In this paper we study the cluster algebraic properties of wavefunction coefficients for massless scalar theories in de Sitter cosmology. We show that the symbol of the wavefunction coefficient of the $n$-site path graph $P_n$ obeys a generalisation of cluster adjacency, where all letters in a given word belong to the same cluster of an $A_{2n-3}$ algebra, with certain additional constraints on the order of the letters. We call this property the ordered single cluster condition, and provide its physical interpretation. This condition is stronger than the usual cluster adjacency obeyed by neighbouring letters, and imposes stronger constraints for the symbol bootstrap. We also show how any tree graph satisfies a cluster-like structure in terms of tubes and tubings on the underlying graph, which allows for a similar bootstrap approach.

We present a comprehensive polarimetric study of 26 nearby molecular clouds in four far-infrared bands (53 $μ$m to 214 $μ$m) using 52 archival SOFIA/HAWC+ datasets. Far-infrared dust polarization observations probe the plane-of-sky magnetic field. To investigate scale-dependent trends, we group the molecular clouds by distance and analyze the data at common angular ($25''$) and common physical (0.052 pc and 0.32 pc) resolutions. The two shorter wavelengths are more impacted by smoothing, exhibiting a larger decrease in percent polarization. We analyze the polarization spectrum -- the polarization fraction as a function of wavelength -- and find that it depends more strongly on column density than dust temperature. We find a "falling" spectrum at the 0.052 pc resolution, but find a "flat" spectrum at the 0.32 pc resolution, suggesting that resolution plays an important role in the observed polarization spectra. We propose that warm dust grain emission in small-scale structures ($\lesssim$ 0.1 pc) traces different magnetic field geometries only resolved in our close regime data. There is no preferred magnetic field orientation across our data, which suggests that the magnetic field in our $\sim$ parsec scale regions is decoupled from the large-scale field that is primarily parallel to the Galactic plane. The relationship between percent polarization and column density varies between clouds, but the correlation between percent polarization and angular dispersion is consistent across regions. This compendium of dust polarization maps highlights the value of observing at multiple far-infrared wavelengths and will enable additional population-level studies of magnetic fields and dust across star-forming environments.

This work presents the summary of calculation of the cross section of the dijet production in deep inelastic scattering at small x at next-to-eikonal accuracy. The cross section is calculated in the back-to-back limit of the produced jets using results obtained in our previous works. The cross section is expressed via the transverse-momentum-dependent (TMD) parton distributions. Specifically, we show how the next-to-eikonal corrections are related to the $x$ dependent phase of twist-2 gluon TMD and to twist-3 unpolarized gluon TMDs.

We consider symmetry protected topological states of 2d quantum spin systems, with a finite symmetry group $G$. It has been conjectured that such states are classified by the cohomology group $H^3(G,U(1))$, but the completeness of this classfication is an open problem. We restrict ourselves to symmetry protected topological states that can be prepared from a product state by a symmetric entangler. For this class of states, we prove that the classification by $H^3(G,U(1))$ is complete.

We analyze the computational complexity of Tetris clearing (determining whether the player can clear an initial board using a given sequence of pieces) and survival (determining whether the player can avoid losing before placing all the given pieces in an initial board) when restricted to a single polyomino piece type. We prove, for any tetromino piece type $P$ except for O, the NP-hardness of Tetris clearing and survival under the standard Super Rotation System (SRS), even when the input sequence consists of only a specified number of $P$ pieces. These surprising results disprove a 23-year-old conjecture on the computational complexity of Tetris with only I pieces (although our result is only for a specific rotation system). As a corollary, we prove the NP-hardness of Tetris clearing when the sequence of pieces has to be able to be generated from a $7k$-bag randomizer for any positive integer $k\geq 1$. On the positive side, we give polynomial-time algorithms for Tetris clearing and survival when the input sequence consists of only dominoes, assuming a particular rotation model, solving a version of a 9-year-old open problem. Along the way, we give polynomial-time algorithms for Tetris clearing and survival with $1\times k$ pieces (for any fixed $k$), provided the top $k-1$ rows are initially empty, showing that our I NP-hardness result needs to have filled cells in the top three rows.

