The tight-binding (TB) model is a widely adopted approximation scheme for describing light propagation in waveguide arrays. Despite its success, its validity in $\mathcal{PT}$-symmetric systems characterized by strong longitudinal modulation has not been rigorously benchmarked against exact analytical solutions. In this work, we address this gap by performing a comparative analysis between exact continuous solutions derived from $z$-dependent supersymmetric (SUSY) transformations and their corresponding discrete TB approximations. To achieve this, we develop a theoretical model for two PT-symmetric coupled waveguides subject to longitudinal modulation. We then evaluate the performance of the TB framework against the exact SUSY benchmark. Our results delineate the specific validity range of the TB approximation, demonstrating its proficiency in reproducing spatial intensity distributions. However, we also identify its limitations in accurately capturing the complex oscillatory phase dynamics inherent to this non-Hermitian evolution.

We investigate the emergence of non-Markovian dynamics in finite-dimensional open quantum systems governed by Weyl dynamical maps and their convex combinations. Using the Hermite normal form, we provide a complete classification of the subgroups of the discrete phase space $\mathbb{Z}_d \times \mathbb{Z}_d$, establishing the algebraic framework underlying the Weyl maps. We characterize isotropic Weyl dynamical maps that generate Markovian semigroups and show that anisotropic Weyl maps with nonuniform weight distributions cannot possess the semigroup property. Furthermore, we analyze the role of convexity in the generation and suppression of memory effects. Remarkably, we prove that convex combinations of eternally non-Markovian Weyl dephasing maps can generate Markovian semigroups, demonstrating that non-Markovianity is not additive under mixing. Conversely, we establish a general condition under which convex mixtures of $N$ distinct Weyl semigroups exhibit eternal non-Markovianity. In contrast to the qubit Pauli setting, we further identify the existence of irreducible eternally non-Markovian Weyl dephasing maps, namely, individual dynamical maps that display eternal memory effects without requiring any mixing mechanism. Finally, explicit qutrit examples illustrate the transition among Markovian, non-Markovian and eternally non-Markovian regimes. Our results uncover a fundamental connection among finite phase-space algebra, convex structures, and quantum memory effects, thereby extending the theory of non-Markovian dynamics beyond the Pauli framework.

A surrogate-based synthesis framework for antenna arrays is presented that incorporates mutual coupling while keeping optimization computationally efficient. The method combines a common characteristic-mode basis, a global modal coupling model, and element-wise generalized scattering matrices (GSMs). Array design variables are formulated and optimized on physically meaningful manifolds, in particular the manifold of unitary symmetric matrices for reciprocal and lossless element GSMs. A staged penalty strategy is used to progressively enforce sidelobe and cross-polarization constraints during multi-beam optimization. The framework is demonstrated for an 8x8 left-handed circularly polarized patch phased array with scan behavior in one principal plane. Different degree-of-freedom assignment strategies are compared, showing that constrained non-identical element classes can satisfy stringent pattern requirements where equal-element designs fail. For the demonstrated case, the optimization converges within seconds on a single CPU core, and full-wave verification of the realized arrays confirms the predicted trends, with good agreement for the SLL and useful accuracy for the XPR. The results indicate that the proposed formulation is a practical and scalable route for coupling-aware array synthesis and realization.

The growing complexity and scale of scientific workflows in high performance computing (HPC) environments have led to significant challenges in managing energy consumption without compromising computational performance. Traditional scheduling strategies often fail to account for the complex interplay between thermal dynamics, workload diversity, and system scalability, leading to inefficient and unsustainable energy usage. This paper introduces a novel, scalable, and AI-assisted scheduling framework for optimizing energy consumption in HPC environments without compromising performance. Central to our approach is the integration of Computational Fluid Dynamics (CFD) with a Physics-Informed Variational Autoencoder (PIVAE), enabling the generation of physically realistic synthetic workload data that bridges the gap between thermodynamic behavior and scheduler decision-making in complex, multi-scale HPC environments. By categorizing workflows based on resource utilization profiles, we evaluate multiple scheduling strategies such as Locality Aware and Speculative Aware Scheduling. These workflows, ranging from event reconstruction to anomaly detection, represent diverse computational intensities. Our results show that modest reductions in CPU performance (e.g., to 15%) can yield substantial energy savings (up to 10%) with only minor turnaround time increases (approximately 5-6%), identifying an optimal operational sweet spot. This work demonstrates how physics-informed generative modeling can enable adaptive, sustainable, and data-efficient scheduling for next-generation HPC infrastructures.

