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We study the existence and qualitative properties of action ground-states (that is, bound-states with minimal action) {of the nonlinear Schr\"odinger equation} over single-knot metric graphs -- which are made of half-lines, loops and pendants, all connected at a single vertex. First, we prove existence of action ground-state for generic single-knot graphs, even in the absence of an associated variational problem. Second, for regular single-knot graphs of length $\ell$, we perform a complete analysis of positive monotone bound-states. Furthermore, we characterize all positive bound-states when $\ell$ is small and prove some symmetry-breaking results for large $\ell$. Finally, we apply the results to some particular graphs to illustrate the complex relation between action ground-states and the topological {and metric} features of the underlying metric graph. The proofs are nonvariational, using a careful phase-plane analysis, the study of sections of period functions, asymptotic estimates and blowup arguments. We show, in particular, how nonvariational techniques are complementary to variational ones in order to deeply understand bound-states of the nonlinear Schr\"odinger equation on metric graphs., Comment: 36 pages

Solving partially observable Markov decision processes (POMDPs) typically requires reasoning about the values of exponentially many state beliefs. Towards practical performance, state-of-the-art solvers use value bounds to guide this reasoning. However, sound upper value bounds are often computationally expensive to compute, and there is a tradeoff between the tightness of such bounds and their computational cost. This paper introduces new and provably tighter upper value bounds than the commonly used fast informed bound. Our empirical evaluation shows that, despite their additional computational overhead, the new upper bounds accelerate state-of-the-art POMDP solvers on a wide range of benchmarks., Comment: AAMAS 2025 submission

Energetic or "hot" electrons and holes generated from the decay of localized surface plasmons in metallic nanoparticles have great potential for applications in photocatalysis, photovoltaics, and sensing. Here, we study the generation of hot carriers in brick-shaped gold nanoparticles using a recently developed modelling approach that combines a solution to Maxwell's equation with large-scale tight-binding simulations to evaluate Fermi's Golden Rule. We find that hot-carrier generation depends sensitively on the aspect ratio of the nanobricks with flatter bricks producing a large number of energetic electrons irrespective of the light polarization. In contrast, the hot-carrier generation rates of elongated nanobricks exhibits a strong dependence on the light polarization. The insights resulting from our calculations can be harnessed to design nanobricks that produce hot carriers with properties tailored to specific device applications.

We consider a general nonlinear dispersive equation with monomial nonlinearity of order $k$ over $\mathbb{R}^d$. We construct a rigorous theory which states that higher-order nonlinearities and higher dimensions induce sharper local well-posedness theories. More precisely, assuming that a certain positive multiplier estimate holds at order $k_0$ and in dimension $d_0$, we prove a sharp local well-posedness result in $H^s(\mathbb{R}^d)$ for any $k\ge k_0$ and $d\ge d_0$. Moreover, we give an explicit bound on the gain of regularity observed in the difference between the linear and nonlinear solutions, confirming the conjecture made in [CorreiaOliveiraSilva24] (doi.org/10.1137/23M156923X). The result is then applied to generalized Korteweg-de Vries, Zakharov-Kuznetsov and nonlinear Schr\"odinger equations., Comment: 15 pages

This paper explores the application of Madelung hydrodynamic models to study two-dimensional electron gases, with a focus on nonlocal plasmonics and nonlinear optics. We begin by reviewing the derivation of the Madelung equations. Using the Madelung equations in conjunction with Poisson's equation, we calculate the spectrum of magnetoplasmons and the magneto-optical conductivity in the electrostatic regime, incorporating nonlocal corrections due to the Fermi pressure. In the absence of a magnetic field, we analyze nonlinear and nonlocal second-harmonic generation, demonstrating how plasmon excitation enhances this process. We further discuss the emergence of self-modulation phenomena driven by nonlinearity, leading to the renormalization of the plasmon dispersion. Notably, we show that nonlinearity amplifies nonlocal effects and, leveraging the hydrodynamic formalism, derive a simple analytic expression for the renormalized spectra., Comment: 14 pages and 4 figures

