Statistical Mechanics
Statistical mechanics of classical fractons on a line
Ylias Sadki, Abhishodh Prakash and S. L. Sondhi
We study the
equilibrium statistical mechanics of one-dimensional classical Machian fractons: particles whose dynamics conserves a global dipole moment and whose
Hamiltonian couples momentum differences through a position-dependent pair-inertia kernel. Compactly supported interaction kernels have a divergence in the Gibbs partition function, and have been shown to break ergodicity and
symmetry by forming non-
equilibrium steady states with particle clusters, evading the Hohenberg-Mermin-Wagner-Coleman
theorem. In this paper, we consider kernels with non-compact support and study their ergodic properties. For exponentially decaying kernels, graph-
Laplacian and
matrix-tree bounds provide an extensive free energy suggesting that a putative statistical mechanical description is valid. Similarly, uniform non-local kernels have a super-extensive free energy and require a Kac rescaling. A generalized Hohenberg–Mermin–Wagner–Coleman argument, supported by finite-size scaling, implies
symmetry-breaking density order parameter vanishes at all wave vectors melting the long-range translation-breaking density order of compact kernels. To study the resulting
equilibrium ensemble, we construct a nonreversible event-chain Monte Carlo (ECMC)
algorithm that samples the coupled position-momentum phase space while preserving the dipole moment and total momentum. The ECMC sampling is shown to quantitatively match long time-averaged quantites in
Hamiltonian dynamics. The
equilibrium liquid exhibits preferred short-range clustering and strongly non-Gaussian single-particle momentum tails associated with the correlated nature of positions and momenta. This paper provides a detailed investigation into the
equilibrium liquid properties of the non-compact regime, whilst the companion paper investigates the mechanisms that relax the
liquid.
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Biomolecules
In Vivo Length Distributions as Mechanistic Fingerprints of Pathological Protein Aggregation
Matthew W. Cotton, David Klenerman and Georg Meisl
Modern imaging techniques can resolve individual pathological
protein aggregates in postmortem human samples, providing detailed measurements of aggregate size distributions that are inaccessible with conventional bulk approaches. These distributions represent mechanistic fingerprints of the microscopic processes that generated the observed pathology, but extracting this mechanistic information requires a quantitative theoretical framework. Here, we develop the mathematical tools needed to interpret aggregate length distributions in living systems, where aggregate growth competes with active removal. We show that, across a class of models, the length distribution of sufficiently large aggregates approaches a
geometric decay. Crucially, the decay rate is determined by the balance between aggregate elongation and removal, providing a direct quantitative readout of these competing processes from a single time point measurement. This enables mechanistic comparisons between healthy and diseased human samples without requiring longitudinal measurements of aggregate dynamics. We further analyse how additional aggregation and removal processes modify the observed length distributions. Together, these results establish the mathematical foundations and tools to use aggregate length distributions as an experimentally accessible route for inferring microscopic aggregation dynamics directly from human tissue.
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Materials Science
Interplay of Composition, Crystallinity, and Chemical Structure in CoHCF and NiHCF Thin Films Prepared at Different Temperatures
Larissa de O. Garcia, Michael Pohlitz, Mohammed F. Kalady et al. (+1 more)
Understanding how growth conditions govern structural order and ion transport in Prussian blue analogues (PBAs) thin films is essential for optimizing their electrochemical performance. Here, cobalt and nickel hexacyanoferrate (CoHCF and NiHCF) thin films were electrodeposited potentiostatically at temperatures between 20 and 60 degrees C. A combination of cyclic voltammetry, scanning electron microscopy, X-ray diffraction, and Raman spectroscopy was employed to elucidate the interplay between composition, crystallinity, and chemical structure. Under identical conditions, CoHCF exhibits a maximum current density approximately 2.2 times higher than NiHCF, indicating significantly faster electrochemical kinetics. X-ray diffraction reveals temperature-dependent
lattice expansion without phase transitions, with a maximum near 40 degrees C, associated with structural relaxation and compositional variations. Raman spectroscopy further reveals temperature-dependent local structural
evolution, where cyanide band narrowing at intermediate temperatures indicates improved short-range order, while band broadening at higher temperatures reflects increased defect density. These findings demonstrate that temperature-controlled defect redistribution governs both short- and long-range structural order in PBA thin films, directly influencing ion transport and electrochemical response. This work provides new insights into structure-property relationships in PBAs and establishes deposition temperature as a key parameter for tuning electrochemical functionality in hexacyanoferrate-based electrodes.
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All authors Larissa de O. Garcia, Michael Pohlitz, Mohammed F. Kalady, Christian K. Muller
Nuclear Theory
Systematic study of macroscopic interaction models and short-range effects in $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion
Azni Abdul Aziz and Norhasliza Yusof
The $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion reaction is central to
stellar carbon burning, yet its cross section at astrophysical energies remains uncertain and theoretical extrapolations depend sensitively on the adopted
nucleus-
nucleus interaction. We systematically assess 24 macroscopic interactions within a common one-dimensional fusion framework and find that their relative agreement with experimental data depends strongly on both the statistical measure and energy interval considered, with no single interaction providing a uniformly superior description across all criteria. A common phenomenological short-range repulsive modification is then applied to all interactions without refitting their underlying parametrizations. Although the external fusion barrier remains essentially unchanged, the modification substantially reorganizes the inner-potential structure and produces strongly model-dependent changes in agreement with experiment. Detailed analysis of five representative interactions shows that the resulting low-energy suppression propagates into the thermonuclear reaction rates, but does not produce the conventional logarithmic-slope signature of fusion hindrance over the calculated energy range. These results demonstrate that additional short-range repulsion does not provide a universal improvement of macroscopic fusion potentials and that the reliability of extrapolations toward
stellar carbon-burning energies remains sensitive to both the choice of interaction and its short-range behavior.
