The coordination of large populations of highly constrained devices, such as micro- and nanoscale agents in biomedical applications, poses fundamental challenges to classical communication paradigms. In scenarios such as targeted drug delivery, devices operate under severe limitations in energy, size, and communication capabilities, while requiring precise and selective activation within spatially localized regions. In this work, we propose the framework of Joint Detection and Identification (JDAI) as a system-level approach for scalable control under such constraints. The key idea is to shift from reliable message transmission to a control-oriented paradigm, in which devices locally decide whether a broadcast signal is relevant. This enables implicit addressing and subset activation without the need for explicit per-device communication. We demonstrate how message identification can be combined with sensing. This enables the realization of a closed-loop system that integrates detection, communication, and actuation. Using the example of targeted nanorobot therapy, we analyze the interplay between sensing resolution, communication constraints, and system dynamics. In particular, we show that while identification exhibits favorable asymptotic scaling, practical implementations are governed by finite blocklength effects, noise, and latency. The proposed framework complements existing physical-layer communication approaches, including molecular, electromagnetic, and acoustic techniques, by providing a control-layer abstraction for scalable subset selection. Overall, JDAI connects identification-theoretic principles with system-level design to control large, resource-limited environments.

Compact, low-power analog RF components are essential for next-generation microwave electronics and wireless systems. We demonstrate an all-electric integrated piezo-magnonic microelectromechanical system that enables efficient voltage control of GHz spin-wave signals via magnetoelastic coupling. Exploiting the large strain in a CoFeB magnonic waveguide integrated on a silicon bridge with piezoelectric actuation, very large values of the magnetoelectric field (up to $30\,\mathrm{mT}$ at $30\,\mathrm{V}$) are obtained, thus achieving reversible phase and amplitude control of propagating spin waves. In the static regime, we achieve either up to $4π$ phase modulation or $\approx 50\,\mathrm{dB}$ amplitude attenuation with drive voltages below $20\,\mathrm{V}$ at $7\,\mathrm{GHz}$. Leveraging the bridge's first bending resonance ($\approx 17\,\mathrm{kHz}$) yields resonant enhancement of the phase modulation efficiency. This allows us to achieve a $2π$ phase swing with just $2.2\,\mathrm{V}$ drive and power consumption of $\approx 6\,μ\mathrm{W}$. Our results highlight piezo-magnonic MEMS as a promising new class of devices for reconfigurable RF front ends and analog signal processors.

Microscopic insights into nonlinear interactions are essential for advancing polaritonic devices. Existing studies often rely on phenomenological models that overlook important many-body processes. Based on a material-specific and predictive approach, we investigate monolayer and homobilayer MoS$_2$ embedded in a Fabry-Pérot cavity to characterize the exchange, saturation, and dipole-dipole contributions to polariton-polariton interactions in these technologically promising materials. A key finding is that the exchange interaction induces asymmetric energy shifts of the lower and upper polariton branches in a detuned cavity, a behavior driven by the difference in their excitonic character. Furthermore, we demonstrate that temperature and electron-photon coupling determine the energy renormalization through the equilibrium polariton distribution. In homobilayers, the dipole-dipole interaction is mediated by the interlayer character, enabling electrical control and facilitating the electric-field-induced closing of anti-crossings due to dipolar-interaction shifts. The gained insights on polariton-polariton interactions are important for the development of ultra-compact polaritonic circuitry.

Energetic particle populations are ubiquitous throughout the Universe. In our solar system, the most prominent sources of energetic particles are solar flares or collisionless shocks often driven by huge eruptions of magnetised plasma called coronal mass ejections (CMEs). Remotely, low energy electrons from the Sun can be observed as solar radio bursts that are produced by accelerated electron beams undergoing beam-plasma interactions. There are still many open questions on the generation of solar energetic particles (SEP): how and where are SEPs accelerated during solar flares and CMEs and how they escape the solar atmosphere? Another important question is: what is the link between the solar radio bursts and the observed SEPs at spacecraft? SKA can provide high-resolution radio images combined with spectroscopic observations to determine the acceleration time, trajectory and escape of low energy electrons from the solar corona. The synergy between SKA and current space missions will help investigate solar activity and energetic particles across a wide range of wavelengths and particle energies. Particle data from spacecraft can be used to make a connection between radio bursts and SEPs by comparing SEP inferred injection times and energies to those of electrons generating radio bursts at the Sun. Radio observations in turn can be used to distinguish between flare and shock acceleration since different radio bursts pinpoint towards different energetic processes. Since the acceleration region and origin of SEPs of various properties is still largely debated, radio observations have the potential to be an invaluable tool in unraveling these processes.