We construct an effective cosmological spin-foam model for a (2+1) dimensional spatially flat universe, discretized on a hypercubical lattice, containing both space- and time-like regions. Our starting point is the recently proposed coherent state spin-foam model for (2+1) Lorentzian quantum gravity. The full amplitude is assumed to factorize into single vertex amplitudes with boundary data corresponding to Lorentzian 3-frusta. A stationary phase approximation is performed at each vertex individually, where the inverse square root of the Hessian determinant serves as a measure for the effective path integral. Additionally, a massive scalar field is coupled to the geometry, and we show that its mass renders the partition function convergent. For a single 3-frustum with time-like struts, we compute the expectation value of the bulk strut length and show that it generically agrees with the classical solutions and that it is a discontinuous function of the scalar field mass. Allowing the struts to be space-like introduces causality violations, which drive the expectation values away from the classical solutions due to the lack of an exponential suppression of these configurations. This is a direct consequence of the semi-classical amplitude only containing the real part of deficit angles, in contrast with the Lorentzian Regge action used in effective spin-foams. We give an outlook on how to evaluate the partition function on an extended discretization including a bulk spatial slice. This serves as a foundation for future investigations of physically interesting scenarios such as a quantum bounce or the viability of massive scalar field clocks. Our results demonstrate that the effective path integral in the causally regular sector serves as a viable quantum cosmology model, but that the agreement of expectation values with classical solutions is tightly bound to the path integral measure., Comment: 51 + 11 pages, 17 figures

With the widespread of digital environments, reliable authentication and continuous access control has become crucial. It can minimize cyber attacks and prevent frauds, specially those associated with identity theft. A particular interest lies on keystroke dynamics (KD), which refers to the task of recognizing individuals' identity based on their unique typing style. In this work, we propose the use of pre-trained language models (PLMs) to recognize such patterns. Although PLMs have shown high performance on multiple NLP benchmarks, the use of these models on specific tasks requires customization. BERT and RoBERTa, for instance, rely on subword tokenization, and they cannot be directly applied to KD, which requires temporal-character information to recognize users. Recent character-aware PLMs are able to process both subwords and character-level information and can be an alternative solution. Notwithstanding, they are still not suitable to be directly fine-tuned for KD as they are not optimized to account for user's temporal typing information (e.g., hold time and flight time). To overcome this limitation, we propose TempCharBERT, an architecture that incorporates temporal-character information in the embedding layer of CharBERT. This allows modeling keystroke dynamics for the purpose of user identification and authentication. Our results show a significant improvement with this customization. We also showed the feasibility of training TempCharBERT on a federated learning settings in order to foster data privacy., Comment: Accepted at WIFS 2024

Identifying driver genes is crucial for understanding oncogenesis and developing targeted cancer therapies. Driver discovery methods using protein or pathway networks rely on traditional network science measures, focusing on nodes, edges, or community metrics. These methods can overlook the high-dimensional interactions that cancer genes have within cancer networks. This study presents a novel method using Persistent Homology to analyze the role of driver genes in higher-order structures within Cancer Consensus Networks derived from main cellular pathways. We integrate mutation data from six cancer types and three biological functions: DNA Repair, Chromatin Organization, and Programmed Cell Death. We systematically evaluated the impact of gene removal on topological voids ($\beta_2$ structures) within the Cancer Consensus Networks. Our results reveal that only known driver genes and cancer-associated genes influence these structures, while passenger genes do not. Although centrality measures alone proved insufficient to fully characterize impact genes, combining higher-order topological analysis with traditional network metrics can improve the precision of distinguishing between drivers and passengers. This work shows that cancer genes play an important role in higher-order structures, going beyond pairwise measures, and provides an approach to distinguish drivers and cancer-associated genes from passenger genes.