We consider Bose-Einstein condensation in flat-band models from a real-space perspective. Using a basis of compact localized states, we reformulate the minimization of the mean-field energy as a Euclidian geometry problem. Within Bogoliubov theory, we show that flat-band models where the solutions to this problem are frameworks consisting of triangles with nonzero area are promising for condensation, whereas for instance square frameworks indicate condensation in a single mode is impossible. When restricting the analysis to Bloch states, this approach can be related to a necessary condition for a non-vanishing quantum distance. This work provides a new perspective on how condensation in flat bands is destabilized, and offers principles for the construction of models where flat-band Bose-Einstein condensation is possible.

We study the interaction of a stress-energy tensor describing a static point mass supported by a string outside a Schwarzschild black hole with the gravitons of the Hawking radiation. We derive a closed-form analytic expression for the total response rate of this stress-energy tensor to the thermal gravitons in the Unruh state, which models the quantum state in the spacetime of a spherically symmetric black hole formed by gravitational collapse. This response rate is finite in contrast with the infrared divergent response rate for a static point mass supported by a string in Rindler spacetime, i.e., a point mass accelerated uniformly by a string in Minkowski spacetime. By comparing the response rate near the black hole horizon with that in Rindler spacetime, we show that the size of the black hole acts as a natural infrared cutoff. We also find that the response rate of this stress-energy tensor to the thermal gravitons incoming from past null infinity in the Hartle-Hawking state vanishes. As a result, the total response rate of a static point mass (supported by a string) in the Unruh and Hartle-Hawking states for gravitons are identical. This is also the case for a static charge interacting with the electromagnetic field but not for a static source for a massless scalar field.

We propose an exact, analytic deformation of the Starobinsky model governed by the strictly positive derivative of its Lagrangian, $f'(R) = αR + \sqrt{α^2 R^2 + 1}$, with $α> 0$. This geometric hyperbolic square-root ansatz is designed to eliminate the well-known strong-coupling singularity that arises in quadratic $f(R)$ gravity when $f'(R)=0$. The construction seamlessly recovers general relativity at low curvatures and preserves the successful slow-roll inflationary plateau at extreme positive curvatures. In the limit $R \to -\infty$, the derivative $f'(R)$ asymptotes to zero strictly from above, removing the pathological branch associated with the vanishing of $f'(R)$. This guarantees that the only admissible constant-curvature ($R=A$) solutions correspond to standard Einstein spaces with an effective cosmological constant $Λ_{\text{eff}} \equiv A/4$. The first and second derivatives of the action, as well as the scalaron mass squared, remain strictly positive globally, ensuring a perfectly ghost-free and tachyon-free cosmological evolution across the entire spacetime manifold. In the Einstein frame, the dynamics of the scalaron is governed by the globally defined potential $V(ϕ) = \frac{1}{8α} [ 1 - (1 + 2\sqrt{2/3}ϕ) \exp(-2\sqrt{2/3}ϕ) ] + Λ\exp(-2\sqrt{2/3}ϕ)$, which naturally establishes an impenetrable energetic wall as $ϕ\to -\infty$, offering a robust, globally stable mechanism for non-singular bouncing cosmologies. For $N = 60$ inflationary e-folds, the model predicts a scalar spectral index of $n_s \simeq 0.967$ and a strongly suppressed tensor-to-scalar ratio of $r \simeq 0.00083$, which position the proposed theory within the observationally favored parameter space of the Planck and BICEP/Keck Array baseline constraints.

Classical approximation and learning methods are typically optimized for interpolation over a sampled domain Ω, with no guarantees on their behavior in an extrapolation region Ξ, where small in-domain errors may amplify. We develop a model-agnostic framework that recasts extrapolation as a feasibility and projection problem with rigorous guarantees. The approach is built around anchor functions, auxiliary constructions for which one can certify an upper bound on the Ξ-distance to the unknown target function. Such certificates define feasible sets that are proven to contain the true function. Given any baseline approximation (e.g., least-squares or regularized regression), we obtain a corrected extrapolation by projecting the baseline onto the feasible set; the resulting predictor is proven not to increase the error on Ξ, and we prove quantitative bounds on the improvement. We establish new stability constants governing extrapolation, including a tight spectral condition number and a numerically stable inner-domain bound that connects in-domain error to extrapolation risk. To reduce conservatism of worst-case certification, we also propose probabilistic anchor functions that yield high-confidence feasible sets. Numerical experiments, including geomagnetic field modeling and nonlinear oscillators, demonstrate substantial reductions in extrapolation error and corroborate the theoretical predictions.

