the critic, exploration, and data) affect transfer efficacy, and we provide recommendations regarding various modeling options. The best set of choices, dubbed ClonEx-SAC, is evaluated on the recent Continual World benchmark. ClonEx-SAC achieves 87% final success rate compared to 80% of PackNet, the best method in the benchmark. Moreover, the transfer grows from 0.18 to 0.54 according to the metric provided by Continual World., Comment: Accepted at NeurIPS 2022

In this paper, we propose a discrete Hamilton--Jacobi theory for (discrete) Hamiltonian dynamics defined on a (discrete) contact manifold. To this end, we first provide a novel geometric Hamilton--Jacobi theory for continuous contact Hamiltonian dynamics. Then, rooting on the discrete contact Lagrangian formulation, we obtain the discrete equations for Hamiltonian dynamics by the discrete Legendre transformation. Based on the discrete contact Hamilton equation, we construct a discrete Hamilton--Jacobi equation for contact Hamiltonian dynamics. We show how the discrete Hamilton--Jacobi equation is related to the continuous Hamilton--Jacobi theory presented in this work. Then, we propose geometric foundations of the discrete Hamilton--Jacobi equations on contact manifolds in terms of discrete contact flows. At the end of the paper we provide a numerical example to test the theory., Comment: Hamilton-Jacobi theory; Discrete dynamics; Contact manifolds; Discrete Hamilton--Jacobi

A majority coloring of a directed graph is a vertex coloring in which each vertex has the same color as at most half of its out-neighbors. In this note we simplify some proof techniques and generalize previously known results on various generalizations of majority coloring. In particular, our unified and simplified approach works for paintability - an on-line analog of the list coloring.

In this article we construct and discuss a new rigorous geometric formalism for gauge field theories. The basis of our work is the notion of the Tulczyjew triple, a geometric structure which successfully solved numerous problems in mathematical description of mechanics and classical field theory. In particular, we construct a Tulczyjew triple for gauge field theories and reduce it for systems that depend only on the value of a connection and curvature instead of the entire first jet of the gauge field. We also introduce new geometric structures such as the vector-affine product of bundles and analyse the connection bundle from a new perspective. Finally, we apply the derived formalism to Yang-Mills theory., Comment: 36 pages

Understanding the origin of electron-phonon coupling in lead-halide perovskites (LHP) is key to interpreting and leveraging their optical and electronic properties. Here we perform femtosecond-resolved, optical-pump, electron-diffraction-probe measurements to quantify the lattice reorganization occurring as a result of photoexcitation in LHP nanocrystals. Photoexcitation is found to drive a reduction in lead-halide octahedra tilts and distortions in the lattice, a result of deformation potential coupling to low energy optical phonons. Our results indicate particularly strong coupling in FAPbBr3, and far weaker coupling in CsPbBr3, highlighting differences in the dominant machanisms governing electron-phonon coupling in LHPs. We attribute the enhanced coupling in FAPbBr3 to its disordered crystal structure, which persists down to cryogenic temperatures. We find the reorganizations induced by each exciton in a multiexcitonic state constructively interfere, giving rise to a coupling strength which scales quadratically with the exciton number. This superlinear scaling induces phonon-mediated attractive interactions between excitations in LHPs.

In this survey, we review the classical Hamilton Jacobi theory from a geometric point of view in different geometric backgrounds. We propose a Hamilton Jacobi equation for different geometric structures attending to one particular characterization: whether they fulfill the Jacobi and Leibniz identities simultaneously, or if at least they satisfy one of them. In this regard, we review the case of time dependent and dissipative physical systems as systems that fulfill the Jacobi identity but not the Leibnitz identity. Furthermore, we review the contact evolution Hamilton Jacobi theory as a split off the regular contact geometry, and that actually satisfies the Leibniz rule instead of Jacobi. Furthermore, we include a novel result, which is the Hamilton-Jacobi equation for conformal Hamiltonian vector fields as a generalization of the well known Hamilton Jacobi on a symplectic manifold, that is retrieved in the case of a zero conformal factor. The interest of a geometric Hamilton Jacobi equation is the primordial observation that if a Hamiltonian vector field can be projected into a configuration manifold by means of a 1-form dW, then the integral curves of the projected vector field can be transformed into integral curves of the Hamiltonian vector field provided that W is a solution of the Hamilton-Jacobi equation. Geometrically, the solution of the Hamilton Jacobi equation plays the role of a Lagrangian submanifold of a certain bundle. Exploiting these features in different geometric scenarios we propose a geometric theory for multiple physical systems depending on the fundamental identities that their dynamic satisfies. Different examples are pictured to reflect the results provided, being all of them new, except for one that is reassessment of a previously considered example.