We study the ideal of the algebraic relations among 3-point functions from a combinatorial and topological perspective. We place this problem in the broader setting of incidence toric ideals associated with incidence matrices of t-subsets contained in k-subsets of n elements. Generators of these ideals admit combinatorial interpretations as null t-designs and topological interpretations as balanced orientable normal d-pseudomanifolds without boundary. Generators arising from octahedra play a fundamental role in the structure of these ideals.

We consider interfaces between critical spin-chains in different universality classes, described in the continuum limit by defect/interface conformal field theory (DCFT/ICFT). We find a new conformal interface between the Tricritical Ising (TIM) and the Ising CFT. We also explore the possibility of its experimental realizations in the context of Rydberg atom arrays. Our analysis emphasizes non-invertible symmetries and consistency under modular transformations, and uses defect couplings and the defect spectrum -- including in the case of mixed boundary conditions -- to make sharp experimental predictions. The structure of the observables hinges on a newly discovered pattern of emergent ${W}_3$ chiral symmetry for the Tricritical-Ising/Ising interface.

Applying the techniques resulting the existence of almost invariant half-spaces, similarity models $\wh T$ can be given for upper triangular operator-matrices $T= \left[\begin{matrix}A&C\\ 0&B\end{matrix}\right]$. The model $\wh T$ is also an operator-matrix, containing two diagonal operators in the general case \cite{ker25}, and the unilateral shift $S$ together with a diagonal operator in the particular case when $A$ is similar to $S$ \cite{ker26}. Well-chosen compressions of operators in the commutant $\{\wh T\}'$ form a linear manifold $\whŁ$ satisfying the condition that every $\wh X\in\wh Ł$ is transformed into $\wh Y$ with $\rank\wh Y\le 2$ by a canonical mapping. Furthermore, a cyclcity property of $\{T\}'$ yields transitivity of $\whŁ$. In \cite{ker25} and \cite{ker26} the 3-dimensional cross-sections of $\whŁ$ have been investigated characterizing the canonical bases occurring in the corresponding subspaces of the matrix-algebra $M_3[\C]$. In this paper new conditions are provided by studying matching of adjacent cross-sections.

The commitment-based AKE model provides a formal security framework for key exchange protocols that avoid long-term cryptographic material, achieving authentication through a final out-of-band verification of session-derived values. Within this model, secure KA-based and KEM-based protocols were previously constructed via a commitment-based MT compiler, yielding optimized 4-pass protocols. In this work, we show that 3-pass protocols secure under this model exist for both primitives. These protocols are constructed ad hoc, following the core ideas of the commitment-based MT authenticator, and their SK security in the unauthenticated model is proved using the same game-based techniques, achieving bounds of the same form as those previously achieved. The resulting protocols provide one-way authentication in three message exchanges.