Quantum transport studies of spin-dependent phenomena in solids commonly employ the Kubo or Keldysh formulas for the nonequilibrium density operator in the steady-state linear-response regime. Its trace with operators of interest, such as the spin density, spin current density, etc., gives expectation values of experimentally accessible observables. For local quantities, these formulas require summing over the manifolds of {\em both} Fermi-surface and Fermi-sea states. However, debates have been raging in the literature about the vastly different physics the two formulations can apparently produce, even when applied to the same system. Here, we revisit this problem using infinite-size graphene with proximity-induced spin-orbit and magnetic exchange effects as a testbed. By splitting this system into semi-infinite leads and central active region, in the spirit of Landauer formulation of quantum transport, we prove the {\em numerically exact equivalence} of the Kubo and Keldysh approaches via the computation of spin Hall current density and spin-orbit torque in both clean and disordered limits. The key to reconciling the two approaches are the numerical frameworks we develop for: ({\em i}) evaluation of Kubo(-Bastin) formula for a system attached to semi-infinite leads, which ensures continuous energy spectrum and evades the need for commonly used phenomenological broadening introducing ambiguity; and ({\em ii}) proper evaluation of Fermi-sea term in the Keldysh approach, which {\em must} include the voltage drop across the central active region even if it is disorder free., Comment: 9 pages, 3 figures, 115 references; Supplemental Material is available from https://wiki.physics.udel.edu/qttg/Publications

We prove a sharp local existence result for the Schr\"odinger-Korteweg-de Vries system with initial data in $H^k(\mathbb{R})\times H^s(\mathbb{R})$. The proof is based on the concept of \textit{integrated-by-parts strong solution}, which generalizes the classical notion of strong solution, and on frequency-restricted estimates. Moreover, we extend the known global well-posedness result to regularities $k,s>1/2$., Comment: 19 pages

Robust POMDPs extend classical POMDPs to handle model uncertainty. Specifically, robust POMDPs exhibit so-called uncertainty sets on the transition and observation models, effectively defining ranges of probabilities. Policies for robust POMDPs must be (1) memory-based to account for partial observability and (2) robust against model uncertainty to account for the worst-case instances from the uncertainty sets. To compute such robust memory-based policies, we propose the pessimistic iterative planning (PIP) framework, which alternates between two main steps: (1) selecting a pessimistic (non-robust) POMDP via worst-case probability instances from the uncertainty sets; and (2) computing a finite-state controller (FSC) for this pessimistic POMDP. We evaluate the performance of this FSC on the original robust POMDP and use this evaluation in step (1) to select the next pessimistic POMDP. Within PIP, we propose the rFSCNet algorithm. In each iteration, rFSCNet finds an FSC through a recurrent neural network by using supervision policies optimized for the pessimistic POMDP. The empirical evaluation in four benchmark environments showcases improved robustness against several baseline methods and competitive performance compared to a state-of-the-art robust POMDP solver.

Large-scale infrastructure systems are crucial for societal welfare, and their effective management requires strategic forecasting and intervention methods that account for various complexities. Our study addresses two challenges within the Prognostics and Health Management (PHM) framework applied to sewer assets: modeling pipe degradation across severity levels and developing effective maintenance policies. We employ Multi-State Degradation Models (MSDM) to represent the stochastic degradation process in sewer pipes and use Deep Reinforcement Learning (DRL) to devise maintenance strategies. A case study of a Dutch sewer network exemplifies our methodology. Our findings demonstrate the model's effectiveness in generating intelligent, cost-saving maintenance strategies that surpass heuristics. It adapts its management strategy based on the pipe's age, opting for a passive approach for newer pipes and transitioning to active strategies for older ones to prevent failures and reduce costs. This research highlights DRL's potential in optimizing maintenance policies. Future research will aim improve the model by incorporating partial observability, exploring various reinforcement learning algorithms, and extending this methodology to comprehensive infrastructure management.

