We have examined the stellar structure of 10 nearby, low stellar mass (10^6 to 6 x 10^7 Msolar) dwarf irregular galaxies by fitting ellipses as a function of surface brightness on ultra-deep V images. These are compared to far ultraviolet images as tracers of the star formation. We find that the often asymmetrical distribution of large patches of star formation activity in dwarfs, even out to low disk surface brightness levels, skews the broad-band optical isophotes in these galaxies. We also looked for evidence of the presence of a stellar halo. Possible hints of such are found in several galaxies from irregularities in the ellipses, but a stack of seven of the galaxies shows a pure exponential out to a V surface brightness of 32.3 mag/arcsec^2 where the stellar surface density is 0.0013 +/- 0.0011 Msolar/pc^2. The extended stellar component, most likely a disk structure, is probably due to internal evolutionary processes rather than external accretion. The UBVI colors of the annuli are consistent with ages of 1-6 Gyr for the far outer stellar disk.

In this paper, we consider remote reconstruction over wireless networks when simultaneous accuracy at the legitimate receiver and confidentiality against eavesdropping are required. These two objectives are often treated separately, even though they arise from the same update process and are marginals of a joint reconstruction event. This paper introduces confidential reconstruction accuracy (CRA), a metric to capture the joint event in which the legitimate receiver reconstructs correctly while the eavesdropper fails. Under randomized stationary policies, we develop a three-dimensional stationary analysis and derive closed-form expressions for the long-term average CRA and the optimal transmission probability. The results show that conventional marginal analysis can misidentify the optimal policy and misestimate the achievable simultaneous accuracy-confidentiality performance. They also reveal nontrivial behaviors: more frequent transmissions or better legitimate channels do not necessarily improve joint accurate and confidential reconstruction, and when the eavesdropping channel is strong, improving the legitimate channel alone may be insufficient. Finally, the framework induces the spatial safety boundary in a geofencing setting for secure remote reconstruction.

Orthogonal frequency-division multiplexing (OFDM) and its static sinusoidal subcarriers have underpinned the 4G and 5G eras, delivering high spectral efficiency and resilience to multipath fading through an efficient multicarrier architecture. However, as future systems move toward doubly dispersive environments driven by high-mobility applications and migration to mmWave/sub-THz bands, the time-invariance assumption underlying OFDM becomes increasingly difficult to maintain, and Doppler-induced degradation becomes prominent. While enhancements such as MIMO, advanced coding, and scheduling provide incremental remedies, they introduce additional overhead, because the sinusoidal subcarrier itself offers no inherent waveform-level robustness to Doppler impairments. Accordingly, two time-frequency spreading philosophies have emerged to improve Doppler resilience by distributing each symbol's energy across both dimensions of the time-frequency plane: (i) 2D isotropic spreading via the delay-Doppler (DD) domain, exemplified by the orthogonal time frequency space (OTFS) family, and (ii) sheared spreading via parameterizable chirps, exemplified by the affine frequency-division multiplexing (AFDM) family. In this article, we examine key considerations for future waveform design across these paradigms and argue that transitioning from the sinusoidal subcarriers of OFDM to the chirp-based subcarriers offers a viable design direction for improving Doppler robustness while retaining much of the mature OFDM infrastructure. This perspective also highlights the suitability of chirp-based waveforms for integrated sensing and communications (ISAC) and their extensibility to emerging physical-layer techniques. Overall, we argue that the transition from sinusoids to chirps is a technically motivated, compelling evolutionary direction for future wireless physical layer design.