Correlation and cluster analyses (k-Means, Gaussian Mixture Models) were performed on Generation Z engagement surveys at the workplace. The clustering indicates relations between various factors that describe the engagement of employees. The most noticeable factors are a clear statement about the responsibilities at work, and challenging work. These factors are essential in practice. The results of this paper can be used in preparing better motivational systems aimed at Generation Z employees., Comment: 14 pages, 10 figures, 2 tables

Let $N$ be a positive integer. A sequence $X=(x_1,x_2,\ldots,x_N)$ of points in the unit interval $[0,1)$ is piercing if $\{x_1,x_2,\ldots,x_n\}\cap \left[\frac{i}{n},\frac{i+1}{n} \right) \neq\emptyset$ holds for every $n=1,2,\ldots, N$ and every $i=0,1,\ldots,n-1$. In 1958 Steinhaus asked whether piercing sequences can be arbitrarily long. A negative answer was provided by Schinzel, who proved that any such sequence may have at most $74$ elements. This was later improved to the best possible value of $17$ by Warmus, and independently by Berlekamp and Graham. In this paper we study a more general variant of piercing sequences. Let $f(n)\geq n$ be an infinite nondecreasing sequence of positive integers. A sequence $X=(x_1,x_2,\ldots,x_{f(N)})$ is $f$-piercing if $\{x_1,x_2,\ldots,x_{f(n)}\}\cap \left[\frac{i}{n},\frac{i+1}{n} \right) \neq\emptyset$ holds for every $n=1,2,\ldots, N$ and every $i=0,1,\ldots,n-1$. A special case of $f(n)=n+d$, with $d$ a fixed nonnegative integer, was studied by Berlekamp and Graham. They noticed that for each $d\geq 0$, the maximum length of any $(n+d)$-piercing sequence is finite. Expressing this maximum length as $s(d)+d$, they obtained an exponential upper bound on the function $s(d)$, which was later improved to $s(d)=O(d^3)$ by Graham and Levy. Recently, Konyagin proved that $2d\leqslant s(d)< 200d$ holds for all sufficiently big $d$. Using a different technique based on the Farey fractions and stick-breaking games, we prove here that the function $s(d)$ satisfies $\left\lfloor{}c_1d\right\rfloor{}\leqslant s(d)\leqslant c_2d+o(d)$, where $c_1=\frac{\ln 2}{1-\ln 2}\approx2.25$ and $c_2=\frac{1+\ln2}{1-\ln2}\approx5.52$. We also prove that there exists an infinite $f$-piercing sequence with $f(n)= \gamma n+o(n)$ if and only if $\gamma\geq\frac{1}{\ln 2}\approx 1.44$., Comment: 16 pages

The addition of tunable couplers to superconducting quantum architectures offers significant advantages for scaling compared to fixed coupling approaches. In principle, tunable couplers allow for exact cancellation of qubit-qubit coupling through the interference of two parallel coupling pathways between qubits. However, stray microwave couplings can introduce additional pathways which complicate the interference effect. Here we investigate the primary spectator induced errors of the bus below qubit (BBQ) architecture in a six qubit device. We identify the key design parameters which inhibit ideal cancellation and demonstrate that dynamic cancellation pulses can further mitigate spectator errors.