This paper presents a novel approach to address the Production Routing Problem with Privacy Preserving (PRPPP) in supply chain optimization. The integrated optimization of production, inventory, distribution, and routing decisions in real-world industry applications poses several challenges, including increased complexity, discrepancies between planning and execution, and constraints on information sharing. To mitigate these challenges, this paper proposes the use of intelligent agent negotiation within a hybrid Multi-Agent System (MAS) integrated with optimization algorithms. The MAS facilitates communication and coordination among entities, encapsulates private information, and enables negotiation. This, along with optimization algorithms, makes it a compelling framework for establishing optimal solutions. The approach is supported by real-world applications and synergies between MAS and optimization methods, demonstrating its effectiveness in addressing complex supply chain optimization problems., Comment: The 15th Workshop on Optimization and Learning in Multiagent Systems

This paper presents an active inference method for Extended Finite State Machines, where inputs and outputs are parametrized, and transitions can be conditioned by guards involving input parameters and internal variables called registers. The method applies to (software) systems that cannot be reset, so it learns an EFSM model of the system on a single trace., Comment: 14 pages (last page blank), 8 figures, 4 algorithms Submitted to LearnAut workshop 2024 (not published)

This thesis is developed in the context of the spin-foam approach to quantum gravity; all results are concerned with the Lorentzian theory and with semiclassical methods. A correspondence is given between Majorana 2-spinors and time-like hypersurfaces in Minkowski 3-space based on complexified quaternions. It is shown that the former suggest a symplectic structure on the spinor phase space which, together with an area-matching constraint, yields a symplectomorphism to $T^*\mathrm{SU}(1,1)$. A complete 3-dimensional Lorentzian spin-foam amplitude for both space- and time-like triangles is proposed. It is shown to asymptote to Regge theory in the semiclassical regime. The asymptotic limit of the 4-dimensional Conrady-Hnybida model for general polytopes is scrutinized. Minkowski's theorem on convex polyhedra is generalized to Lorentzian signature, and new boundary states for time-like polygons are introduced. It is found that the semiclassical amplitude for such polygons is insufficiently constrained. A method for the asymptotic evaluation of integrals subject to external parameters is discussed. The method is developed in detail for the special problem of spin-foam gluing constraints away from their dominant critical points. A relation to the gluing constraints of effective spin-foams is suggested., Comment: PhD Dissertation, 210 pages; v2: implemented minor corrections and added additional references

We study the semi-classical limit of the recently proposed coherent spin foam model for (2+1) Lorentzian quantum gravity. Specifically, we analyze the gluing equations derived from the stationary phase approximation of the vertex amplitude. Typically these exhibit two solutions yielding a cosine of the Regge action. However, by inspection of the algebraic equations as well as their geometrical realization, we show in this note that the behavior is more nuanced: when all triangles are either spacelike or timelike, two solutions exist. In any other case, only a single solution is obtained, thus yielding a single Regge exponential., Comment: 5 pages, 2 figures

We consider the modified Korteweg-de Vries equation. Given a self-similar solution, and a subcritical perturbation of any size, we prove that there exists a unique solution to the equation which behaves at blow-up time as the self-similar solution plus the perturbation. To this end, we develop the first robust analysis in spaces of functions with bounded Fourier transforms. To begin, we prove the local well-posedness in subcritical spaces through an appropriate restriction norm method. As this method is not sufficient to capture the critical self-similar dynamics, we develop an infinite normal form reduction (INFR) to derive time-dependent a priori $L^\infty$ bounds in frequency variables. Both approaches rely on frequency-restricted estimates, which are specific positive multiplier estimates capable of capturing the oscillatory nature of the equation. As a consequence of our analysis, we also prove local well-posedness for small subcritical perturbations of self-similar solutions at positive time.