A recurring challenge in theoretical physics is to make reliable global statements about bounded but combinatorially large model spaces. Exhaustive scans quickly become opaque or impractical, while statistical exploration does not by itself provide theorem-backed guarantees. This motivates workflows in which the model-building problem itself is formalized inside an interactive theorem prover (ITP). In this paper we develop an API-based methodology for formalizing such bounded model-building questions inside Lean, an interactive theorem prover. The central step is to represent the relevant charge spectra, predicates, and reduction moves as reusable ITP definitions, and then to derive the classification from proved reduction theorems rather than from an ad hoc scan. We demonstrate the strategy in a concrete $SU(5)$ case study motivated by F-theory model building with additional Abelian symmetries. At the charge-spectrum layer, we classify bounded spectra that admit a top-quark Yukawa coupling, avoid a selected set of dangerous operators, and satisfy a minimal charge-spectrum completeness condition. Our main result shows that every such spectrum in the bounded search space arises from finitely many minimal top-Yukawa witnesses together with controlled completions and certified closure steps. This classification represents a formally verified description of the full viable class in the charge-spectrum setting studied here. The development is implemented inside PhysLib as reusable infrastructure rather than as a one-off verification script. It provides a proof of principle for how interactive theorem provers can turn combinatorially difficult model-building problems into correctness-first, reusable workflows, and we discuss how the resulting certified classification can serve as reliable input for downstream analyses.

One of the most important contributions of Heinz Langer in the area of operator theory in Krein spaces is the introduction of the notion of definitizable operators and the construction of the corresponding spectral function. In this note we obtain a new characterization for the subclass of non-negative operators in Krein spaces which is based on local sign type properties of the spectrum and growth conditions on the resolvent. Based on these local properties, a notion of local non-negativity for self-adjoint operators in Krein spaces is defined and it is shown that such classes of operators appear naturally as perturbations of non-negative operators.

We introduce relational semantics for "flat Heyting-Lewis logic" $\mathsf{HLC}^{\flat}$. This logic arises as the extension of intuitionistic logic with a Lewis-style strict implication modality that, contrary to its "sharp" counterpart $\mathsf{HLC}^{\sharp}$, does not turn meets into joins in its first argument. We prove completeness and the finite model property for $\mathsf{HLC}^{\flat}$ and for several extensions with additional axioms.

Microlensing detections are uniquely well-suited to probing the population of planets outside the water iceline, down to planetary masses comparable to the Earth. Here, we perform 1D pebble-accretion population synthesis simulations to explore a sample of iceline planets around stars with masses and metallicities similar to the target population of the Galactic Bulge Time-domain microlensing survey of the Nancy Grace Roman Space Telescope. We find that the planet distribution in the microlensing sensitivity space deviates from a log-uniform distribution in mass and orbital radius. When planetary core growth comes to a halt as planets reach the pebble isolation mass, $M_{\mathrm{iso}}$, the combined effects of planetary migration and runaway gas accretion create an occurrence break. Our simulations highlight that, between 1 and 50 AU, the fraction of stars hosting isolation-mass planets (1 to 5 $M_{\mathrm{iso}}$) is lower by a factor 20 compared to less massive planets (0.2 to 1 $M_{\mathrm{iso}}$). If this break in planetary occurrence rates around the pebble isolation mass is detected in future lensing surveys, it would further validate the core accretion paradigm for giant planet formation.