We construct a $d$-dimensional dissipative colored fluid by Scherk--Schwarz reduction of a neutral viscous conformal fluid in $D=d+n$ dimensions on an $n$-dimensional unimodular group manifold. The off-diagonal components of the higher-dimensional stress tensor become non-Abelian color currents, while the higher-dimensional shear tensor induces shear, bulk-like and vector-dissipative structures in the reduced theory. We derive the map for the equation of state, sound speed, color current, entropy current and first-order transport coefficients. In particular, \[ η=\ee^{αφ}\coshξ\,\heta,\qquad τ=η\,\frac{n}{(D-1)(d-1)},\qquad κ=η\sinh^2ξ. \] We also spell out the hydrodynamic-frame issue induced by dimensional reduction, discuss the status of the internal rapidity field $ξ$, and give a detailed account of how the second law descends from the parent theory, including the roles of temperature-dependent viscosity, non-unimodular groups and possible choices for $ξ$. The construction should be regarded as a toy model for non-Abelian dissipative hydrodynamics with the potential of paving the way to direct phenomenological model of, for example, quark--gluon plasma.

cloelike is a Python package providing modular, composable Gaussian likelihood classes for the main cosmological large-scale structure observables targeted by the ESA Euclid space mission. It is a core component of the CLOE (Cosmology Likelihood for Observables in Euclid) ecosystem and interfaces directly with cloelib for theoretical predictions and euclidlib for reading official Euclid data products. The package implements Gaussian likelihoods covering harmonic angular power spectra and real-space two-point correlation functions for weak lensing (WL), photometric galaxy clustering (GCph), and Galaxy-Galaxy Lensing (GGL) in all joint probe combinations (3x2pt, 2x2pt), as well as spectroscopic full-shape power spectrum multipoles, and baryonic Acoustic oscillations (BAO). cloelike is actively used in internal Euclid Consortium analyses and is openly released to support community validation and reproducibility.

cloelib is a Python library developed to compute cosmological observables within the Cosmology Likelihood for Observables in Euclid (CLOE) ecosystem (cloe-org). As cosmology enters a precision era driven by galaxy survey missions such as Euclid, there is a growing need for flexible, efficient, and differentiable software capable of supporting next-generation inference pipelines. cloelib addresses these demands through a modular architecture that interfaces seamlessly with established Boltzmann solvers whilst incorporating JAX-based automatic differentiation to enable gradient-based methods. The library defines consistent protocols for background evolution, perturbations, and non-linear structure formation, and supports a wide range of observables, including photometric and spectroscopic large-scale structure probes, as well as cross-correlations with the Cosmic Microwave Background and galaxy clusters. In its finalised form, cloelib is intended to serve as the reference theory computation infrastructure for Euclid's first cosmological release, bridging traditional numerical cosmology with modern optimisation techniques and emerging machine learning approaches to inference.

The interplay between disorder and vortex--vortex interactions in strongly disordered superconductors in a magnetic field can stabilize a vortex-glass state, characterized by strong pinning and the absence of positional order. Yet its role in the destruction of superconductivity at the field-driven superconductor--insulator transition has remained unresolved. Here we use plasmonic microwave spectroscopy of superconducting resonators patterned from amorphous indium oxide thin films to directly track the superfluid density up to the critical field $B_c$. We find an unexpected resilience of the superfluid density, which decreases only logarithmically over nearly three orders of magnitude in field, in stark contrast to the rapid power-law suppression expected for vortex lattices. We attribute this anomalously slow decay to a collective vortex-pinning mechanism counterintuitively enhanced by vortex--vortex interactions. The superfluid density then vanishes linearly at $B_c$, where independent magnetoresistance measurements identify a continuous quantum critical point, unlike the abrupt transition observed at zero field. We further uncover an exceptionally large nonlinear electromagnetic response of the vortex glass, manifested as a pronounced positive-Kerr effect with potential for quantum sensing. These results show how disorder controls the critical magnetic field and identify the vortex glass as the key intermediate state governing the magnetic-field-induced superconductor--insulator transition.