We propose an explicit spin-foam amplitude for Lorentzian gravity in three dimensions, allowing for both space- and time-like boundaries. The model is based on two main requirements: that it should be structurally similar to its well-known Euclidean analog, and that geometricity should be recovered in the semiclassical regime. To this end we introduce new coherent states for space-like boundary edges, derived from the continuous series of unitary $\mathrm{SU}(1,1)$ representations. We show that the relevant objects in the amplitude can be written in terms of the defining representation of the group, just as so happens in the Euclidean case. We derive an expression for the semiclassical amplitude at large spins, showing it relates to the Lorentzian Regge action., Comment: Version accepted for publication; 23 pages, 1 table, 3 figures

Hot electrons and holes generated from the decay of localized surface plasmons in metallic nanoparticles can be harnessed for applications in solar energy conversion and sensing. In this paper, we study the generation of hot carriers in large spherical gold-silver alloy nanoparticles using a recently developed atomistic modelling approach that combines a solution of Maxwell's equations with large-scale tight-binding simulations. We find that hot-carrier properties depend sensitively on the alloy composition. Specifically, nanoparticles with a large gold fraction produce hot carriers under visible light illumination while nanoparticles with a large silver fraction require higher photon energies to produce hot carriers. Moreover, most hot carriers in nanoparticles with a large gold fraction originate from interband transitions which give rise to energetic holes and "cold" electrons near the Fermi level. Increasing the silver fraction enhances the generation rate of hot carriers from intraband transitions which produce energetic electrons and "cold" holes. These findings demonstrate that alloy composition is a powerful tuning parameter for the design of nanoparticles for applications in solar energy conversion and sensing that require precise control of hot-carrier properties., Comment: 19 pages, 5 figures

This work is developed in the context of Lorentzian spin-foams with space- and time-like boundaries. It is argued that the equations describing the semiclassical regime of the various spin-foam amplitudes admit a common biquaternionic structure. A correspondence is given between Majorana 2-spinors and time-like surfaces in Minkowski 3-space based on such complexified quaternions. A symplectic structure for Majorana spinors is constructed, with which the unitary representation theory of $\mathrm{SU}(1, 1)$ is re-derived. As the main result, we propose a symplectomorphism between Majorana spinor space (with an area constraint) and $T^*\mathrm{SU}(1, 1)$, generalizing previous studies on twisted geometries to the case of time-like 2-surfaces., Comment: 23 pages, 2 figures

The challenge of accessing specialized adhesives designed for strain gage applications has been highlighted due to failures in logistic chains, requiring the exploration of local alternatives. A direct simulation of strain gage bonding behavior with two steel plates is infeasible due to the unique construction of strain gages. Therefore, an indirect simulation method, comparing local alternatives to a widely accepted adhesive, Loctite 496, was employed in this study. Two potential replacements, Loctite 401 and Tekbond 793, were tested and matched against the benchmark adhesive, with a focus on the key mechanical properties: Proportional Shear Strain (PSS), Proportional Shear Stress (PSSt), and Apparent Shear Modulus (G*). Loctite 401 exhibited the highest G*, suggesting its potential use in strain gage installations if G* is considered most important. However, Tekbond 793 demonstrated superior PSS, Maximum Shear Stress (MSSt), and Rupture Shear Stress (RSSt) performance, displaying linear behavior even without an accelerator. Surface preparation considerations were also discussed, noting that hand abrading results in double the surface roughness than using an orbital sander. The study further identified two main regions concerning failure modes related to Ra, with values below 0.31 {\mu}m causing significant variations in observed mechanical properties, pointing towards factors beyond adhesive layer thickness affecting bond properties. Lastly, the general recommendation is the use of an accelerator for all tested adhesives, while the use of a surface conditioner and neutralizer was found to negatively impact adhesive performance., Comment: 44 pages, 24 figures

Spectral lightcurves consisting of time series single-pixel spectral measurements of spacecraft are used to infer the spacecraft's attitude and rotation. Two methods are used. One based on numerical optimisation of a regularised least squares cost function, and another based on machine learning with a neural network model. The aim is to work with minimal information, thus no prior is available on the attitude nor on the inertia tensor. The theoretical and practical aspects of this task are investigated, and the methodology is tested on synthetic data. Results are shown based on synthetic data., Comment: 20 pages, 14 figures Accepted for presentation at SciTech 2024 in Orlando, Florida, USA