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Audio and Speech Processing
HRTF Upsampling Across Varying Measurement Configurations with Geometry-Aware Query-Conditioned Aggregation
Xingyu Chen, Hanwen Bi, Sipei Zhao et al. (+3 more)
Personalized head-related transfer functions (HRTFs) are essential for spatial audio rendering, but densely measuring an individual's HRTFs is costly and time-consuming. HRTF upsampling reduces this burden by estimating dense HRTFs from sparse measurements. Recent learning-based methods have achieved promising performance, but many remain tied to predefined measurement configurations. In this work, we propose GeoAtt, a variable-context HRTF upsampling framework that uses a single trained model across varying measurement configurations. GeoAtt performs geometry-aware, query-conditioned spatial aggregation over the available measurements independently at each frequency bin, followed by frequency-domain modeling using Conformer blocks. The relative geometry between the target and measured directions is incorporated as an additive bias in the cross-
attention. Experiments on the SONICOM
dataset show that a single trained model achieves the lowest log-spectral distortion across all four canonical Listener Acoustic Personalization (LAP) challenge measurement configurations and further generalizes to configurations that are not explicitly included during training.
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All authors Xingyu Chen, Hanwen Bi, Sipei Zhao, Fei Ma, Eva Cheng, Ian S. Burnett
Robotics
Safety-Constrained Model Predictive Control for an Omnidirectional Walking Assistive Robot Using Control Barrier Function
Andrea Fortuna, Marta Lorenzini, Elisa Motta et al. (+3 more)
Providing safe and effective mobility assistance plays a crucial role in restoring independence and enhancing the quality of life for individuals with motor impairments. In this context, robotic walking assistive devices have recently emerged as promising solutions to provide physically compliant interaction while ensuring user safety and support. This paper presents a novel control framework for an omnidirectional Walking Assistive
Robot (I-WANDER) that integrates a Control Barrier Function (CBF) formulation into a Model Predictive Control (MPC) scheme to explicitly enforce collision-avoidance safety constraints while optimizing for energy efficiency and smooth human-
robot collaboration. The method was experimentally evaluated with 12 healthy participants performing two different walking tasks using both the proposed CBF-based MPC controller (CB-MPC) and a variable admittance controller (AC). The first task involved structured
navigation through a U-shaped corridor, whereas the second consisted of a single-obstacle avoidance task performed blindfolded to ensure the obstacle was unexpected. Comparative results show that the CB-MPC architecture significantly reduces energy consumption and mechanical work (p < 0.01) without compromising motion smoothness, while also decreasing the number of obstacle collisions. Overall, the findings highlight the potential of the proposed control architecture to enhance both safety and efficiency in robotic walking assistance.
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All authors Andrea Fortuna, Marta Lorenzini, Elisa Motta, Alberto Ranavolo, Elena De Momi, Arash Ajoudani
Medical Physics
Towards real-time ion range verification via hybrid Compton-PET 3D imaging at isochronous cyclotrons
Javier Balibrea-Correa, V. Babiano-Suarez, J. Lerendegui-Marco et al. (+8 more)
Range uncertainties remain a major limitation to the full clinical exploitation of
proton therapy, motivating reliable in-vivo range-verification techniques. This work presents an experimental investigation of a hybrid
Prompt-Gamma Imaging (PGI)–Positron-Emission
Tomography (PET) concept at the isochronous cyclotron of the West German
Proton Therapy Centre under clinically representative pencil-beam-scanning conditions. Because this accelerator delivers a quasi-continuous beam, a pulsed shoot-and-step structure was imposed to mimic the interruptions associated with clinical energy-layer switching. This enabled PGI during irradiation and PET and delayed Compton imaging during beam-off intervals within the same sequence. Four two-plane Compton cameras were arranged in a co-planar cross-shaped geometry around the beam isocenter. Polyethylene phantoms were irradiated with 100~MeV
protons at known positions along the beam axis. Their positions were estimated from reconstructed one-dimensional profiles using supervised machine-learning models trained exclusively on Monte Carlo simulations. PET achieved the best performance, with a root-mean-square deviation of 0.8~mm, followed by PGI with 1.6~mm. Delayed Compton imaging based on e$^{+}$ annihilation
photons and $^{10}$C$^{*}$ decays yielded 2.4~mm and 3.8~mm, respectively. PET retained good performance down to 1% of the original event statistics, whereas PGI became increasingly statistics-limited. These results demonstrate the complementary strengths of hybrid PGI–PET and support its development towards millimetre-scale
proton-range verification under clinically relevant irradiation conditions.