Magnetic topological semimetals provide a promising platform for emergent quantum phenomena driven by the interplay between magnetism and relativistic fermions, including anomalous transport effects and tunable topological phases. Here, we investigate the electronic structure and orbital character of EuAgAs, a magnetic topological Dirac semimetal candidate, using density functional theory (DFT) and polarization dependent angle resolved photoemission spectroscopy (ARPES). Fermi surface mapping and constant energy contours measured at 9 eV reveal ring like features that systematically expand with increasing binding energy, consistent with nearly linear low energy Dirac like dispersion. ARPES measurements at different photon energies hint at the presence of a van Hove singularity predicted by DFT calculations. Furthermore, this indicates that the photoemission matrix elements are highly sensitive to the excitation energy, allowing different photon energies to selectively probe distinct orbital characters. Polarization dependent ARPES measurements performed in s- and p-polarized geometries exhibit pronounced variations in spectral intensity, indicating symmetry selective orbital contributions to electronic states. These matrix element driven intensity modulations are well reproduced by DFT calculations. Furthermore, the observed Dirac like states remain nearly unchanged over the temperature range from 9 K to 30 K, suggesting that the magnetic ordering has minimal influence on the electronic structure. Our combined experimental and theoretical results provide detailed insight into the orbital selective electronic structure of EuAgAs and its implications for magnetic topological quantum states.

In this work, we study the removability of boundary singular sets for certain classes of quasilinear elliptic equations in domains $Ω$ of an $n$-dimensional Finsler manifold ( $\mathcal{M}, F, \vartheta$ ). We work with Lipschitz functions $ρ_1$ and $ρ_2$ satisfying distance-type properties; in particular, $F(\cdot, \boldsymbol{\nabla} ρ_1) \leq 1$ and $F(\cdot, \boldsymbol{\nabla} ρ_2) \leq 1$ a.e. in $\mathcal{M}$. The singular set is defined by $Γ=ρ_1^{-1}(\{0\})$. The model problem is $-Δ_{p(x)} u+|u|^{q-1} u=0$ in domains of $\mathbb{R}^n \cong \mathbb{R}^d \times \mathbb{R}^{n-d} \cong ρ_1^{-1}(\{0\}) \times ρ_2^{-1}(\{0\})$, where $ρ_1(x)=|(x_{d+1}, \ldots, x_n)|$ and $ρ_2(x)=|(x_1, \ldots, x_d)|$. The main tool in our analysis is the estimate $$ |u(x)| \leq \mathbf{C} ρ_1(x)^{-τ} $$ near $Γ$ for weak solutions $u \in W_{loc}^{1, p(x)}(\barΩ \backslash(Γ\cup Σ) ; \vartheta) \cap L_{loc}^{\infty}(\barΩ \backslash(Γ\cup Σ))$, where the constants $\mathbf{C}>0$ and $τ>0$ converge to positive values as $p^{+} \rightarrow 1$. This estimate is a key ingredient in proving that the singularity at $Γ$ is removable. Moreover, in a bounded domain $Ω$, using this estimate and assuming that, for every variable exponent satisfying $1<p^{-} \leq p^{+}<\min \{2, q+1\}$, there exists a weak solution $u_p \in W_{loc}^{1, p(x)}(Ω; \vartheta) \cap L_{loc}^{\infty}(Ω)$ of $$ -\operatorname{div}\left(|\boldsymbol{\nabla} u_p|_F^{p-2} \boldsymbol{\nabla} u_p\right)+|u_p|^{q-1} u_p=0 \quad \text { in } Ω, $$ we prove that, for every $U \Subset Ω$, there exists a subsequence $\{u_{p_m}\}$, with $p_m^{+} \rightarrow 1$, that converges to a solution $u \in B V(U ; \vartheta) \cap L^{q+1}(U ; \vartheta)$ of $$ -Δ_1 u+|u|^{q-1} u=0 \quad \text { in } U . $$

Thermodynamics and transport are investigated in a holographic QCD model that extends the Einstein--Maxwell--Dilaton framework by incorporating Gauss--Bonnet corrections. Model parameters are fixed using state-of-the-art lattice QCD thermodynamics. The analysis then examines the equation of state at zero and finite baryon chemical potential, the phase structure in the temperature and chemical potential plane, as well as the shear and bulk viscosity to entropy ratios, $η/s$ and $ζ/s$, via the corresponding fluctuation equations. For a constant Gauss--Bonnet coupling, the model preserves a reasonable description of the equation of state and generates a temperature-dependent $η/s$, although the resulting profile remains monotonic near the crossover region, which does not satisfy the phenomenological expectation. When the Gauss--Bonnet coupling is allowed to depend on the dilaton, a non-monotonic $η/s$ and a peaked $ζ/s$ are obtained while maintaining agreement with thermodynamic constraints. The resulting phase diagram contains a critical end point in a phenomenologically relevant region.