In centralized multi-agent systems, often modeled as multi-agent partially observable Markov decision processes (MPOMDPs), the action and observation spaces grow exponentially with the number of agents, making the value and belief estimation of single-agent online planning ineffective. Prior work partially tackles value estimation by exploiting the inherent structure of multi-agent settings via so-called coordination graphs. Additionally, belief estimation methods have been improved by incorporating the likelihood of observations into the approximation. However, the challenges of value estimation and belief estimation have only been tackled individually, which prevents existing methods from scaling to settings with many agents. Therefore, we address these challenges simultaneously. First, we introduce weighted particle filtering to a sample-based online planner for MPOMDPs. Second, we present a scalable approximation of the belief. Third, we bring an approach that exploits the typical locality of agent interactions to novel online planning algorithms for MPOMDPs operating on a so-called sparse particle filter tree. Our experimental evaluation against several state-of-the-art baselines shows that our methods (1) are competitive in settings with only a few agents and (2) improve over the baselines in the presence of many agents., Comment: Extended version (includes the Appendix) of the paper accepted at AAAI-24

Partial observability and uncertainty are common problems in sequential decision-making that particularly impede the use of formal models such as Markov decision processes (MDPs). However, in practice, agents may be able to employ costly sensors to measure their environment and resolve partial observability by gathering information. Moreover, imprecise transition functions can capture model uncertainty. We combine these concepts and extend MDPs to robust active-measuring MDPs (RAM-MDPs). We present an active-measure heuristic to solve RAM-MDPs efficiently and show that model uncertainty can, counterintuitively, let agents take fewer measurements. We propose a method to counteract this behavior while only incurring a bounded additional cost. We empirically compare our methods to several baselines and show their superior scalability and performance., Comment: Accepted at AAAI 2024

We extensively investigate the electronic and transport properties of a twisted bilayer graphene when subjected to both an external perpendicular electric field and a magnetic field. Using a basic tight-binding model, we show the flat electronic band properties as well as the density of states (DOS), both without and with the applied electric field. In the presence of an electric field, the degeneracy at the Dirac points is lifted where the non-monotonic behavior of the energy gap exists, especially for twist angles below 3$^\circ$. We also study the behavior of the Landau levels (LL) spectra for different twist angles within a very low energy range. These LL spectra get modified under the influence of the external electric field. Moreover, we calculate the dc Hall conductivity ($\sigma_{xy}$) for a very large system using the Kernel Polynomial Method (KPM). Interestingly, $\sigma_{xy}$ makes a transition from a half-integer to an integer quantum Hall effect, \textit{i.e.} the value of $\sigma_{xy}$ shifts from $\pm 4(n+1/2) (2e^2/h)$ ($n$ is an integer) to $\pm 2n (2e^2/h)$ around a small twist angle of $\theta=2.005^\circ$. At this angle, $\sigma_{xy}$ acquires a Hall plateau at zero Fermi energy. However, the behavior of $\sigma_{xy}$ remains unaltered when the system is exposed to the electric field, particularly at the magic angle where the bands in both layers can hybridize and strong interlayer coupling plays a crucial role., Comment: 13 pages, 10 figures