Engineering single atomic defects into wide bandgap materials has become an attractive field in recent years due to emerging applications such as solid-state quantum bits and sensors. The simplest atomic-scale defect is the lattice vacancy which is often a constituent part of more complex defects such as the nitrogen-vacancy (NV) centre in diamond, therefore an understanding of the formation mechanisms and precision engineering of vacancies is desirable. We present a theoretical and experimental study into the ultra-fast laser generation of vacancy-interstitial pairs (Frenkel defects) in diamond. The process is described by a set of coupled rate equations of the pulsed laser interaction with the material and of the non-equilibrium dynamics of charge carriers during and in the wake of the pulse. We find that a model for Frenkel defect generation via the recombination of a bound biexciton as the electron plasma cools provides good agreement with experimental data, reproducing an effective non-linearity of $\sim$ 40 for Frenkel defect generation with respect to laser pulse energy., Comment: 17 pages, 11 figures

Continual learning (CL) -- the ability to continuously learn, building on previously acquired knowledge -- is a natural requirement for long-lived autonomous reinforcement learning (RL) agents. While building such agents, one needs to balance opposing desiderata, such as constraints on capacity and compute, the ability to not catastrophically forget, and to exhibit positive transfer on new tasks. Understanding the right trade-off is conceptually and computationally challenging, which we argue has led the community to overly focus on catastrophic forgetting. In response to these issues, we advocate for the need to prioritize forward transfer and propose Continual World, a benchmark consisting of realistic and meaningfully diverse robotic tasks built on top of Meta-World as a testbed. Following an in-depth empirical evaluation of existing CL methods, we pinpoint their limitations and highlight unique algorithmic challenges in the RL setting. Our benchmark aims to provide a meaningful and computationally inexpensive challenge for the community and thus help better understand the performance of existing and future solutions. Information about the benchmark, including the open-source code, is available at https://sites.google.com/view/continualworld., Comment: NeurIPS 2021

Recently, T. Masson, J. Francois, S. Lazzarini, C. Fournel and J. Attard have introduced a new method of the reduction of gauge symmetry called a dressing field method. In this paper we analyse this method from the fiber bundle point of view and we show the geometric implications for a principal bundle underlying a given gauge theory. We show how the existence of the dressing field satisfying certain conditions naturally leads to the reduction of the principal bundle and, as a consequence, to the reduction of the configuration and phase bundle of the system., Comment: 17 pages

In this paper we aim at presenting a concise but also comprehensive study of time-dependent (tdependent) Hamiltonian dynamics on a locally conformal symplectic (lcs) manifold. We present a generalized geometric theory of canonical transformations and formulate a time-dependent geometric Hamilton-Jacobi theory on lcs manifolds. In contrast to previous papers concerning locally conformal symplectic manifolds, here the introduction of the time dependency brings out interesting geometric properties, as it is the introduction of contact geometry in locally symplectic patches. To conclude, we show examples of the applications of our formalism, in particular, we present systems of differential equations with time-dependent parameters, which admit different physical interpretations as we shall point out., Comment: 25 pages

In this paper we provide a matched pair decomposition of the space of symmetric contravariant tensors $\mathfrak{T}\mathcal{Q}$. From this procedure two complementary Lie subalgebras of $\mathfrak{T}\mathcal{Q}$ under \textit{mutual} interaction arise. Introducing a lift operator, the matched pair decomposition of the space of Hamiltonian vector fields is determined. According to these realizations, Euler-Poincar\'{e} flows on such spaces are decomposed into two subdynamics: one of which is the Euler--Poincar\'{e} formulation of isentropic fluid flows, and the other one corresponds with Euler--Poincar\'{e} equations on higher order contravariant tensors ($n\geq 2$), Comment: arXiv admin note: text overlap with arXiv:2004.12595

Strongly correlated materials that exhibit an insulator-metal transition are key candidates in the search for new computing platforms. Understanding the pathways and timescales underlying the electrically-driven insulator-metal transition is crucial for uncovering the fundamental limits of device operation. Using stroboscopic electron diffraction, we perform synchronized time-resolved measurements of atomic motions and electronic transport in operating vanadium dioxide switches. We discover an electrically-triggered, isostructural state that forms transiently on microsecond timescales, stabilized by local heterogeneities and interfacial interactions between the equilibrium phases. This metastable phase bears striking similarity to that formed under photoexcitation within picoseconds, suggesting a universal transformation pathway across eight orders of magnitude of timescale. Our results establish a new route for uncovering non-equilibrium and metastable phases in correlated materials, and open avenues for engineering novel dynamical behavior in nanoelectronics.