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All authors Javier Balibrea-Correa, V. Babiano-Suarez, J. Lerendegui-Marco, P. Torres-Sánchez, I. Ladarescu, M. Pallàs, B. Brusasco, J. Wulff, C. Bäumer, A. Tarifeño-Saldivia, C. Domingo-Pardo
Quantum Physics
Maximum-Likelihood Amplitude Estimation for Quantum Monte Carlo Integration on Trapped-Ion Hardware: Convergence, Noise-Floor Saturation, Depth-Dependent Bias
Aditi Lal, Alex Khan, Rut Lineswala et al. (+1 more)
Quantum Amplitude Estimation promises to accelerate Monte Carlo integration by replacing the classical $\varepsilon \propto N^{-1/2}$ sampling law with the Heisenberg-limited $\varepsilon \propto N^{-1}$ scaling, but whether any part of that advantage survives on present-day hardware is an empirical question. We report a systematic experimental
benchmark of a Maximum-Likelihood Amplitude Estimation QMC pipeline on IonQ trapped-ion processors, comprising 60 hardware trials on IonQ Forte-1 across five settings(5 & 9
qubits, 100-200 shots per depth, linear & exponential amplification schedules, ~113 device-hours), together with 100 trials on IonQ Aria-1 & Forte-1 noise models at 5, 9 & 19
qubits. The pipeline combines controlled-$R_y$ rotational state preparation, Grover-based amplitude amplification and maximum-likelihood inference and is benchmarked against $b_{\max}^{-1}\!\int_0^{b_{\max}}\!\sin^2\!x\,\mathrm{d}x$ with $b_{\max}=\pi/5$ ,given results emerge. First, the noiseless limit it attains $\varepsilon \propto N^{-0.88}$, close to the Heisenberg-scaling reference, reducing the error 54-74x over a 133x increase in oracle calls. Second, scaling does not survive on hardware. Every noisy backend saturates at an error floor of (2-5)x 10^{-2}, with fitted exponents of 0.04-0.15 on Forte-1 linear schedules and $\alpha \le\!0$ on the vendor noise models: beyond the optimal shallow depth, however, deeper amplification provides no sustained accuracy gain and instead returns to the noise floor. Forte-1 hardware also outperformed IonQ's own Aria-1 noise model at every depth $m \ge 2$, indicating that vendor noise models are bad predictors of MLAE accuracy. The practical implication for UQ is that on current devices the useful operating point is a shallow, schedule-tuned amplification depth chosen so that the deepest
circuit lands near p~1/2 not the deepest schedule the coherence budget allows.
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All authors Aditi Lal, Alex Khan, Rut Lineswala, Abhishek Chopra
Information Retrieval
Knowledge-as-Skill: A Structural Design for Autonomous Knowledge-Base Use by LLM Agents
Jiangxu Wu
Retrieval-augmented generation (RAG) gives large
language models (LLMs) access to external knowledge, but its conventional retrieve-concatenate-generate pipeline makes
retrieval decisions on behalf of the model. As tool use and
agent loops become more reliable, an
agent can decide whether to retrieve, what to inspect, and when to stop. This shift exposes a new bottleneck: the
agent may not know what a knowledge base contains. Traditional knowledge bases expose documents as anonymous text chunks with limited information about scope, purpose, provenance, or relations. We propose Knowledge-as-Skill, an organization scheme that makes a knowledge base discoverable, navigable, and self-descriptive. It has three layers: a discovery layer centered on SKILL.md; a
navigation layer with one index.md per directory; and a knowledge layer containing documents with YAML frontmatter for topic, type, provenance, and lifecycle. The design follows the Open Knowledge Format (OKF) and the Skill protocol without modifying the
agent framework. We also provide knowledge-as-skill, a pipeline for converting heterogeneous collections of PDFs, Word files, web exports, and notes into this structure. In a preliminary evaluation on the WixQA enterprise customer-support
benchmark, our setup obtains 0.889 Factuality and 0.816 Context Recall, compared with reported Corpus2Skill values of 0.767 and 0.708. It obtains slightly lower Faithfulness, lower Context Precision, and more interaction turns. Because the models,
prompts, and knowledge-package construction differ, these results are directional cross-work evidence rather than a controlled comparison.
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High Energy Astrophysical Phenomena
Einstein Probe discovery of the magnetar EP J223759.5+531421
N. Rea, F. Coti Zelati, A. Borghese et al. (+44 more)
We report the discovery and early outburst
evolution of the new
Galactic magnetar EP J223759.5+531421, detected by the Einstein Probe Wide-field X-ray
Telescope on 2026 June 28. Follow-up observations with Einstein Probe, XMM–Newton, NuSTAR, SVOM, and IXPE revealed coherent X-ray pulsations at P ~ 6s and an average period derivative of Pdot ~ 2.8x10^{-12} s/s. These values imply a nominal polar dipolar
magnetic field of B_dip ~ 2.6x10^{14} Gauss and a characteristic age of tau_c ~ 34 kyr, although the structured timing residuals suggest possible torque variability. The rms pulsed fraction is approximately 20-25% below ~7 keV and decreases at higher energies. The broadband spectra require multiple thermal components and a hard power-law tail. Adopting a distance of 3.3 kpc, the 0.5-30 keV luminosity declined from 1.2x10^{35} to 5.7x10^{34} erg/s during the first month, accompanied by a decrease in the inferred thermal-emitting areas. At this distance, the
Galactic latitude b=-4.56 deg corresponds to a height of approximately 0.26 kpc below the
Galactic plane, which is difficult to reconcile with the nominal characteristic age under a simple midplane-birth scenario even for an extreme proper motion velocity. Short X-ray bursts independently confirm the magnetar nature of the source. No near-infrared or
radio counterpart were detected by GTC, Medicina or FAST, respectively, down to K_s>21 mag and S_{1.25 GHz} <2.3 microJy. These observations demonstrate the potential of the Einstein Probe WXT monitoring to uncover previously quiescent
Galactic magnetars and follow their outbursts from their earliest observed stages.