Many quantum-network applications require end-to-end Bell pairs whose fidelity exceeds a request-specific threshold, but existing entanglement routing algorithms either optimize only throughput without regard for fidelity or enforce fidelity guarantees using centralized controllers with global link-state knowledge. We present Q-GUARD, an online entanglement routing algorithm that enforces per-request fidelity thresholds within a distributed protocol model in which nodes exchange link-state information only with their $k$-hop neighbors. After link outcomes are realized in each slot, Q-GUARD builds per-link purification cost tables from realized Bell pairs, allocates per-hop fidelity targets using a Werner-state equal-split rule, and selects between candidate path segments using a segment-local expected-goodput (EXG) metric that jointly accounts for swap success, purification overhead, and resource availability. We also introduce Q-GUARD-WS, an extension that exploits per-link hardware quality estimates to allocate purification effort non-uniformly across hops. On synthetic 100-node topologies with heterogeneous link fidelity and stochastic BBPSSW purification, Q-GUARD raises the qualified success rate from under 20\% to over 85\% on 4-hop paths and nearly doubles the qualified service radius in Euclidean distance relative to throughput-only and naive-purification baselines, while Q-GUARD-WS provides additional throughput gains under high hardware heterogeneity.

Interactions between inertia-gravity waves and balanced flows lead to a spectral diffusion of wave action. Prior work has established that this diffusion is weak across constant frequency surfaces in three-dimensional settings, but can be significant in two dimensions with a non-stationary balanced flow. We investigate the two-dimensional setting through numerical simulations that simultaneously evolve a turbulent quasigeostrophic balanced flow and advect rotating shallow water wave packets. In contrast to earlier predictions based on the synthetic flows used by Dong et al. (J. Fluid Mech., 2020, vol. 905, R3), we find that frequency spreading from wave mean-flow interactions is weaker for realistic turbulent flows. We derive a timescale for frequency diffusion and show that frequency spreading with a realistic background flow is an order of magnitude smaller than with the synthetic flow. We narrow the discrepancy between the two- and three-dimensional induced diffusion theories, which suggests other mechanisms are responsible for the broadband frequency spectra seen in the atmosphere and ocean.

This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of symplectic structures in describing mechanical states. The study highlights the formal analogy between classical phase space and the Hilbert space used in quantum mechanics. The second part is devoted to the geometric description of quantum states through the projective structure of Hilbert space. Emphasis is placed on the geometric interpretation of quantum evolution, particularly via the Fubini-Study metric, associated symplectic structures, and the geometric phase acquired during unitary evolutions. The final two parts are dedicated to the study of spin systems (both two-body and many-body) under different interaction models (XXZ Heisenberg and all-range Ising). Both the dynamical aspects (evolution speed, entanglement, and the quantum brachistochrone problem) and the geometric and topological structures of the corresponding quantum states are analyzed.

Thermal referral enables thermal sensations in locations lacking thermal actuators--this is achieved using vibrotactile actuators to redirect a nearby thermal sensation to where a tactile sensation is applied. However, we found that its reliance on vibration introduces critical limitations: it struggles to produce cold referral, and the inherent strong tactile "buzz" makes it unsuitable for simulating non-contact thermal events, such as the chill of an open freezer in VR (in contrast to contact-based thermal events like touching the freezer's cold handle). To improve this, we propose a shift from vibrotactile to electrotactile-based thermal referral. We evaluated in two user studies--a psychophysics experiment (N=22) and a VR deployment (N=20)--where we contrasted electrotactile with vibrotactile-based thermal referral. Our results reveal key advantages of the electrotactile based thermal referral: (1) increases the referral rate for cold sensations; (2) increases thermal perception while minimizing tactile; and (3) improves realism across a range of VR thermal scenarios, specifically distinguishing between contact-based and non-contact thermal events. Finally, we provide design guidelines for choosing tactile cues to create immersive multimodal thermal experiences in VR.

The ramp filter kernel and cutoff frequency are fundamental parameters of the Feldkamp-Davis-Kress (FDK) algorithm that determine the resolution and noise characteristics of the reconstructed image. Despite their importance, systematic evaluations of their combined effect on task-based image quality in preclinical micro-CT are scarce, and many studies do not report the filter configuration used. We reconstruct identical data from a GE eXplore CT 120 scanner using four filter kernels (ramp, Shepp-Logan, cosine, Hamming) at four cutoff frequencies (1.0, 0.8, 0.6, and $0.379\times$ Nyquist, matched to the detector-to-voxel size ratio) and evaluate each of the sixteen configurations using the modulation transfer function (MTF), noise power spectrum (NPS), and non-prewhitening detectability index (NPW $d'$). Qualitative assessment is performed on a mouse lung specimen. Across the sixteen configurations, $\mathrm{MTF}_{10}$ ranges from 0.93 to 2.35 lp/mm, integrated NPS from 75,670 to 13,259 $\mathrm{HU}^2$, and the Rose criterion crossing diameter from 2.86 to 0.93 mm at $ΔC = 500$ HU and from 7.74 to 3.62 mm at 100 HU. This note presents the data as a concise visual and quantitative reference for groups selecting FDK filter parameters for preclinical cone-beam CT.