We study partially hyperbolic homoclinic classes of $C^1$-generic diffeomorphisms with a one-dimensional central bundle, so that the central Lyapunov exponent $χ^c(μ)$ is well defined for any ergodic measure $μ$ supported on the class. We focus on nonhyperbolic homoclinic classes supporting ergodic measures with positive, zero, and negative central exponents. For each $α$ and a nontrivial homoclinic class $H$ of a $C^1$-generic diffeomorphism $f$, we consider the level set of measures \[ \mathcal{M}^α_{\mathrm{erg}}(f,H)= \left\{\text{$μ$ ergodic, supported on $H$, with } χ^c(μ)=α\right\}. \] In this generic setting, the range of $α$ for which $\mathcal{M}^α_{\mathrm{erg}}(f,H)$ is nonempty forms a nontrivial closed interval $I$. Since the set of periodic measures is countable, most of these sets contain no periodic measures. We show that for every $α$ in the interior of $I$, the so-called Axiomatized GIKN measures, a class of low-complexity, zero-entropy measures, are dense in $\mathcal{M}^α_{\mathrm{erg}}(f,H)$. This result can be viewed as an analogue of Sigmund's classical density of periodic measures for systems with the specification property, obtained here in a setting where the specification property does not hold and periodic measures are typically absent (in the considered level sets). We also present a similar result for the open class of blender-minimal diffeomorphisms, contained in the class of $C^1$-robustly transitive ones.

Disordered fiber networks exhibit a floppy to rigid mechanical phase transition as a function of connectivity. Sub-isostatically connected networks can undergo this transition via straining. Critical exponents governing this transition have been estimated theoretically and by numerical simulations of various types of networks. In this study, we present improved results, achieved through a combination of refined numerical simulations, larger system sizes and incorporation of theoretical predictions for better post-simulation analysis. We also report the evolution of the critical strain and critical exponents as the network is sheared while being subjected to non-volume-preserving uniaxial deformations.

Rare disease diagnosis is inherently challenging due to heterogeneous symptoms, limited clinical familiarity, and fragmented evidence across specialties. Recent large language model (LLM)-based agentic systems have shown promise by simulating multidisciplinary team discussions to generate and evaluate diagnostic hypotheses. However, fully automated diagnosis remains unrealistic, and existing human-in-the-loop approaches provide limited support for effective clinician-agent collaboration. In practice, clinicians are often presented with final diagnostic outputs and lengthy, unstructured agent discussion logs, making it difficult to inspect reasoning, intervene in a timely manner, or guide agent deliberation effectively. To address these challenges, we developed MDTRoom, an interactive system that transforms multi-agent discussions from linear transcripts into a structured, inspectable workspace. The system externalizes patient data, evidence provenance, hypothesis evolution, and inter-agent conflicts as interconnected visual objects, enabling clinicians to efficiently examine, intervene in, and guide agent reasoning. Our evaluation demonstrates the effectiveness of MDTRoom in supporting clinician-agent collaboration.

Let $G = GL(n)$ and $K = GL(p) \times GL(q)$ with $p+q=n$, where the groups are taken over $\C$. In this paper we study a certain family of $K$-orbit closures on the flag variety $X$ of $G$. The geometry of these orbit closures plays a central role in the infinite-dimensional representation theory of the real Lie group $U(p,q)$, and has applications to degeneracy loci and combinatorics. In this paper we use small resolutions to study orbit closures in this family. We prove that the fibers of these resolutions are smooth and strongly reduced, as well as a general result that if a variety has a resolution of singularities with these properties, then its characteristic cycle is irreducible. Hence these orbit closures have irreducible characteristic cycles. A result of Jones then allows us to calculate the torus-equivariant Chern-Mather classes of these orbit closures. We describe torus fixed points and tangent spaces of the resolutions, and use localization to obtain a formula for these classes. We conjecture that the Chern-Mather classes of a $K$-orbit closure are equivariantly positive when expressed in a Schubert basis of equivariant Borel-Moore homology, and use our results to verify the conjecture in an example.