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All authors N. Rea, F. Coti Zelati, A. Borghese, Y.L. Wang, H. Yang, X. Mao, C.-Y. Dai, E. Arrigoni, J. Bai, G. Bernardi, M. Burgay, S. Cao, A. Coleiro, D. De Grandis, P. Esposito, H. Feng, Y.-C. Fu, A. Geminardi, D. Götz, S. Guillot, Y. Huang, M. Imbrogno, G. L. Israel, C. Jin, A. Kong, Y. Li, L. Lin, C.-S. Liu, C. Maitra, A. Marino, S. Mereghetti, J.-U. Ness, S. Ng, M. Pilia, A. Possenti, H. Sun, L. Tao, R. Taverna, A. Tiengo, R. Turolla, W. Yuan, S. Zane, B. Zhang, L.-X. Zhang, Z. Zhang, W.-W. Zhu, Y.-C. Zou
Fluid Dynamics
Intrinsic dynamical shadowing of point vortices and finite time singularities
Xavier Leoncini, Perla El Kettani and Edgardo Ugalde
The trajectories of point
vortices after a division using reverse collapse route are studied. In this setting, an unexpected peculiar phenomenon appears, corresponding to the shadowing of the
vortex breakup. This occurs at least for a finite time, when the system evolves from three to five
vortices after a breakup. An analytical study reveals that this observed numerical phenomenon is related to the condition of scale invariance, a condition necessary for the finite time singularity. Further simulations agree with our analytical findings and indicate that shadowing can occur with more than five
vortices, and as well with higher order singularities. This phenomenon leads to question what a
vortex is actually measuring, triggering speculations if this shadowing property could be generalized to other
Hamiltonian systems with finite-time singularities.
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Instrumentation and Methods for Astrophysics
Options for Compression of radio interferometry data: lossy compression of visibilities and lossless compression of uv-visibility grids for the MHONGOOSE survey
Richard Dodson, Jonghwan Rhee, W.J.G. de Blok et al. (+6 more)
Next generation
radio astronomy
telescopes are challenging existing data reduction paradigms. With ever more
antennas, larger bandwidths, and sometimes multiple primary beams, they often generate more observed data products than can readily be stored long-term. Thus, data storage becomes a major cost driver and processing constraint. In this paper, we test two methods of addressing this problem: grid-stacking, a two-stage lossless compression solution; and the lossy compression of the raw visibilities before traditional processing. To demonstrate these solutions we utilised a deep imaging pipeline based on software for the ASKAP
telescope, ASKAPSoft, but applied to a strong source (NGC1566) from the deep MeerKAT HI spectral line project, MHONGOOSE. The grid-stacking solution reproduces the spectrum from traditional processing to within better than 0.7%, and also allows for the reconstruction of other weighting scales without significant computing costs. In comparison, image-stacking also reproduces the spectrum from the traditional processing, to within better than 3% but with worse image residuals in the cube. The lossy compression, even at a near ten-fold reduction in file size, reproduces the spectra almost perfectly (to better than ~0.01% in all cases). Thus both compression methods are promising solutions, and we discuss considerations for their application.
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All authors Richard Dodson, Jonghwan Rhee, W.J.G. de Blok, Martin Meyer, Alexander Williamson, Daniel Mitchell, Kristóf Rozgonyi, María J. Rioja, Pascal J. Elahi
Machine Learning
Theory for groupoid equivariant neural networks: an approach for steerable CNNs on bounded domains
Alberto Ibort, Maria Jimenez-Vazquez and Juan M. Perez-Pardo
Equivariant convolutional neural networks are usually built from a group acting globally on the space of signals. This hypothesis is inappropriate for many bounded or stratified domains: an ambient rigid motion may be admissible only on part of the domain, and the boundary introduces
geometric types that are invisible to a transitive group action. We develop a theory of groupoid-equivariant neural networks in which the
symmetry datum consists of a groupoid, a selected pseudogroup of local bisections, a measure, and input and output representation bundles. For integral channels on the object space, we prove a bisection-equivariant kernel
theorem: equivariance is equivalent to a transport constraint on the two-point kernel, and its solutions are classified by one joint-stabilizer intertwiner on each orbit of pairs. As a case study we apply the theory to bounded planar domains. The resulting architecture is implemented through offline nullspace bases and sparse gather–transform–scatter operations. A Poisson–Dirichlet kernel study is used separately to assess boundary-aware inductive bias; the exact inverse is shown to preserve the global
symmetries of the rectangle but not general proper local bisections. The numerical results show that the proposed architectures provide significant advantages when
symmetries cannot be globally implemented by group actions and provide an accuracy improvement of at least one order of magnitude with respect to the models tested.