We investigate the qualitative dynamics of smooth solutions to the radially symmetric isentropic compressible Euler equations, focusing specifically on the evolution of rarefactive and compressive wave characters across three distinct configurations: the outward supersonic, subsonic, and inward supersonic regimes. For each case, we establish structural restrictions on wave-character transitions and identify invariant sign domains for gradient variables under specific initial data conditions. While our findings refine existing invariance properties in the outward supersonic regime, they reveal novel asymmetric transition mechanisms in the subsonic and inward regimes that are absent in purely supersonic expanding cases. Consequently, we derive sufficient conditions for finite-time singularity formation. To complement the analytical results where closed-form solutions are unavailable, we provide numerical experiments using a Semi-Discrete Lagrangian-Eulerian (SDLE) formulation. These simulations reproduce the predicted wave-character dynamics and offer qualitative evidence that supports our theoretical findings, providing a unified description of wave transitions in radially symmetric isentropic gas dynamics.

We introduce a two-phase approximation method designed to resolve singularities in three-dimensional harmonic Dirichlet problems. The approach utilizes the classical Green's function representation, decomposing the function into its singular and regular components. The singular phase employs Green's formula with the singular part, for which we show that it induces the necessary singularities in the solution. The regular phase then introduces a smooth correction to recover the remaining regular part of the solution. The construction employs high-order quadrature rules in the first phase, followed by collocation with a suitable harmonic basis in the second.

Elliptic diffusion problems with multiscale heterogeneous coefficients lead to poorly conditioned discrete systems and therefore require effective preconditioning strategies. While subspace decomposition preconditioners perform well for fixed realizations of the coefficient, their repeated construction becomes prohibitively expensive in uncertainty quantification settings, particularly in Monte-Carlo simulations, where a large number of fine-scale realizations must be treated. In this study, we propose an offline-online approximation of a subspace decomposition preconditioner that exploits the localized structure of the random defects. The preconditioner is constructed from local subspace solves that are precomputed offline for a small set of reference configurations and efficiently combined online for arbitrary realizations. We analyze the spectral properties of the resulting offline-online approximation operator and confirm its robustness and efficiency through numerical experiments.

We present a methodology for acquiring and reducing transiting exoplanet light curves obtained with the OPTICAM instrument in the Observatorio Astronómico Nacional en la Sierra de San Pedro Mártir (OAN-SPM). The OPTICAM sCMOS detectors generate significant warm pixels at exposures $\geq$10s, affecting both science and calibration frames. These warm pixels are not removed by standard dark subtraction because they vary unpredictably from frame to frame. We evaluate six pre-processing methods applied to science and calibration images using the transit of TOI-7149~b observed in g$^\prime$r$^\prime$i$^\prime$. A median filter with a 3$\times$3-pixel window minimizes the effect of warm pixels without affecting stellar signals. This median filter best reduces dispersion and red noise in the light curves when stellar peak counts are close to the dark current level. The improvement is less significant when the stellar peak is several thousand counts above the dark current level. We fit a multiband transit model to the light curves, measuring photometric precision, correlated noise, and retrieved planetary parameters. The transit model fitted to the light curves with pre-processing using a 3$\times$3-median filter achieves the highest Bayesian evidence. Thus, it is our recommended method for correcting warm pixels. Finally, we present a reduction pipeline that combines Python modules (PROFE) and AstroImageJ to implement our proposed method for OAN-SPM 2.1m+OPTICAM transiting planet observations.

The main aim of this paper is to establish the Reshetnyak's theorem for quasiregualr values from generalized $n$-manifold with suitable controlled geometry to Euclidean space $\mathbb{R}^{n}.$ This generalizes a previous result due to Kangasniemi and Onninen on the setting of Euclidean space [A single-point Reshetnyak's theorem, Trans. Amer. Math. Soc., 378(2025): 3105-3128].