The $Λ$CDM model successfully explains a wide range of cosmological observations; however, persistent discrepancies most notably the $H_0$ tension between early and late time measurements challenge its completeness. No proposed extension has yet resolved this tension while retaining the overall success of $Λ$CDM. In this work, we investigate whether the $H_0$ tension can be associated with a specific epoch in the cosmic expansion history and identify the redshift range most relevant for understanding its origin. In addition to the cosmological constant, we consider three phenomenological models based on general parametrizations of key quantities governing cosmic expansion: the dark energy (DE) equation of state, the DE pressure density, and the scale factor. Using early time Planck data and late time Pantheon+ (with and without SH0ES calibration) and DESI measurements, we constrain model parameters and examine the evolution of the Hubble parameter $H(z)$. We find that $Λ$CDM exhibits discrepancies across all redshifts, whereas the other models shift the dominant deviations toward low redshifts. Among the models considered, the pressure density parametrization alleviates the $H_0$ tension, reducing it to $\sim 2.7σ$, while the other models do not provide significant improvement. A detailed analysis of DESI DR2 data further reveals notable deviations in $H(z)$ at $z=0.51$ and 0.706, whereas higher redshift measurements remain consistent within $1σ$. These results suggest that late-time modifications primarily reshape the redshift dependence of the mismatch in $H(z)$ rather than fully resolve it, in the absence of systematic effects. Furthermore, the reconstructed DE dynamics exhibit qualitatively distinct behaviors across parametrizations, highlighting a persistent inconsistency between early and late Universe probes in describing the nature of DE.

We report on recent developments of the Heavy-Flavor Non-Relativistic evolution (HF-NRevo) scheme, a framework designed to describe heavy-hadron formation through leading-power fragmentation at moderate and large transverse momentum. The approach combines short-distance inputs obtained from next-to-leading-order NRQCD calculations with collinear scale evolution in a variable-flavor-number scheme, ensuring a consistent treatment of heavy-flavor thresholds and partonic hierarchies. Within this setup we have constructed the NRFF1.0 family of fragmentation functions for $S$-wave heavy quarkonia in their leading NRQCD Fock states. We discuss prospective applications of the HF-NRevo framework in the heavy-ion environment, where it can provide a perturbative baseline for investigating medium-induced modifications of heavy-flavor fragmentation. Its explicit treatment of partonic channels and heavy-flavor thresholds makes it particularly suitable for exploring jet-quenching sensitivity, energy-loss mechanisms, and the emergence of medium-modified fragmentation patterns in the quark-gluon plasma. The HF-NRevo scheme has also been extended to the exotic sector through the TQ4Q1.x and newly released TQ4Q2.0 fragmentation sets, which describe the formation of fully heavy tetraquarks in multiple quantum configurations. These developments open a novel pathway to study quarkoniumlike states and to probe the intrinsic charm content of the proton in forward hadron-collision environments. Altogether, this program broadens the phenomenological reach of heavy-flavor fragmentation studies at the HL-LHC and future collider facilities, opening access to previously unexplored aspects of QCD and potential portals to New Physics.

The explicit expression of ergotropy (a.k.a. available energy) of a classical system is known for the case when the system phase space density is continuous and with no plateaus. Here we provide the general expression of ergotropy that applies without those limitations. It easily follows upon casting the ergotropy problem as a function rearrangement problem. This leads to the notion of "ergotropic rearangement" which generalises that of "symmetric decreasing rearrangement" (an advanced topic of measure theory). We apply it to investigate the fate of classical ergotropy in the thermodynamic limit, and find that any density of the form $ρ=f(H_0)$ is asymptotically passive, where $H_0$ is the system Hamiltonian and $f$ a generic function.

Artificial spin ice provides a versatile setting for emergent gauge fields and magnetic monopole excitations. Here we propose a driven-dissipative polariton realization of artificial spin ice, in which the circular polarization of each link mode plays the role of an Ising degree of freedom, while an auxiliary lossy vertex mode dynamically enforces a local ice-rule constraint. Adiabatic elimination of the vertex mode yields an effective spin-ice penalty, favoring the two-in two-out manifold in the steady state. We show that local polarization flips generate monopole-antimonopole defects, and that sequential flips transport these defects across the lattice while defining a Dirac string. In an extended spin-ice geometry, the vertex charges and their dynamics can be directly reconstructed from polarization-resolved real-space imaging. Our results establish polariton lattices as a controllable photonic platform for creating, manipulating, and observing emergent gauge charges in nonequilibrium spin-ice systems.