We consider the Schwarzian KP and Harry Dym hierarchies in the framework of the bilinear formalism which is well known for such integrable hierarchies as KP, modified KP, BKP, Toda lattice and other. We show that, similarly to the bilinear formulation of the modified KP hierarchy, the Schwarzian KP can be reformulated as an integral bilinear equation for a pair of KP tau-functions with the property that any linear combination of them is again a tau function of the KP hierarchy. The Harry Dym hierarchy is then obtained as the Lax-Sato formulation of the SchKP one. The close connection with Backlund-Darboux transformations for integrable hierarchies is also discussed. Besides, it is shown that the SchKP hierarchy has a natural embedding into the multi-component KP hierarchy.

A boundary integral equation (BIE) formulation for 2-D transient elastic wave propagation problems is presented. On the basis of the three-dimensional integral identity, the time-dependent kernels for the two-dimensional boundary integral equation are obtained. A linear time variation of displacements and tractions is assumed over each time step and an implicit time marching scheme is deduced. The formulation is used to obtain an analytical solution for the cylindrical cavity under transient pressure at the boundary surface.

The KM3NeT research infrastructure instruments a large volume of seawater using photomultiplier tubes, which are sensitive to the Cherenkov radiation stimulated by the products of neutrino interactions in the water, as well as that stimulated by atmospheric muons which penetrate the sea depths. The KM3NeT/ARCA and KM3NeT/ORCA detectors are situated at different depths in the Mediterranean Sea, with different extension and densities of the photo-detection elements. Although operating independently, taken as a whole the two detectors provide a wide energy coverage for the atmospheric muons flux. Through the detection and analysis of these atmospheric muons, a variety of physics studies are possible with the KM3NeT telescope. A measurement of the atmospheric muon neutrino flux has been carried out with data from the initial six detection units of the KM3NeT/ORCA detector. Relatedly to the atmospheric muon flux, the recent atmospheric lepton model `Daemonflux' has been incorporated into the KM3NeT Monte Carlo event generator for atmospheric muon bundles. This has resulted in a stark alleviation of the atmospheric muon data-Monte Carlo simulation discrepancy - a systemic issue in cosmic ray experiments referred to as the `Muon Puzzle' - and a comprehensive description of the atmospheric muon data in KM3NeT. These atmospheric muons are also used in the calibration of the detectors, as well as constraining systematic uncertainties in the detectors such as the optical properties of the instrumented seawater. An overview of these topics, and other cosmic ray analyses, is presented.

The increasing integration of distributed energy resources (DERs), variable renewable energy sources, and emerging technologies presents new challenges for transmission system expansion planning (TSEP). Traditional snapshot-based and deterministic approaches are inadequate for capturing the temporal dynamics and operational constraints of modern power systems. This paper introduces an annual quasi-static time-series simulation (AQSTSS) framework that enables high-resolution, year-round modeling of transmission systems, incorporating detailed equipment behavior, control strategies, and DER interactions. By simulating system performance across all seasons and operating conditions, AQSTSS uncovers flexibility opportunities and operational constraints that static methods overlook. Applied to Hydro-Québec's projected 2035/2036 grid, the framework reveals critical insights under high wind and electric vehicle penetration. It also integrates an energy storage control strategy designed to mitigate wind variability and support grid reliability. Furthermore, AQSTSS facilitates the assessment of system resilience under diverse scenarios, including extreme weather and load variability. The simulation results underscore the importance of aligning planning with operational realities to ensure secure, efficient, and future-ready grid development. Overall, the proposed framework enhances the robustness of TSEP by bridging the gap between long-term planning and real-time operational needs.