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Signal Processing
Information in Polarization, Energy from Optical Power: Stokes-Orthogonal Inter-Satellite Links
Meysam Ghanbari, Mohammad Taghi Dabiri, Mazen O. Hasna et al. (+1 more)
Joint information and energy transfer over inter satellite free space optical links is commonly based on explicit resource splitting, which couples communication reliability and energy delivery. This paper proposes a constant total power Stokes orthogonal architecture that conveys information through polarization while preserving the received optical power for photovoltaic conversion. Complementary polarization branches support balanced information detection through their AC components, while their DC components drive matched multi junction photonic power converters. The developed framework jointly characterizes pointing impaired propagation, bit error rate, outage, and nonlinear harvested power. The analysis establishes that the two information symbols only exchange the branch powers, leaving the unordered input power pair unchanged. Hence, the total harvested energy remains symbol invariant even under nonlinear conversion, without an explicit information energy power split or linear efficiency approximation. Numerical results confirm the analytical model, with the closed form BER approximation remaining within 0.43 percent of the exact evaluation over the examined pointing conditions. Compared with ideal lossless power splitting, the proposed architecture avoids the conventional BER versus harvested power tradeoff and provides an analytical baseline for power neutral joint information and energy transfer in inter satellite optical links.
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All authors Meysam Ghanbari, Mohammad Taghi Dabiri, Mazen O. Hasna, Khalid A. Qaraqe
Number Theory
Large values of the Hurwitz zeta function with rational parameter
Qiyu Yang, Shengbo Zhao and Guang-Liang Zhou
In this paper, we establish lower bounds for large values of the Hurwitz
zeta function with rational parameter when the real part $\sigma \in [1/2,1]$. These results improve the earlier results of Ramachandra and Sankaranarayanan in 1989. On the critical line, our result recovers the corresponding lower bound of de la Bretèche and Tenenbaum (2019) for the Riemann
zeta function, while for $1/2< \sigma \leq 1$, our lower bounds attain the same order as the corresponding lower bounds for large values of the Riemann
zeta function. Our proofs are based on the resonance method.
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Nuclear Experiment
Photoneutron reactions on $^{165}$Ho and $^{169}$Tm in the giant dipole resonance region
I. Gheorghe, S. Goriely, K. Stopani et al. (+19 more)
Photoneutron reactions were investigated for the deformed $^{165}$Ho and $^{169}$Tm
nuclei from the vicinity of the
neutron emission threshold up to $\sim$40~MeV, well above the
giant dipole resonance (GDR) region, using quasimonochromatic
laser Compton scattering $\gamma$-ray beams provided at the NewSUBARU facility, Japan. A high-and-flat efficiency moderated array of $^3$He counters was used for the
neutron detection and an associated
neutron multiplicity sorting method for extracting the $(\gamma,\,1nX)$, $(\gamma,\,2nX)$, $(\gamma,\,3nX)$ and $(\gamma,\,4nX)$ reaction cross sections and average
neutron emission energies. The present $^{165}$Ho cross sections were compared to existing data, revealing discrepancies with the Saclay multiplicity sorting results and an overall 10$\%$ strength difference with the Livermore ones. There are no other data for $^{169}$Tm. GDR parameters based on phenomenological Lorentzian models were extracted by fitting the present $\sigma(\gamma,\,Sn)$ data with adjustments for the missing contribution of charged-particle-only reactions not observed experimentally. For both
nuclei we observed high energy structures at 20-25~MeV, matching
giant quadrupole resonance KMFR predictions. Based on the present centroid energies of the first and second GDR peaks, hydrodynamic model predictions gave intrinsic electric quadrupole moments of +7.00(34)~b and +7.38(28)~b for the ground states of $^{165}$Ho and $^{169}$Tm, respectively. The present experimental excitation functions and photoneutron energies were compared to statistical model calculations. Using the EMPIRE code, we performed a sensitivity test to phenomenological models of
photon strength functions and
nuclear level densities. The TALYS code was used to reproduce the present experimental $(\gamma,\,inX)$ cross sections and average
neutron energies using microscopic
nuclear level density models.
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All authors I. Gheorghe, S. Goriely, K. Stopani, S. Belyshev, M. Krzysiek, D. Filipescu, H. Wang, G. Fan, L. Liu, H. Scheit, D. Symochko, T. Aumann, T. Renstrøm, G.M. Tveten, F. Furmyr, A. Görgen, A.C. Larsen, S. Siem, V. Orlin, T. Ari-izumi, S. Miyamoto, H. Utsunomiya
Rings and Algebras
Graphs of Moore-Penrose inverse of matrices possessing the treeangle property
A. M. Encinas, K. Kranthi Priya and K. C. Sivakumar
It is known that the inverse of an invertible real square
matrix satisfying the treeangle property, is a treediagonal
matrix. A converse statement also holds. We show that the verbatim analogues are not true for the Moore-Penrose inverse, and obtain the precise structure of graphs corresponding to the Moore-Penrose inverse of
matrices possessing the treeangle property.