As deep neural networks develop significantly more diverse and complex, achieving high performance and efficiency on complicated DNN models faces pressing challenges. Modern DNN workloads are increasingly diverse in operation types, tensor shapes, and execution dependencies, making it difficult to sustain high hardware efficiency across models. In addition, a generic accelerator often incurs substantial overhead when executing diverse workloads. To address these problems, we propose DORA, an instruction-based overlay architecture that explicitly describes dataflow via a proposed ISA, enabling fine-grained control of data movement, computation, and synchronization at the layer level. To support flexibility while achieving high performance, DORA adopts a novel on-chip memory management and computation parallelism management mechanism. DORA proposes a compilation framework that can generate instructions for given DNN workloads after a two-stage design space exploration. DORA framework also incorporates a MILP-based and a heuristic-based search engine to generate the schedule solution for different needs and constraints. We prototype DORA on the AMD Versal VCK190 platform, demonstrating its deployability on existing reconfigurable systems. Experimental results show that DORA maintains stable efficiency, with less than 5\% variation on a single vector processor across workloads exhibiting up to 6$\times$ variation in operation counts. Compared to state-of-the-art accelerators, DORA consistently achieves higher performance, delivering up to 5$\times$ throughput improvement. The heuristic-based scheduler further achieves up to 90\% optimality under practical time constraints. DORA is open-sourced at https://github.com/arc-research-lab/DORA.git.

3rd Generation Partnership Project (3GPP) Technical Report (TR) 38.901 channel models (Releases 15-19) are widely used for physical-layer design and system-level evaluation in dense urban outdoor-to-indoor (O2I) and indoor environments. These models capture ensemble-averaged channel statistics but do not account for site-specific geometry. In this paper, we compare Power Delay Profiles (PDPs) derived from a deterministic ray-tracing model (Remcom Wireless InSite software) with those from the 3GPP TR 38.901 Tapped Delay Line (TDL) channel models. This comparative analysis is performed using a dense urban O2I scenario and a representative single-story indoor layout modeled in Washington, D.C., under matched link-distance and Non-Line-of-Sight (NLOS) conditions. All Wireless InSite PDPs are power-normalized to enable comparison of relative multipath delay structure. We evaluate root-mean-square (RMS) delay spread, mean excess delay, effective maximum delay, and Kullback-Leibler (KL) distribution divergence. Results indicate that 3GPP TDL models generally exhibit longer delay spreads and often fail to capture deterministic, site-specific features such as late-arriving energy and irregular spikes. While TDL models can approximate primary channel features in some cases, their reliance on ensemble-averaged statistics rather than geometry limits their representation of fine multipath structures. We conclude that while 3GPP TDL models are suitable for large-scale system evaluation, deterministic or hybrid approaches are more appropriate for site-specific physical-layer design.

We prove that the outer automorphism group of a one-ended hyperbolic group is virtually a hierarchically hyperbolic group (HHG), under mild orientability conditions on the associated JSJ decomposition. This is done by proving that a finite-index subgroup is a central extension of a product of orbifold mapping class groups, and the extension has bounded Euler class. Our theorem is sharp: we exhibit a surface amalgam whose fundamental group has full outer automorphism group which is not a HHG. To prove this, the main technical tool is the fact that a top-dimensional Abelian subgroup of a HHG is a standard flat.