We present a DFT-based investigation of the twist-angle dependent proximity spin-orbit coupling (SOC) in graphene/TMDC structures. We find that for Mo-based TMDCs the proximity valley-Zeeman SOC exhibits a maximum at around 15--20{\deg}, and vanishes at 30{\deg}, while for W-based TMDCs we find an almost linear decrease of proximity valley-Zeeman SOC when twisting from 0{\deg} to 30{\deg}. The induced Rashba SOC is rather insensitive to twisting, while acquiring a nonzero Rashba phase angle, $\varphi \in [-20;40]${\deg}, for twist angles different from 0{\deg} and 30{\deg}. This finding contradicts earlier tight-binding predictions that the Rashba angle can be 90{\deg} in the studied systems. In addition, we study the influence of several tunability knobs on the proximity SOC for selected twist angles. By applying a transverse electric field in the limits of $\pm 2$ V/nm, mainly the Rashba SOC can be tuned by about 50\%. The interlayer distance provides a giant tunability, since the proximity SOC can be increased by a factor of 2--3, when reducing the distance by about 10\%. Encapsulating graphene between two TMDCs, both twist angles are important to control the interference of the individual proximity SOCs, allowing to precisely tailor the valley-Zeeman SOC in graphene, while the Rashba SOC becomes suppressed. Finally, based on our effective Hamiltonians with fitted parameters, we calculate experimentally measurable quantities such as spin lifetime anisotropy and charge-to-spin conversion efficiencies. The spin lifetime anisotropy can become giant, up to $10^4$, in encapsulated structures. The charge-to-spin conversion, which is due to spin-Hall and Rashba-Edelstein effects, can lead to twist-tunable non-equilibrium spin-density polarizations that are perpendicular and parallel to the applied charge current., Comment: 23 pages, 14 figures, 4 tables + supplemental material

In the realm of plasmonic catalytic systems, much attention has been devoted to the plasmon-derived mechanisms, yet the influence of nanoparticles' crystal facets in this type of processes has been sparsely investigated. In this work, we study the plasmon-assisted electrocatalytic CO2 reduction reaction using three different shapes of plasmonic Au nanoparticles - nanocube (NC), rhombic dodecahedron (RD) and octahedron (OC) - with three different exposed facets: {100}, {110} and {111}, respectively. These particles were synthesized with similar sizes and LSPR wavelengths to reveal the role of the facet more than other contributions to the plasmon-assisted reaction. Upon plasmon excitation, Au OCs exhibited nearly a doubling in the Faradaic efficiency of CO (FE(CO)) and a remarkable threefold enhancement in the partial current density of CO (j(CO)) compared to the non-illuminated response, NCs also demonstrated an improved performance under illumination. In contrast, Au RDs showed nearly the same performance in dark or light conditions. Temperature-dependent experiments ruled out heat as the main factor in the enhanced response of Au OCs and NCs. Large-scale atomistic simulations of the nanoparticles' electronic structure and electromagnetic modeling revealed higher hot carrier abundance and electric field enhancement on Au OCs and NCs compared to RDs. Abundant hot carriers on edges facilitate molecular activation, leading to enhanced selectivity and activity. Thus, OCs with the highest edge/facet ratio exhibited the strongest enhancement in FE(CO) and j(CO) upon illumination. This observation is further supported by plasmon-assisted H2 evolution reaction experiments. Our findings highlight the dominance of low coordinated sites over facets in plasmonic catalytic processes, providing valuable insights for designing more efficient catalysts for solar fuels production.

We prove that the quartic Korteweg-de Vries equation is globally well-posed for real-valued initial data in $H^s(\mathbb{R})$, $s>-1/24$., Comment: 15 pages

Protein-Protein Interaction Networks aim to model the interactome, providing a powerful tool for understanding the complex relationships governing cellular processes. These networks have numerous applications, including functional enrichment, discovering cancer driver genes, identifying drug targets, and more. Various databases make protein-protein networks available for many species, including Homo sapiens. This work topologically compares four Homo sapiens networks using a coarse-to-fine approach, comparing global characteristics, sub-network topology, specific nodes centrality, and interaction significance. Results show that the four human protein networks share many common protein-encoding genes and some global measures, but significantly differ in the interactions and neighbourhood. Small sub-networks from cancer pathways performed better than the whole networks, indicating an improved topological consistency in functional pathways. The centrality analysis shows that the same genes play different roles in different networks. We discuss how studies and analyses that rely on protein-protein networks for humans should consider their similarities and distinctions.