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Nuclear Experiment
Observation of a magnetic shift in neutron whispering-gallery states
K. Schreiner, J. A. Pioquinto, S. Baeßler et al. (+19 more)
We developed experimental and theoretical methods to create and describe high-resolution whispering-gallery interference patterns and show the feasibility of measuring their small shifts by external interactions. Such experiments can be used to search for extra fundamental interactions, time parity violations, nonzero electric charges, precisely measuring the gravitational properties of (anti)matter, parity violations,
neutron polarizability,
quantum reflection, surface state effects, etc. Here, we measure a
magnetic shift of such a
neutron pattern $\delta g/g\sim (6.5 \pm 0.8_{st} \pm 1.2_{sys}) \cdot 10^{-4}$, and our sensitivity to
spin-dependent differences between the scattering lengths was $\delta b_n/b_n \sim 10^{-4}$.
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All authors K. Schreiner, J. A. Pioquinto, S. Baeßler, V. V. Nesvizhevsky, P. Clade, P. Crivelli, R. Cubitt, J. Guyomard, C. Killian, U. Miniotaite, F. Nez, E. Perry, S. Reynaud, T. Saerbeck, L. Shen, K. Stinson, J. Vivier, A. Vorobiev, J. Walsh, E. Widmann, P. Yzombard, A. Zhao
Optimization and Control
Volumes of the strong and weak relaxations of the uncapacitated facility-location polytope
Jon Lee
Lee, Skipper, and Speakman (2018) asked for formulae or asymptotic expressions for the volumes of the strong and weak relaxations $\mathcal{P}_{m,n}\cap \mathcal{D}_{m,n}$ and $\mathcal{Q}_{m,n}\cap \mathcal{D}_{m,n}$ of the uncapacitated facility-location polytope with $m$ facilities and $n$ customers (their Problem~3, “Texas Hot”). We give exact formulae for all $m$ and $n$, and we give asymptotics that hold uniformly as $m+n\to\infty$, whatever the relative growth of $m$ and $n$. The volume ratio satisfies $Vol(\mathcal{Q}_{m,n}\cap \mathcal{D}_{m,n})/Vol(\mathcal{P}_{m,n}\cap \mathcal{D}_{m,n})\sim \prod_{j=2}^{n}\mleft(1+\tfrac{1}{(m-1)j}\mright)^{m}$. From this, we read off the behavior in every growth regime of $m$, and we identify a sharp transition at $m\asymp\ln n$. Below it, in a uniformly random point of the strong relaxation, each facility variable is close to $1$ with high probability, and the ratio grows superlinearly in $n$. Above it, in a uniformly random point of either relaxation, each facility variable is asymptotically uniform on $[0,1]$, and the ratio grows linearly in $n$.
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Machine Learning
Interweaving Marginals into Multivariate Sample Paths: Training-Free Dependence Construction for Probabilistic Time Series Foundation Models
Jinmyeong Choi, Jinkwan Jang, Seul Lee et al. (+1 more)
Probabilistic time series foundation models (TSFMs) provide coordinate-wise predictive distributions, but these marginals do not determine a joint distribution over multivariate future trajectories. We study training-free coupling of frozen TSFM marginals into multivariate forecast sample paths. Our primary evaluation fixes the empirical marginal sample multiset at every channel–horizon coordinate across methods, isolating the effect of coupling alone. Historical temporal and channel relations substantially improve their corresponding dependence diagnostics. The same pattern persists when the fixed-marginal constraint is removed and paths are sampled directly, and remains present under native multivariate backbone inference. These results support treating dependence reconstruction as a distinct post-processing problem for probabilistic TSFMs.
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All authors Jinmyeong Choi, Jinkwan Jang, Seul Lee, Taesup Kim
Signal Processing
LUNA: Luneburg-Lens-Aided Reconfigurable Array for 6G-and-Advanced Wireless Networks
Ziwei Wan, Zhen Gao, Shuping Dang et al. (+3 more)
This article introduces the LUneburg-lens-aided recoNfigurable Array (LUNA), an
antenna architecture that unifies multiple-input multiple-output (
MIMO) and network-controlled repeater (NCR) functionalities in the Luneburg lens-enabled hardware platform. A Luneburg lens, fabricated from graded-index dielectric materials, passively converts the radiation of a low-gain feed into a highly directional beam without active phase shifting, while a dense passive feed bank and a reconfigurable feed-selection network electronically switch the beam directions with minimal hardware complexity and power consumption. We commence by reviewing the basic principles and application history of Luneburg lenses in radar and wireless communications, which motivates their role in 6G-and-advanced networks. Then, we highlight how a Luneburg lens and a reconfigurable feed array construct both LUNA-
MIMO and LUNA-NCR, where the lens and feed bank can be reused across functions and frequency bands. Case studies demonstrate that LUNA achieves the satisfactory spectral and energy efficiency with a few
radio-frequency chains, and it also improves positioning performance for sensing tasks. Finally, some open problems and research directions are provided to inspire follow-up research on LUNA.