Controlled experimental studies of percolation are challenging due to difficulties in tuning site connectivity, isolating local interactions, and mitigating finite-size effects. In this work, we experimentally investigate percolation with a platform of coupled lasers, where connectivity, interaction strength, and system size can be controlled. Using a square array of 100 lasers with astronomical number of possible cluster configurations, we show that the emergence of a percolating cluster corresponds to the onset of phase locking among the lasers. We also show that the percolation probability undergoes a second-order alike transition as a function of the site-occupation probability, with a threshold consistent with classical theoretical predictions. Surprisingly, we find that at low pump level, amplified mode competition (nonlinear regime) alters the effective behavior of the lasing sites and modify the nature of the percolation transition. The experimental results are interpreted by the means of a theoretical toy model with connectivity rules to the classical percolation.

We study the Schrödinger evolution generated by the Pauli-Fierz Hamiltonian, a model for nonrelativistic quantum electrodynamics, in the classical limit $\hbar \rightarrow 0$. In this regime, we rigorously derive the Newton-Maxwell equations of classical electrodynamics as effective dynamics approximating the time evolution. Our result complements prior work by an alternative derivation that provides explicit estimates on the rate of convergence, justifying the validity of the approximation for a special class of initial data.

The Nuclear Bulge of the Milky Way harbors stellar populations that provide crucial insights into galaxy formation processes and serve as a nearby analog for understanding bulge formation in external galaxies. However, detailed studies of this region are severely hampered by extreme and highly variable interstellar extinction, which obscures the intrinsic stellar properties and impedes accurate stellar mass determinations. Our goal is to measure the extinction law towards the Nuclear Bulge and to estimate its stellar density. We developed a method to determine the extinction law towards the Nuclear Bulge by kinematically selecting red clump stars belonging to this region. We created a high-spatial resolution reddening map, and computed stellar mass with completeness-corrected red clump star counts, scaled from empirical measurements. We find a total-to-selective extinction ratio of $\mathrm{A_K/{E_{H-K}} = 1.259 \pm 0.074}$, and an extinction ratio of $\mathrm{A_H/A_K = 1.794 \pm 0.046}$, which are consistent with previous works. The high-spatial resolution reddening map shows clear filamentary structures, and a gradient in the extinction over the giant molecular cloud G0.253+0.016 (i.e., the Brick). From the star counts, we measured a stellar mass of $\mathrm{12.2~\pm2.6\times10^8~M_{\odot}}$ for the Nuclear Bulge, in agreement with other mass estimates.

Dilute Mg-Zn wires are of great interest for biodegradable small-bone fixation, as magnesium degradation can support bone-related processes, while low zinc additions may provide biological benefits without compromising biocompatibility. In this work, the influence of Zn content below the room-temperature solubility limit was assessed in Mg-Zn wires intended for resorbable implant applications. Mg-0.4Zn, Mg-0.6Zn, Mg-0.8Zn, and Mg-1.5Zn alloys were processed by single-step direct hot extrusion into thin wires and characterized by correlative microstructural analysis, tensile testing, bending experiments, and in vitro degradation. All compositions achieved a recrystallized fine equiaxed grain size of 5.0-5.9 um and exhibited ultimate tensile strengths of 246-256 MPa with elongations of 23-28 %. In these thin wires, Zn content had only a limited effect on grain size, tensile properties, and bending behavior, although lower-Zn alloys showed a pronounced sharp yield point. Bending was governed mainly by extrusion texture and preserved reversible plasticity through twinning and detwinning. Simulated body fluid caused rapid localized degradation and loss of mechanical integrity within 7 days, while the biologically more relevant DMEM-based medium better reflected the expected in vivo response. Together, these findings support dilute Mg-Zn wires as a simple material platform for the development of future resorbable bone fixation devices.