Motivated by majority vertex-colorings of graphs and digraphs and majority edge-colorings of graphs, we introduce two concepts of strong majority colorings. A strong majority vertex-coloring of a graph $G=(V,E)$ is a mapping $c:V\rightarrow C$ such that for every vertex $v\in V$ and every color $α\in C$, at most half of the neighbors of $v$ have color $α$. The strong majority number of $G$, denoted Maj$(G)$, is the least number of colors in such a coloring. We show that Maj$(G)$ can be arbitrarily large and prove a tight upper bound Maj$(G)\le 2Δ(G)+1$ for every graph $G$ without pendant vertices. A strong majority edge-coloring of a graph $G$ is a mapping $c:E\rightarrow C$ such that for every edge $e\in E$ and every color $α\in C$, at most half of the edges adjacent to $e$ have color $α$. The strong majority index of $G$, denoted Maj'$(G)$, is the least number of colors in such a coloring. It is shown that there is an upper constant bound for Maj'$(G)$ of all admissible graphs $G$. We conjecture that this constant is as small as 4 and confirm this conjecture for numerous graph classes.

We revisit natural inflation within the framework of metric-affine gravity, considering the impact of a periodic non-minimal coupling between the inflaton and the Nieh-Yan term. Such a term, alone, leads to linear inflation predictions in the strong coupling limit and cannot help to rescue the natural inflation scenario. However, once an analogous non-minimal coupling with the Ricci scalar is added, agreement with data can be easily achieved. Remarkably, the scenario remains viable even with a sub-Planckian periodicity scale and relatively small (order of one) non-minimal couplings.

Vacuum entanglement is a fundamental feature of quantum field theory exhibiting rich structure that is not completely understood. Here, we provide a complete characterization of the entanglement between two bounded spacelike-separated regions in a (1+1)-dimensional free massless real scalar field. Employing Gaussian state methods, we analytically compute the logarithmic negativity and construct closed-form solutions for the localized modes carrying it, called negativity cores. These results deepen our understanding of quantum fields and suggest extensions to higher dimensions and fermionic fields.

Computing courses often feature active learning techniques that promote collaboration and social interaction between students. However, neurodivergent students' preferences and experiences with these techniques are not well understood. We conducted a survey of neurodivergent computing students (n=24), specifically autistic students or students with ADHD, and neurotypical computing students (n=20) to understand how the structure of collaborative active learning affects their comfort in computing courses. We also interviewed four computing students on the autism spectrum or with ADHD to gain more contextualized insights into their experiences and accessibility recommendations. Our survey surfaces how team dynamics and assignment structure can impact neurodivergent students' comfort in computing courses. Neurodivergent students expressed discomfort with assignments that lack structure or have ambiguous expectations. Neurodivergent students prefer smaller teams that work together frequently with explicitly defined roles. Our interviews identified ways that neurodivergent students cope with discomfort in collaborative active learning, including self-selecting roles and self-disclosure. While preliminary, our results highlight how instructors can design collaborative active learning to be more equitable and accessible for neurodivergent students.

Given a closed normal subgroup $H$ of a topological group $G$, we address the question of whether the left coarse structure on the quotient group $G/H$ equals the quotient of the left coarse structure on $G$. We provide a counterexample among Polish groups, namely, the mapping class group of the Loch Ness monster surface seen as a quotient of the mapping class group of the punctured Loch Ness monster surface, and establish both equivalent and sufficient conditions for when this holds in special settings. The latter are formulated in terms of liftings of bounded sets, existence of transversals and metrisability of the left coarse structure of $G$ restricted to $H$.