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All authors Ziwei Wan, Zhen Gao, Shuping Dang, Michail Matthaiou, Zhaocheng Wang, Sheng Chen
Computer Vision
Faithful Faithfulness Evaluations: Challenges & Pitfalls Learned from a Breast MRI Case Study
Peachapong Poolpol, Henrik H. J. Detjen and Eike Petersen
Saliency maps are widely used to explain deep learning predictions in medical imaging, yet visually plausible explanations do not necessarily reflect a model's true decision process and may therefore mislead clinicians. We investigate this problem using a
Vision Transformer-based breast MRI classifier trained on the ODELIA Breast MRI Challenge
dataset and evaluate multiple saliency methods, including Last-layer
Attention,
Attention Rollout, Grad-SAM, Gradient
Attention Rollout, GMAR, Grad-CAM, and HiResCAM. Our study highlights two often-overlooked challenges in perturbation-based faithfulness evaluation. First, method rankings depend strongly on the perturbation strategy, varying across intensity-based perturbations and
transformer-based
attention masking. Second, benchmarking saliency methods requires distinguishing between class-specific and class-agnostic explanations. To enable fair comparisons, we introduce non-class-specific variants of gradient-based methods and evaluate both settings separately. Across protocols, Grad-CAM and Gradient
Attention Rollout consistently emerged as the strongest class-specific methods, although their relative ranking depended on the evaluation design. These findings expose important limitations of current saliency-based explainability approaches and highlight the need for more robust and standardized evaluation frameworks for trustworthy clinical AI systems.
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Quantum Physics
Dynamical, thermal, and ground-state multiparameter quantum metrology: Fundamental limits and their attainability in magnetometry
Riccardo Pedroni, Víctor Izquierdo, Advay Burte et al. (+3 more)
We consider the simultaneous estimation of multiple parameters in
Hamiltonians of the form $H_{\vec{\theta}}= H_{\vec{\theta}}^P + H^C$, where $H_{\vec{\theta}}^P$ encodes the unknown parameters and $H^C$ is a control term. We consider three basic paradigmatic frameworks for metrology: (i) dynamical, where the parameters are encoded unitarily, (ii) thermal, and (iii) ground state. We generalize previous bounds for single-parameter estimation to simultaneous multiparameter estimation for all three metrological settings and establish the conditions required for their saturability. We then focus on vector magnetometry, deriving tight bounds for the simultaneous estimation of
magnetic-field components and identifying optimal many-body control
Hamiltonians $H^C$ that saturate them. These results establish the fundamental limits of vector magnetometry for
unitary dynamics, thermal
equilibrium states, and ground states.
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All authors Riccardo Pedroni, Víctor Izquierdo, Advay Burte, Paolo Abiuso, John Calsamiglia, Martí Perarnau-Llobet
Computational Engineering
Multimaterial topology optimization using SIMP, DMO and gSF: A comparative study with honeycomb tessellations
Bhargav kumar Duru and Prabhat Kumar
This paper presents a comparative study of multimaterial
topology optimization (MMTO) using the extended SIMP, Discrete Material Optimization (DMO), and generalized shape functions (gSF) approaches. The computational domain is discretized into hexagonal
cells. Each
cell is connected to its neighbors with edges. This characteristic reduces mesh-related effects on the optimized designs compared with conventional triangular and quadrilateral discretizations. Structural compliance is minimized at the prescribed volume fractions. The method of moving asymptotes is employed to update the design variables. The resulting optimized
topologies are compared in terms of material distribution, structural performance, convergence behavior, and the characteristics of the obtained material interfaces. The comparative investigation provides insights into the working principles and performance of the extended SIMP, DMO, and gSF interpolation schemes for MMTO.
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Signal Processing
Receiver-Side Physics-Informed Residual Digital Twin for Predictive Fine Tracking in Inter-Satellite Optical Links
Mahtab Dashtebozorgi, Meysam Ghanbari, Rula Ammuri et al. (+2 more)
Fine tracking in inter-satellite optical links must compensate residual line-of-sight (LOS) motion despite sensor noise, vibration, model mismatch, and actuator latency. This paper develops a receiver-side physics-informed residual digital twin (PIR-Twin) that combines a nominal LOS transition, Gaussian optics, a nonlinear quadrant-photodetector observation, and extended Kalman filter synchronization. A normalized autoregressive ridge model learns the transition mismatch from independent calibration estimates, while the known delayed fine-steering-mirror correction remains separate from the physical LOS dynamics. The synchronized twin predicts the LOS at the command-actuation instant and enables proactive fine tracking. A controlled evaluation compares open-loop, reactive, nominal-predictive, and PIR-Twin operation using disjoint tuning, calibration, and test realizations. Under the nominal scenario, PIR-Twin reduces RMS pointing error by 14.1% relative to reactive tracking and also improves actuation-time prediction accuracy. Extended robustness tests show that the proposed method retains the lowest mean pointing error over a broad actuator-delay range and under increased time-varying LOS-motion amplitudes without residual-model retraining. The results demonstrate that correcting systematic short-horizon model mismatch, rather than relying on nominal extrapolation alone, is the key mechanism enabling effective predictive fine tracking.