In nearly every discipline, scientific computations are limited by the cost and speed of computation. For example, the best-known exact algorithms for the canonical Traveling Salesman Problem would take centuries to run on an instance of size 1 million. A natural response to such limits is to try to find new algorithms or to parallelize existing ones, but many algorithms are already at their theoretically-optimal level and parallelization is often impossible or prohibitively expensive. Starting in the 1960's, computer scientists pursued another solution: allowing solutions to have a small amount of error (i.e. approximating them). In this paper, we survey 118 of the most important algorithm problems in computer science, quantifying the gains and tradeoffs from approximation that have been discovered over the history of the field. Overall, only $\approx$20\% of problems have benefited from approximation. However, those with good approximate algorithms can be dramatically faster to compute with little cost to accuracy. For example, a quarter of computationally intractable problems (e.g. those that take exponential time to compute) have polynomial time approximate algorithms. Approximation also increases the number of algorithms that can run in linear time by 23\%, opening up new computational opportunities for those working in the big data regime. This work also sheds light on what should be expected from progress in AI, where approximation is at the heart of how deep learning works.

In this paper, we show that for a given degenerate bivector $π= y^n\partial_x \wedge \partial_y$ with $n>1$, the classical Poisson cohomology group and the logarithmic Poisson cohomology group along the ideal $\mathcal{I}=y^n\mathbb{F}[x,y] $ are isomorphics in every dégrée. This result follows from determination of the logarithmic Hamiltonian operator and the logarithmic Poisson cochain complexe in order to compute the cohomological invariants associated to $π$. $\mathbb{F}$ is the field of characteristic 0.

Person-fit statistics are widely used to detect aberrant response patterns in educational and psychological measurement. Snijders (2001) suggested an asymptotically correct standardization for a broad class of such statistics. This paper presents an alternative derivation of this standardization. The derivation yields several advantages including a simpler formula and simpler description of several person-fit statistics including the lz* statistic (van Krimpen-Stoop & Meijer, 1999) and a theoretical explanation of simulation findings reported by Snijders (2001) and van Krimpen-Stoop and Meijer (1999), among others.

We investigate multi-objective adaptive beamformer design strategies for non-invasive microwave hyperthermia. Our focus is to address the challenges of maintaining focused power deposition in desired locations while reducing unwanted heating elsewhere under conditions of changing dielectric properties. The process of heating the media causes changes in the dielectric properties of the media, which can degrade the effectiveness beamformers with static weights. Typical hyperthermic beamformer designs calculate antenna beamforming weights using patient-specific high resolution dielectric maps obtained by MRI or microwave tomography, however this process is time consuming and difficult to perform in real-time. In this work, we explore the efficacy of microwave hyperthermia in various inhomogeneous media under changing dielectric conditions, with the goal of informing the design of future adaptive real-time microwave hyperthermia techniques. We aim to achieve cell apoptosis by obtaining temperatures of $\sim$ 45 $^\circ\text{C}$ through selective absorption of electromagnetic wave focusing at a 2.5 GHz carrier frequency with little to no knowledge of the changes in the dielectric media and simultaneously place nulls to avoid unwanted heating outside of the treatment zone. We investigate the effectiveness of the linear constrained minimum power (LCMP) algorithm for near-field multi-objective beamforming and examine the power density obtained from finite-difference time-domain (FDTD) simulations on simple analytical models and anatomically realistic numerical breast phantoms. To gain a comprehensive knowledge of the efficacy of the beamformer we evaluate the resulting thermal maps of the models in simple homogeneous cases, heterogeneous cases and MRI-derived phantom breast models.

Entangled photon pairs play a major role in various modern technologies such as quantum imaging, communication, and computing. Conventional photon-pair sources are often based on spontaneous parametric down-conversion in bulk nonlinear crystals. Recent advances have also shown entangled photon-pairs from transition metal dichalcogenide thin-films, however, these materials are not widely available and are not compatible with existing fabrication capabilities. We present a new thin-film lithium niobate source of polarization-entangled photon pairs at the telecom wavelength that requires no additional optical elements for entanglement generation and allows for easy application using the existing lithium niobate fabrication technologies. We demonstrate tunable entanglement generation using the three-fold rotational crystal symmetry of lithium niobate, allowing the generation of different maximally entangled Bell states or completely separable states depending on the polarization of the pump beam.