Hundreds of millions of users now hold detailed, multi-turn conversations with ChatGPT and similar LLM assistants. We measure two privacy-relevant features of these conversations on a corpus of complete ChatGPT histories donated by over 1,000 users in four Global South countries (Brazil, India, Nigeria, Pakistan). First, on explicit disclosure: 34.5% of user messages contain personal information across a twenty-category taxonomy, with the median user first revealing identifying content within the first 14% of their conversation history. Second, on inference beyond explicit disclosure: we restrict to a cohort whose conversations contain no messages flagged by an LLM-based filter for explicit demographic self-identification (a separate NER pass marks PII for the disclosure audit but does not drive cohort exclusion). On this filtered cohort, an off the shelf large language model still recovers each user's age, gender, and country at weighted F1 of 0.84, 0.90, and 0.88, respectively, with the median user identified from the first 5% of their conversation history. Reading the model's natural-language reasoning traces, we identify four recurring stereotype patterns that drive both successful inference and an asymmetric error distribution concentrating on women in technical fields, older users with contemporary skills, and Global South tech professionals. We also compare ChatGPT against the same users' Google Search and YouTube histories as inference surfaces, and find it competitive with these older substrates that have driven behavioral advertising for two decades. Message-level PII removal is insufficient on its own as a privacy intervention for conversational AI data.

We present a multi-wavelength study of GRB 260310A, a nearby long-duration gamma-ray burst at $z\simeq0.153$ associated with a broad-lined Type Ic supernova. Despite its modest prompt gamma-ray output, $E_{γ,\rm iso}\simeq3.5\times10^{50}$ erg, GRB\,260310A exhibits one of the brightest afterglows ever observed in the X-ray, optical, and radio bands. Its apparent brightness is not its only remarkable feature. The optical afterglow displays a delayed onset, characterized by a slow rising phase, with slope $α\approx-1$, and a late peak at $\approx$0.1 d. We argue that the combination of weak prompt emission, hard peak energy, and late afterglow onset is naturally explained by a GRB jet viewed off-axis. The radio spectral energy distributions are consistent with synchrotron radiation and indicate the presence of both reverse- and forward-shock components, thus providing a first test of reverse-shock models in an off-axis geometry. The X-ray afterglow displays a prominent rebrightening, monitored for up to $\approx$68 d with no evidence of spectral evolution. A low level of linear polarization, $Π\approx1.7\%$, is measured at 15 GHz at $T_0+55$ d and suggests that, at these late times, the forward-shock is the dominant emission component from radio to X-rays. This late-time rebrightening represents a critical test for the two-component jet model. If interpreted as the emergence of a narrow jet core viewed further off-axis, it would imply extreme luminosities and energetics for an on-axis observer.

In Poisson Boolean models with deterministic ball grains, the directional visible range from an uncovered point is known to be exponentially distributed in Euclidean and real hyperbolic space. We show that the same phenomenon holds on every simply connected non-compact homogeneous harmonic manifold. The geometric mechanism behind this fact is the affine-linear growth of tube volumes around geodesic segments. As a consequence, we identify the finiteness regime for the expected volume of the visible region, including a geometric interpretation of the critical threshold in the positive-entropy case. We also construct explicit complete non-homogeneous Riemannian manifolds showing that exact exponentiality is tied to exact tube linearity: superlinear tube growth leads to Weibull-type tails, while asymptotic tube linearity still yields an exponential decay rate.

An SDN-like centralized control architecture is increasingly popular and has been widely explored in cyber-physical systems (CPS) such as manufacturing, internet-of-things, and autonomous vehicle systems for higher flexibility, programmability and scalability. However, no existing frameworks can offer domain-agnostic, easily extensible support for data-driven CPS applications. In this work, we design, implement, and open-source \textit{SDNator}, the first framework to enable extensible, data-driven control in CPS. SDNator embraces an application- and data-driven design where applications function as data consumers and producers to collectively define the workflows of the controller. SDNator also incorporates two data store backends to support both event-driven and data-driven programming patterns. Benchmarks show that SDNator is highly scalable, and delivers comparable performance to Ryu, a widely used SDN controller. Moreover, we demonstrate the capabilities and usability of SDNator through our case studies of manufacturing and networking systems. By integrating applications from respective domains, we build different ``controllers'' for different scenarios. Most notably, we leverage SDNator to implement the first digital-twin-equipped central controller for additive manufacturing fleets. We show through extensive and realistic simulations that SDNator-based scheduling can (1) significantly shorten production time and improve reliability in the presence of anomalies compared to decentralized approaches, and (2) flexibly adjust and optimize production plans upon urgent requests such as producing Personal Protective Equipment during the COVID-19 pandemic.