In this article we continue the research, carried out in \cite{zajac}, on computing the $*$-product of domains in $\CC^N$. Assuming that $0\in G\subset\CC^N$ is an arbitrary Runge domain and $0\in D\subset\CC^N$ is a bounded, smooth and linearly convex domain (or a non-decreasing union of such ones), we establish a geometric relation between $D*G$ and another domain in $\CC^N$ which is 'extremal' (in an appropriate sense) with respect to a special coefficient multiplier dependent only on the dimension $N$. Next, for $N=2$, we derive a characterization of the latter domain expressed in terms of planar geometry. These two results, when combined together, give a formula which allows to calculate $D*G$ for two-dimensional domains $D$ and $G$ satisfying the outlined assumptions.

Implementation of high-fidelity two-qubit operations is a key ingredient for scalable quantum error correction. In superconducting qubit architectures tunable buses have been explored as a means to higher fidelity gates. However, these buses introduce new pathways for leakage. Here we present a modified tunable bus architecture appropriate for fixed-frequency qubits in which the adiabaticity restrictions on gate speed are reduced. We characterize this coupler on a range of two-qubit devices achieving a maximum gate fidelity of $99.85\%$. We further show the calibration is stable over one day.

Nonradiative processes limit optoelectronic functionality of nanocrystals and curb their device performance. Nevertheless, the dynamic structural origins of nonradiative relaxations in nanocrystals are not understood. Here, femtosecond electron diffraction measurements corroborated by atomistic simulations uncover transient lattice deformations accompanying radiationless electronic processes in semiconductor nanocrystals. Investigation of the excitation energy dependence shows that hot carriers created by a photon energy considerably larger than the bandgap induce structural distortions at nanocrystal surfaces on few picosecond timescales associated with the localization of trapped holes. On the other hand, carriers created by a photon energy close to the bandgap result in transient lattice heating that occurs on a much longer 200 ps timescale, governed by an Auger heating mechanism. Elucidation of the structural deformations associated with the surface trapping of hot holes provides atomic-scale insights into the mechanisms deteriorating optoelectronic performance and a pathway towards minimizing these losses in nanocrystal devices., Comment: 17 pages, 4 figures

We report on the status of the Tierras Observatory, a refurbished 1.3-m ultra-precise fully-automated photometer located at the F. L. Whipple Observatory atop Mt. Hopkins, Arizona. Tierras is designed to limit systematic errors, notably precipitable water vapor (PWV), to 250 ppm, enabling the characterization of terrestrial planet transits orbiting $< 0.3 \, R_{\odot}$ stars, as well as the potential discovery of exo-moons and exo-rings. The design choices that will enable our science goals include: a four-lens focal reducer and field-flattener to increase the field-of-view of the telescope from a $11.94'$ to a $0.48^{\circ}$ side; a custom narrow bandpass ($40.2$ nm FWHM) filter centered around $863.5$ nm to minimize PWV errors known to limit ground-based photometry of red dwarfs; and a deep-depletion $4K \times 4K$ CCD with a 300ke-full well and QE$>85\%$ in our bandpass, operating in frame transfer mode. We are also pursuing the design of a set of baffles to minimize the significant amount of scattered light reaching the image plane. Tierras will begin science operations in early 2021., Comment: SPIE Astronomical Telescopes & Instrumentation 2020 Proceedings (11445-168), 20 pages, 11 figures