A theoretical study of the 7Be(p,gamma)8B reaction in the astrophysical energy range with the use of ab initio methods is presented. The used approaches are No-Core Shell Model and Cluster Channels Orthogonal Functions Method. The scheme also contains elements of R-matrix theory and procedures for extrapolating various data obtained in ab initio computations. The developed approach as a whole allows one not only to calculate the astrophysical S-factor and all nuclear characteristics that determine its value, but also to evaluate the reliability of the obtained results and to identify the dominant reaction mechanisms against a background of insignificant ones.The high accuracy of the obtained results and has been demonstrated.

Inspired by Brown's collapsing method (or discrete Morse theory) to obtain a free resolution of $\bbZ$ over the monoid ring $\bbZ M$, we apply algebraic discrete Morse theory to compute the homology groups of Lawvere theories, which is defined as Tor of a certain module. We reinterpret known partial free resolutions arising from complete term rewriting systems in terms of collapsing of the normalized bar resolution. This perspective yields homological inequalities that bound the number of equational axioms in presentations and recovers classical results, such as lower bounds for group axiomatizations. Our main contribution is to extend these resolutions to higher dimensions.

Static timing analysis (STA) is crucial for Electronic Design Automation (EDA) flows but remains a computational bottleneck. While existing GPU-based STA engines are faster than CPU, they suffer from inefficiencies, particularly intra-warp load imbalance caused by irregular circuit graphs. This paper introduces Warp-STAR, a novel GPU-accelerated STA engine that eliminates this imbalance by orchestrating parallel computations at the warp level. This approach achieves a 2.4X speedup over previous state-of-the-art (SoTA) GPU-based STA. When integrated into a timing-driven global placement framework, Warp-STAR delivers a 1.7X speedup over SoTA frameworks. The method also proves effective for differentiable gradient analysis with minimal overhead.

In this letter, we derive the interaction energy and the force between two parallel metal plates, arising from quantum vacuum fluctuations when they are very close to each other. We consider the vacuum to be composed of a meson field. In Quantum Hadrodynamics, mesons are the carriers of the nuclear force.

Cosmological peculiar velocities have traditionally been studied within the framework of Newtonian theory. Around the turn of the century, a few quasi-Newtonian analyses appeared in the literature, but led to equations and results identical to those of the purely Newtonian approach [1]. More recently, a series of studies introduced a relativistic treatment of the peculiar-velocity problem, criticising the quasi-Newtonian approach as effectively Newtonian in nature [2]. These works also reported a linear growth-rate of $v \propto t$ for peculiar velocities, in contrast to the slower Newtonian/quasi-Newtonian scaling of $v \propto t^{1/3}$. In a manuscript uploaded to the archives a few days ago [3], the authors defended their earlier quasi-Newtonian work and criticised the more recent relativistic treatments. However, the limitations of the quasi-Newtonian approach are not a new concern, but they have been noted at least since [4]. There, it was clearly stated that the quasi-Newtonian approximation leads to Newtonian-like equations and results, and readers were cautioned against applying it to large-scale cosmological studies. Given that one of the authors of [3] was also a coauthor of [4], the self-contradiction is evident. The relativistic analyses have, in fact, confirmed the concerns of [4], clarified the underlying issues and shown how they can be resolved. Motivated by [3], we present a critical comparison of the two approaches and in the process identify several internal inconsistencies in that manuscript.