Learned indexes have emerged as a promising alternative to traditional index structures, offering higher throughput and lower memory usage by approximating the cumulative key distribution function with lightweight models. Despite these benefits, adoption in production systems remains limited, partly because learned indexes that support concurrency and persistence as effectively as, e.g., the B+-Tree, do not yet exist, while many research prototypes introduce substantial complexity. In this paper, we investigate whether off-the-shelf learned indexes can be integrated into a production database with minimal storage-engine redesign. Using RocksDB as a case study, we exploit its separation between in-memory Memtables and immutable on-disk files to deploy specialized indexes at each level. We show that directly applying existing learned indexes is insufficient under write-heavy workloads because frequent Memtable replacement prevents models from fully adapting. To address this, we introduce a reuse mechanism that preserves structural knowledge across Memtable instances. At the storage level, we replace RocksDB's disk index with a learned index without modifying the storage layer or read path. We further adapt a read-only learned index to be block-aware, enabling worst-case single-I/O lookups. We implement these techniques in MountDB, an extension of RocksDB. Experiments on large-scale workloads with diverse data distributions and access patterns show up to 1.5X higher write throughput and 2.1X higher read throughput than state-of-the-art systems, demonstrating that established learned indexes can be integrated into production systems with minimal overhead and substantial performance benefits.

Modern optimal control theory involves adjoining the already known equations of motion of a dynamic system to the objective function using dynamic costates; this is done in order to constrain the optimal control solutions to satisfy the equations of motion. The use of costates increases the number of variables and hence increases the complexity of the problem. On the other hand, variational methods of analytical mechanics finds the equations of motion by minimizing an action functional of the dynamic system, realizing control forces as external input to the system. In this paper a new disruptive approach for computing the optimal control is presented. This approach adopts the variational methods of analytical mechanics to derive equations for the control, in addition to the equations of motion. This is achieved by recognizing the control actuator as part of the dynamic system. In addition to the kinetic energy and potential energy, the action functional in this new approach includes additional energy terms that represent the control energy of the system. Two different methods are presented to write the modified action functional. The proposed approach is a significant departure from the modern optimal control theory, and it eliminates the need for costates when solving for the control. In this paper, a case study is presented to demonstrate the new approach.

Designing effective optimisation strategies for unsteady flows in the presence of complex dynamics is challenging. Gradient-based optimisation algorithms that rely on gradient information obtained from adjoint equations are efficient for high-dimensional control problems such as those considered here. However, they can be prone to numerical sensitivities when the underlying physics is complex, i.e. when it is highly nonlinear, non-differentiable and chaotic. This work proposes an ensemble-variational (EnVar) framework, which provides a non-intrusive alternative to classical, adjoint-based approaches for flow control applications. This framework approximates cost-function gradients through a finite ensemble of perturbed control vectors. A formulation based on a finite-difference approximation in the ensemble space is employed to address high-dimensional parameter spaces. The methodology is evaluated on two-dimensional cavity flows across Reynolds regimes spanning quasi-periodic to chaotic dynamics, where a steady forcing is optimised. In the quasi-periodic regime, the method identifies control strategies consistent with adjoint-based optimization and achieves a significant reduction of kinetic energy fluctuations, driving the flow toward a periodic limit cycle. In the chaotic regime, the framework remains effective in estimating gradients and mitigating flow fluctuations in situations where adjoint-based approaches typically exhibit convergence issues. This work demonstrates that the EnVar method serves as a computationally efficient, parallelizable, and non-intrusive alternative for high-dimensional optimization problems in complex fluid dynamic regimes.