Let $\Gamma$ be an Abelian group and let $G$ be a simple graph. We say that $G$ is $\Gamma$-colorable if for some fixed orientation of $G$ and every edge labeling $\ell:E(G)\rightarrow \Gamma$, there exists a vertex coloring $c$ by the elements of $\Gamma$ such that $c(y)-c(x)\neq \ell(e)$, for every edge $e=xy$ (oriented from $x$ to $y$). Langhede and Thomassen proved recently that every planar graph on $n$ vertices has at least $2^{n/9}$ different $\mathbb{Z}_5$-colorings. By using a different approach based on graph polynomials, we extend this result to $K_5$-minor-free graphs in the more general setting of field coloring. More specifically, we prove that every such graph on $n$ vertices is $\mathbb{F}$-$5$-choosable, whenever $\mathbb{F}$ is an arbitrary field with at least $5$ elements. Moreover, the number of colorings (for every list assignment) is at least $5^{n/4}$., Comment: 14 pages

Precise control of the properties of semiconductor quantum dots (QDs) is vital for creating novel devices for quantum photonics and advanced opto-electronics. Suitable low QD-density for single QD devices and experiments are challenging to control during epitaxy and are typically found only in limited regions of the wafer. Here, we demonstrate how conventional molecular beam epitaxy (MBE) can be used to modulate the density of optically active QDs in one- and two- dimensional patterns, while still retaining excellent quality. We find that material thickness gradients during layer-by-layer growth result in surface roughness modulations across the whole wafer. Growth on such templates strongly influences the QD nucleation probability. We obtain density modulations between 1 and 10 QDs/${\mu}m^{2}$ and periods ranging from several millimeters down to at least a few hundred microns. This novel method is universal and expected to be applicable to a wide variety of different semiconductor material systems. We apply the method to enable growth of ultra-low noise QDs across an entire 3-inch semiconductor wafer.

The typical problem in Data Science is creating a structure that encodes the occurrence frequency of unique elements in rows and relations between different rows of a data frame. We present the probability tree abstract data structure, an extension of the decision tree, that facilitates more than two choices with assigned probabilities. Such a tree represents statistical relations between different rows of the data frame. The Probability Tree algorithmic structure is supplied with the Generator module that is a Monte Carlo generator that traverses through the tree. These two components are implemented in TreeGen Python package. The package can be used in increasing data multiplicity, compressing data preserving its statistical information, constructing hierarchical models, exploring data, and in feature extraction., Comment: 13 pages, 10 figures

Some recent works reveal that there are models of differential equations for the mean and variance of infected individuals that reproduce the SIS epidemic model at some point. This stochastic SIS epidemic model can be interpreted as a Hamiltonian system, therefore we wondered if it could be geometrically handled through the theory of Lie--Hamilton systems, and this happened to be the case. The primordial result is that we are able to obtain a general solution for the stochastic/ SIS-epidemic model (with fluctuations) in form of a nonlinear superposition rule that includes particular stochastic solutions and certain constants to be related to initial conditions of the contagion process. The choice of these initial conditions will be crucial to display the expected behavior of the curve of infections during the epidemic. We shall limit these constants to nonsingular regimes and display graphics of the behavior of the solutions. As one could expect, the increase of infected individuals follows a sigmoid-like curve. Lie--Hamiltonian systems admit a quantum deformation, so does the stochastic SIS-epidemic model. We present this generalization as well. If one wants to study the evolution of an SIS epidemic under the influence of a constant heat source (like centrally heated buildings), one can make use of quantum stochastic differential equations coming from the so-called quantum deformation.

There exists a variety of coloring problems for plane graphs, involving vertices, edges, and faces in all possible combinations. For instance, in the \emph{entire coloring} of a plane graph we are to color these three sets so that any pair of adjacent or incident elements get different colors. We study here some problems of this type from algebraic perspective, focusing on the \emph{facial} variant. We obtain several results concerning the \emph{Alon-Tarsi number} of various graphs derived from plane embeddings. This allows for extensions of some previous results for \emph{choosability} of these graphs to the game theoretic variant, know as \emph{paintability}. For instance, we prove that every plane graph is facially entirely \emph{$8$-paintable}, which means (metaphorically) that even a color-blind person can facially color the entire graph form lists of size $8$.