We characterize bounded, compact, and Hilbert-Schmidt composition-differentiation operators on weighted Dirichlet spaces. The essential norm is estimated via the asymptotic behavior of a function that involves the generalized Nevanlinna counting function of the inducing map. Norm estimates for particular inducing maps are given, and examples are provided to demonstrate the applicability of the results.

We develop a structure-preserving solution framework for the optimal control of the time-dependent Maxwell's equations. Building on a well-posedness theory for a weak form of the forward problem, we first analyze a forward solver that couples Nédélec and Raviart--Thomas finite elements with Crank--Nicolson time stepping. The solver preserves the de~Rham structure, enforces a discrete Gauss law, exactly satisfies a per-time-step energy balance, and converges to the weak solution under low regularity assumptions on the problem data, which are dictated by the optimal control setting. To control the Maxwell system, we add the curl of a space-time current density as a source to Ampére's law. The curl form yields charge conservation without auxiliary constraints. We prove the well-posedness and continuity of the control-to-state map, derive the adjoint system and a gradient representation for a tracking-type objective functional, and formulate a discrete optimization scheme that inherits structure preservation from the forward solver. Our discrete stationarity conditions are consistent with their continuous counterparts, and the discrete optimal controls converge, with mesh and time refinements, to the continuous optima. We demonstrate the merits of our optimal control formulation and the theoretical developments by numerically solving a series of source-cloaking model problems.

Collective excitations in fermionic systems play a crucial role in determining their physical properties. An important challenge is to develop efficient theoretical approaches for describing these excitations and their coupling to fermionic degrees of freedom. In this work, we revisit the problem of quantifying the contributions of individual bosonic modes of collective fluctuations to observable properties of correlated fermion systems within the framework of the Fluctuating Local Field (FLF) method. Whereas the auxiliary field in this method was previously considered only classically, we formulate its systematic extension termed Quantum FLF (Q-FLF) that incorporates selected bosonic Matsubara modes, thus tailoring it to description of quantum collective fluctuations. As a testbed, we apply the approach to a half-filled one-dimensional Hubbard chain and compute the Green's function, the total energy, and the antiferromagnetic susceptibility. Our results demonstrate that the proposed scheme enables an efficient and selective characterization of the contributions of individual bosonic modes. In particular, low Matsubara frequencies are found to have a quantitative impact on integrated observables such as total energy and antiferromagnetic susceptibility. At the same time, an accurate description of single-particle properties requires inclusion of higher-frequency bosonic modes.

This paper addresses the problem of distributed state estimation for discrete-time linear time-invariant systems. Building on the framework proposed in Gao & Yang (2025), we exploit the Jordan canonical form of the system matrix to develop two distributed estimation schemes that ensure asymptotic convergence of local estimates to the true system state. In both approaches, each node reconstructs the components of the state that are locally detectable for it via a Luenberger observer, while employing a consensus-based mechanism to estimate the components that are not directly detectable. The first scheme relies on local observers whose dimension matches that of the original state vector; however, its applicability requires the satisfaction of a large set of inequalities. The second scheme, in contrast, can be implemented under less restrictive conditions, but results in observers of increased (augmented) order. For both methods, we derive necessary and sufficient conditions - expressed in terms of the eigenvalues of the system matrix and certain submatrices of the communication network Laplacian - that guarantee the existence of a distributed observer achieving asymptotically accurate estimation. Compared to Gao & Yang (2025), the proposed approaches offer greater flexibility in the selection of coupling gains and impose less stringent solvability conditions.