While artificial intelligence (AI) technology is becoming increasingly popular, its underlying mechanisms tend to remain opaque to most people. To address this gap, the field of AI literacy aims to develop various resources to teach people how AI systems function. Here we contribute to this line of work by proposing two games that demonstrate principles behind how large language models (LLMs) work and use data. The first game, Learn Like an LLM, aims to convey that LLMs are trained to predict sequences of text based on a particular dataset. The second game, Tag-Team Text Generation, focuses on teaching that LLMs generate text one word at a time, using both predicted probabilities of the data and randomness. While the games proposed are still in early stages and would benefit greatly from further discussion, we hope they can contribute to using game-based learning to teach about complex AI systems like LLMs.

Coded caching (CC) exploits cumulative cache memory at user devices and coding to transform unicast traffic into multicast transmissions. While information theoretic results show significant gains over uncoded caching for various network topologies, its practical benefits remain unclear. In this work, we investigate CC for on-demand video streaming over large wireless local area networks, where multiple users are served simultaneously by spatially distributed access points. Users asynchronously request video chunks from a content library. We propose a decentralized, asynchronous, and location-independent cache placement scheme combined with an "over IP" delivery mechanism operating at higher network layers, leaving the physical and MAC layers unchanged. For this scheme, we characterize the achievable goodput region, where goodput is defined as the number of video chunks per unit time delivered to users' playback buffers, and formulate the corresponding fairness problem as a convex maximization. We develop a dynamic scheduling algorithm that provably achieves the optimal fairness point under stationary conditions with reduced complexity, and introduce a heuristic to further lower complexity. Numerical results demonstrate significant gains over baseline schemes, including conventional prefix caching, orthogonal sub-channel allocation with spatial reuse, and a CSMA-inspired distributed coordination approach, showing that CC can be implemented as a scalable and compatible over IP solution for existing WLANs.

This work introduces a framework for analyzing the Age of Incorrect Information (AoII) in a real-time monitoring system with a generic discrete-time Markov source. We study a noisy communication system employing a hybrid automatic repeat request (HARQ) protocol, subject to a transmission rate constraint. The optimization problem is formulated as a constrained Markov decision process (CMDP), and it is shown that there exists an optimal policy that is a randomized mixture of two stationary policies. To overcome the intractability of computing the optimal stationary policies, we develop a multiple-threshold policy class where thresholds depend on the source, the receiver, and the packet count. By establishing a Markov renewal structure induced by threshold policies, we derive closed-form expressions for the long-term average AoII and transmission rate. The proposed policy is constructed via a relative value iteration algorithm that leverages the threshold structure to skip computations, combined with a bisection search to satisfy the rate constraint. To accommodate scenarios requiring lower computational complexity, we adapt the same technique to produce a simpler single-threshold policy that trades optimality for efficiency. Numerical experiments exhibit that both thresholdbased policies outperform periodic scheduling, with the multiplethreshold approach matching the performance of the globally optimal policy.

Simulating cavity quantum electrodynamics in synthetic platforms offers a promising route to exploring light-matter interactions without real photons, while enabling the transfer of cavity-based techniques to other systems. Among such platforms, Bose-Einstein condensates with synthetic spin-orbit coupling provide a controllable setting where internal and motional degrees of freedom become coupled, mimicking aspects of cavity quantum electrodynamics. In this work, we critically assess the extent to which spin-orbit coupled Bose-Einstein condensates can emulate cavity quantum electrodynamics phenomena, with a focus on squeezing and entanglement generation. We show that spin-orbit coupled Bose-Einstein condensates can faithfully reproduce the physics of a single atom coupled to a quantized field, realizing an analogue of the quantum Rabi model but inherently fail to capture genuine collective effects characteristic of the Dicke model, such as cavity-mediated many-body entanglement. Our results clarify both the potential and the fundamental limitations of spin-orbit coupled Bose-Einstein condensates as analogue quantum simulators of cavity quantum electrodynamics, offering guidance for future strategies to generate and control non-classical states of matter in photon-free, highly tunable platforms.

The rise of 3D anime-style avatars in gaming, virtual reality, and other digital media has driven significant interest in automated generation methods capable of capturing their distinctive visual characteristics. These include stylized proportions, expressive features, and non-photorealistic rendering. This paper reviews the advancements and challenges in using deep learning in 3D anime-style avatar generation. We analyze the strengths and limitations of these methods in capturing the aesthetics of anime characters and supporting customization and animation. Additionally, we identify and discuss open problems in the field, such as difficulties in resolution and detail preservation, and constraints regarding the animation of hair and loose clothing. This article aims to provide a comprehensive overview of the current state-of-the-art and identify promising research directions for advancing 3D anime-style avatar generation.