Three-dimensional Coulomb branches have a prominent role in the study of moduli spaces of supersymmetric gauge theories with $8$ supercharges in $3,4,5$, and $6$ dimensions. Inspired by simply laced $3$d $\mathcal{N}=4$ supersymmetric quiver gauge theories, we consider Coulomb branches constructed from non-simply laced quivers with edge multiplicity $k$ and no flavor nodes. In a computation of the Coulomb branch as the space of dressed monopole operators, a center-of-mass $U(1)$ symmetry needs to be ungauged. Typically, for a simply laced theory, all choices of the ungauged $U(1)$ (i.e. all choices of ungauging schemes) are equivalent and the Coulomb branch is unique. In this note, we study various ungauging schemes and their effect on the resulting Coulomb branch variety. It is shown that, for a non-simply laced quiver, inequivalent ungauging schemes exist which correspond to inequivalent Coulomb branch varieties. Ungauging on any of the long nodes of a non-simply laced quiver yields the same Coulomb branch $\mathcal{C}$. For choices of ungauging the $U(1)$ on a short node of rank higher than $1$, the GNO dual magnetic lattice deforms such that it no longer corresponds to a Lie group, and therefore, the monopole formula yields a non-valid Coulomb branch. However, if the ungauging is performed on a short node of rank $1$, the one-dimensional magnetic lattice is rescaled conformally along its single direction and the corresponding Coulomb branch is an orbifold of the form $\mathcal{C}/\mathbb{Z}_k$. Ungauging schemes of $3$d Coulomb branches provide a particularly interesting and intuitive description of a subset of actions on the nilpotent orbits studied by Kostant and Brylinski arXiv:math/9204227. The ungauging scheme analysis is carried out for minimally unbalanced $C_n$, affine $F_4$, affine $G_2$, and twisted affine $D_4^{(3)}$ quivers, respectively., Comment: 21 pages, v2: added references, v3: fixed hyperlink for abstract citation

In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description of field theories, and the conformal character has been added to account for field theories that are scale invariant, flat spaces, and because some conformal fields can be exactly solved or classified. In particular, we will solve the example of a conformal scalar field using the geometric Hamilton-Jacobi theory that is explicitly proposed for conformal fields on a multisymplectic manifold. To complete the geometric approach to study field theories, we propose the Hamilton-Jacobi theory for conformal fields in a Cauchy data space, in which space and time are split separately and the dynamics is depicted in an infinite-dimensional manifold.

By using Laurent graph polynomials instead of the usual ones, i.e. by allowing negative powers of the variables, we simplify an existing method of determining the Alon-Tarsi numbers of planar graphs.

In this paper we aim at addressing the globalization problem of Hamilton-DeDonder-Weyl equations on a local $k$-symplectic framework and we introduce the notion of {\it locally conformal $k$-symplectic (l.c.k-s.) manifolds}. This formalism describes the dynamical properties of physical systems that locally behave like multi-Hamiltonian systems. Here, we describe the local Hamiltonian properties of such systems, but we also provide a global outlook by introducing the global Lee one-form approach. In particular, the dynamics will be depicted with the aid of the Hamilton--Jacobi equation, which is specifically proposed in a l.c.k-s manifold., Comment: 25 pages

In this article we provide a Hamilton-Jacobi formalism in locally conformally symplectic manifolds. Our interest in the Hamilton-Jacobi theory comes from the suitability of this theory as an integration method for dynamical systems, whilst our interest in the locally conformal character will account for physical theories described by Hamiltonians defined on well-behaved line bundles, whose dynamic takes place in open subsets of the general manifold. We present a local l.c.s. Hamilton-Jacobi in subsets of the general manifold, and then provide a global view by using the Lichnerowicz-deRham differential. We show a comparison between the global and local description of a l.c.s. Hamilton--Jacobi theory, and how actually the local behavior can be glued to retrieve the global behavior of the Hamilton-Jacobi theory.