The efficient parallel execution of complex computations requires balancing the workload across processors while minimizing the communication between them. This inherent trade-off is often captured by graph partitioning or DAG scheduling problems. For the sake of model simplicity, most works on these problems assume that nodes can be assigned to only a single processor. However, in reality, replicating an operation on several processors can easily be beneficial: it may increase the computational costs only by a small amount, while significantly reducing the communication requirements. Our goal is to provide a comprehensive analysis of the impact of replication on partitioning and scheduling problems. On the theoretical side, we show that for graph partitioning, replication makes the problem significantly harder in terms of approximation complexity, whereas for scheduling, its impact on complexity seems less prominent. On the experimental side, we conduct a thorough analysis of the cost reduction obtainable by replication, on a wide range of graphs from real-world applications. For hypergraph partitioning, we use Integer Linear Programming (ILP) formulations to compare the optimal costs; our experiments show that replication can reduce the cost by 17%-65% on average, or even entirely remove the need for communication in some cases. For DAG scheduling, we similarly use ILPs on smaller graphs, and develop a sophisticated heuristic that is also applicable to much larger workloads. Our experiments here demonstrate a mean cost reduction of 11.61%-23.13% with replication, or even up to 58.17% in some cases.

We explore the theoretical viability of modeling a decaying dark matter sector through a unified scalar field approach. Using exact analytical solutions of the Friedmann constraints, we map the fluid phenomenology onto a scalar field potential. Our analysis reveals that physical viability, specifically the existence of a well-defined potential minimum; inevitably forces the dark energy equation of state into the phantom domain. To resolve the kinetic pathologies at late times, we propose reinterpreting the framework within a complex scenario, mapping the imaginary transition to the angular dynamics of a $U(1)$ phase. This mapping naturally yields an ultra-light mass scale of $m_ϕ\sim 10^{-33} \ \text{eV}$, classifying the model as a unified dark fluid. Finally, we employ a dynamical approach to study the effects of non-minimal coupling, proving that the phantom-dominated epoch acts as a stable, late-time cosmic attractor in this kind of cosmological scenario.

To explain the ubiquity of power laws and fractals in nature, Bak, Tang, and Wiesenfeld formulated simple conditions for a system to self-organize into a critical state. Dickman, Muñoz, Vespignani, and Zapperi postulated that the self-organized critical state matches the critical state in corresponding fixed-energy models undergoing traditional phase transitions. Although the theory has been applied broadly over the past five decades, no mathematical model has been proven to exhibit the conjectured behavior. Indeed, the originally proposed abelian sandpile model displays nonuniversal behavior stemming from its slow mixing. Marking the first result of its kind, we prove that the 1-d activated random walk model mixes quickly into a stationary state with power-law avalanches and limiting critical density that equals the critical value for the fixed-energy version.

We establish range characterizations, or data consistency conditions, for an integral transform that maps a function to its weighted integrals over conical surfaces in $\mathbb{R}^n$. We consider two different geometries for the cone vertices, which lead to mathematically distinct range conditions. We use the term \emph{conical Radon transform} when the vertex set is a bounded convex subset of $\mathbb{R}^n$ including support of the unknown function. The second geometry is motivated by Compton camera imaging: the vertex set represents planar detector locations and is disjoint from the support of the radiation density. We refer to the corresponding transform as the \emph{Compton transform}. Our approach is based on a factorization into the $k$-weighted divergent beam transform and the spherical section transform. In the bounded convex vertex geometry, the range of the divergent beam component is described by a higher-order transport boundary-value problem, as studied by Derevtsov, Volkov, and Schuster \cite{Derevtsov2021}. In the planar detector geometry, we derive range conditions for the $k$-weighted divergent beam transform that generalize the planar cone-beam consistency conditions of Clackdoyle and Desbat \cite{ClackdoyleDesbat2013}. Combining these results with the range characterization of the spherical section transform yields complete range descriptions for both the $k$-weighted conical Radon transform and the $k$-weighted Compton transform.

In recent years, many interesting works providing a topological description for black hole (BH) properties have appeared in the literature. In particular, in this framework BHs correspond to topological defects in an enlarged (off-shell) parameter space, with an associated total topological charge. In gauge/gravity duality the transition from the confined to the deconfined phase is mapped into the dominance of a BH phase in the gravity side. Here we show, using a holographic AdS/QCD model, that the introduction of an energy scale in anti-de Sitter (AdS) space results in a change in the topological class. Such a modification corresponds to the existence of confined and deconfined phases, separated by a Hawking Page transition at a finite critical temperature.