Laser-induced magnetization precession measurements in ferromagnets often reveal an anomalous decrease in the damping time near a field-induced second-order spin-orientation transition, a behavior that cannot be described by the linearized Landau-Lifshitz-Gilbert equation. Here we demonstrate that this anomaly is not a material property but results from interference of precessing local magnetizations within the inhomogeneously excited region. By combining pump-probe experiments, analytical modeling that accounts for the finite sizes of the pump and probe spots, and micromagnetic simulations, we show that the standard macrospin approach fails to capture the observed dynamics. The inhomogeneous relaxation of magnetic parameters within the excitation area distorts the measured precession envelope, while dipole fields give rise to a temporally non-monotonic term in its frequency. Our results highlight the critical role of excitation locality in a vicinity of critical fields.

This paper studies high-dimensional M-estimation in the proportional asymptotic regime (p/n -> gamma > 0) when the noise distribution has infinite variance. For noise with regularly-varying tails of index alpha in (1,2), we establish that the asymptotic behavior of a regularized M-estimator is governed by a single geometric property of the loss function: the boundedness of the domain of its Fenchel conjugate. When this conjugate domain is bounded -- as is the case for the Huber, absolute-value, and quantile loss functions -- the dual variable in the min-max formulation of the estimator is confined, the effective noise reduces to the finite first absolute moment of the noise distribution, and the estimator achieves bounded risk without recourse to external information. When the conjugate domain is unbounded -- as for the squared loss -- the dual variable scales with the noise, the effective noise involves the diverging second moment, and bounded risk can be achieved only through transfer regularization toward an external prior. For the squared-loss class specifically, we derive the exact asymptotic risk via the Convex Gaussian Minimax Theorem under a noise-adapted regularization scaling. The resulting risk converges to a universal floor that is independent of the regularizer, yielding a loss-risk trichotomy: squared-loss estimators without transfer diverge; Huber-loss estimators achieve bounded but non-vanishing risk; transfer-regularized estimators attain the floor.

In the paper, one of the physical consequences of the recently developed theory of dual relativity (TDR) is considered. The general framework of TDR is described and some results previously obtained within this theory are summarized. The total action functional of TDR includes the action functionals of matter fields of two kinds: ordinary and dual. Based on the general equations of the theory, formulas are derived for the effective action functional of a system of point-like massive particles belonging to both kinds of matter, in the Newtonian limit. This functional includes an interaction term, which has the form of the gravitational interaction energy in Newtonian mechanics. It is shown that this energy is positive in the case of interaction between particles of ordinary and dual matter. This result indicates that this interaction has antigravitational nature.

Chemical waves of CO oxidation on platinum surfaces exhibit complex spatio-temporal self-oscillations, yet the local electronic mechanisms driving their propagation remain poorly understood under operando conditions. In this work, we combine operando scanning electron microscopy with frequency-modulated Kelvin probe force microscopy (FM-KPFM) to simultaneously map secondary electron contrast and local work-function variations during CO oxidation on Pt. By utilizing the KPFM tip as a localized sensor, we provide the first work-function-resolved imaging of reaction fronts, enabling an unambiguous physical assignment of CO- and oxygen-covered states. Our results demonstrate that the spillover process of chemical wave-the transition and expansion of adsorbate phases-is characterized by a pronounced temporal asymmetry and spatial heterogeneity transition thresholds. KPFM identifies a rapid onset of oxygen coverage followed by a gradual, diffuse relaxation back to the CO-covered state, indicative of relaxation-type oscillations even at low pressures (10^-2 Pa). Correlative reaction-diffusion simulations reproduce this wave morphology, confirming that the high-resolution work-function signal provides unique insights into the internal structure and kinetic heterogeneity of the working catalyst surface.