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All authors Mahtab Dashtebozorgi, Meysam Ghanbari, Rula Ammuri, Mazen O. Hasna, Khalid A. Qaraqe
Combinatorics
Exact Second-Order Zarankiewicz Numbers for Complete-Graph Incidence Families
Yannan Chen, Johan Löfberg and Liqun Qi
For $n\ge6$, $m=\binom n2$, let the complete-graph incidence family on $K_n$ have the vertices of $K_n$ as columns, its edges as rows, and the incidence graph as one-edge graph. The universal
cell bound of Löfberg and Qi gives $z_2(m,n)\le Z(n):=\lfloor n(n-1)(n+2)/4\rfloor$. We implement the nested one-factorization construction of that family and determine exactly what it certifies. For $n=2q$ with $q$ an odd
prime, $q\ge5$, the construction has no hole and the cross-factor transfer equations apply verbatim, giving $z_2=z_{SL}=z_{RL}=Z(n)$; $n=6$ is settled by a separate cyclic witness. For odd $n=2p+1$ the near-perfect one-factorization yields Hamilton paths closed into odd cycles, and the transfer argument breaks: that scheme certifies only $R(G_p)\le Z(n)$. The orders $n=7,8,9,12,13,16,17,18,20,21$ are settled by explicit configurations of a different shape, each attaining the
cell bound and satisfying $(\mathrm{RW}3^+)$, obtained from a larger configuration by deleting vertex
stars and repairing the restricted grid. At each of these orders $z_2=z_{SL}=z_{RL}=Z(n)$; all remaining orders are conjectural. The first settled order $n=7$ is the only one whose grid has a hole, grounded by a zero-companion rule. Machine-readable configurations and a certificate checker accompany the paper.
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Algebraic Geometry
Symbols at infinity and Lie algebras of vector fields
Emile Bouaziz
If $X$ is smooth projective complex variety, $D$ is a simple normal crossings divisor and $A$ an ample divisor with support $D$, then there is an associated filtration of the Lie
algebra of on the affine variety $U=X\setminus D$ induced from the subspaces $T_X(\log D)(nA)\subset T_U.$ We show that the associated graded Lie
algebra is finitely generated in a strong sense. We deduce as a consequence that vector fields on any smooth affine variety form a finitely generated Lie
algebra.
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Computer Vision
NAWE: Digital Watermarking with Neural-Assisted Watermark Extraction
Roman Chaban, Vitaliy Kinakh, Lilian Rouzaire et al. (+1 more)
NAWE (Neural-Assisted Watermark Extraction) combines an explicit signal-processing watermarking construction with a pretrained neural host predictor. A periodic, perceptually masked watermark carrier provides synchronization, Polar coding supplies redundancy, and denoising followed by subtraction extracts the embedded watermark. The denoiser remains frozen, without watermark-specific training. A one-factor-at-a-time study compares Wiener, BM3D, DRUNet, and GS-DRUNet host
estimators. Comparisons with TrustMark, SSL Watermarking, PixelSeal, and WAM show NAWE's lowest
geometric and photometric class BER and strong message recovery, while filtering and noise remain limitations consistent with the non-adaptive selection of the watermark extractor. The comparison retains the systems' different payloads and coding.
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All authors Roman Chaban, Vitaliy Kinakh, Lilian Rouzaire, Slava Voloshynovskiy
Signal Processing
Integrated Optical Receiver for Communication and Fine Tracking in Inter-Satellite Links
Meysam Ghanbari, Mohammad Taghi Dabiri, Akram Alomainy et al. (+3 more)
Inter-satellite optical links demand high-precision fine tracking while preserving sufficient received power for data communication, yet these functions are often treated separately at the receiver. This paper proposes a dual-function optical receiver that integrates data reception and fine tracking on a shared, intentionally defocused receiver plane. The architecture combines a central data lens with an annular four-segment tracking detector, creating a fundamental tradeoff between datapower collection and angular-estimation capability. A scalar Fresnel wave-optical model is developed together with nonlinear two-dimensional calibration and a noise-aware worstcase angular-accuracy framework. The receiver geometry is then jointly optimized to maximize the guaranteed fine-tracking range subject to a minimum data-power constraint. Results demonstrate that appropriate co-design of the central aperture and defocus substantially enlarges the usable fine-tracking region while maintaining the required communication-path power. The proposed framework provides a receiver-level
benchmark for analyzing and designing integrated communication-and-tracking architectures in future optical inter-satellite terminals.
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All authors Meysam Ghanbari, Mohammad Taghi Dabiri, Akram Alomainy, Qammer H. Abbasi, Mazen O. Hasna, Khalid A. Qaraqe
Physics and Society
Emotions as intrinsic colored noise in biological systems
V.I. Yukalov and E.P. Yukalova
The idea that
emotions in biological systems are analogous to intrinsic colored noise is advanced and justified. A model describing the dynamics of operation of biological networks under the influence of colored noise is suggested. The
agents of a biological network can be represented either by biological species, such as humans and animals, or by
neurons of the
brain, or by the nodes of a neural network. Operational actions, or decisions, in a biological noisy network are based not only on the evaluation of utility of alternatives, but also on the
agents emotions. The model is probabilistic, with the choice of alternatives characterized by the related probabilities. At the initial step, the
agents make decisions individually and then start exchanging information with each other and imitating the actions of other
agents, thus forming a biological network of interacting
agents. Numerical simulations are accomplished for a heterogeneous society consisting of three groups of
agents, one group possessing long-range
memory, the other group, short-range
memory, and the third group of super-rational
agents acting strictly on the basis of utility, being deprived of
emotions. Dynamics of opinions in different groups can be smooth, oscillatory, or chaotic. Altogether, eight types of operation are found, depending on the dynamics of group decisions. Under strong imitation effect, there appears chaotic motion in the
evolution of decision choice. It is shown how the Ellsberg paradox can be resolved and how the exchange of information influences the dynamics of this paradox.
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