The progressive electrification of aircraft systems under the more electric aircraft (MEA) paradigm is reshaping the design and qualification constraints of safety-critical avionics. Emergency locator transmitters (ELTs), which are essential for post-accident localization and search and rescue (SAR) operations, have evolved from legacy 121.5/243 MHz beacons to digitally encoded 406 MHz systems, typically retaining 121.5 MHz as a homing signal in combined units. In parallel, the modernization of the Cospas-Sarsat infrastructure, especially MEOSAR, together with multi-constellation global navigation satellite system (GNSS) integration and second-generation beacon capabilities, is reducing detection latency and enabling richer distress messaging. However, MEA platforms impose stricter constraints on available power, thermal management, wiring density, and electromagnetic compatibility (EMC). As a result, ELT performance increasingly depends not only on the device itself, but also on its installation conditions and on the aircraft's overall electrical environment. This review summarizes the ELT architectures and activation/operational cycles, outlines key technological milestones, and consolidates the main integration challenges for MEA, with emphasis on energy autonomy, battery qualification frameworks, EMC and installation practices, and survivability-driven failure modes (e.g., antenna/feedline damage, mounting, and post-impact shielding). Finally, emerging trends include ELT for distress tracking (DT), energy-based designs, advanced health monitoring, and certification-ready pathways for next-generation SAR services are discussed, highlighting research directions that can deliver demonstrable, certifiable gains in reliability, energy efficiency, and robust integration for future electrified aircraft.

In 1951 paper \cite{Ki} Kippenhahn conjectured that if the characteristic polynomial \ $P_A(x_1,x_2,x_3)=\mbox{det}(x_1A_1+x_2A_2-x_3I)$, \ where $A_1$ and $A_2$ are $n\times n$ Hermitian matrices, has a repeated factor in the polynomial ring $\C[x_1,x_2,x_3]$, then the pair $(A_1,A_2)$ is unitary equivalent to a direct sum $(C_1\oplus C_2, \ D_1\oplus D_2)$ where $C_i, D_i\in M_{n_i}(\C) $ for some $1\leq n_i<n, \ n_1+n_2=n, i=1,2$. Kippenhahn verified the conjecture whenever the degree of the minimal polynomial of $x_1A_1 + x_2A_2$ is 1 or 2. In subsequent works \cite{Sh1,Sh2} Shapiro obtained a number of results which supported the conjecture. In particular, she showed that it held if $n \leq 5$. In 1983 Laffey \cite{La} showed that, in general, Kippenhahn's conjecture was not true by constructing a counterexample for $n=8$. Since then additional counterexamples were worked out (see \cite{Wa} for example). Some positive results in this direction including the quantum version of the conjecture can be found in \cite{F1, F2, KVo1, Law}. In this paper we use methods of recently developed local spectral analysis to give some necessary and sufficient conditions for the affirmative answer to Kippenhahn's conjecture in terms of the characteristic polynomials of certain elements of the algebra generated by the matrices in the tuple.

Qubits are typically reset into a known state by coupling them to a low-temperature environment. When treated in the Born-Markov approximation such couplings produce exponential relaxation to equilibrium, giving high reset fidelities limited only by temperature. We investigate qubit reset beyond this approximation, using numerically exact tensor network methods and the time-dependent variational principle, focussing on a spin-boson model describing a transmon qubit coupled to a resistor. Beyond the Born-Markov approximation the reset fidelity becomes limited by the buildup of system-environment correlations which corresponds to the formation of a polaron. We implement numerical optimal control to find time-dependent qubit Hamiltonians which overcome this limitation by steering the dynamics of the correlated system-environment state. The optimal controls becomes more effective when the environment is filtered to span a smaller spectral range, and remain effective when the multilevel nature of the transmon is considered. A related paper [C. Ortega-Taberner, E. O'Neill and P. R. Eastham, arXiv:XXXX.XXXX] addresses the complementary case of control via a time-dependent system-environment coupling. Our results show how limitations on reset speed and fidelity can be overcome, and how time-dependent driving can steer system-environment correlations and reverse polaron formation.

Qubit reset is crucial in quantum technology and is typically achieved by coupling the qubit to a dissipative environment. However, the achievable speed and fidelity are limited by qubit-environment entanglement. We use exact tensor-network simulations and a time-dependent variational approach to investigate these effects for transmon qubits with a time-dependent system-environment coupling. We show that they are due to the formation of a polaron state and how this can be reversed using a time-dependent coupling. Coupling protocols are identified which achieve reset with an excited-state population of $10^{-6}$ in $10$ ns. A related paper [C. Ortega-Taberner, E. O'Neill and P. R. Eastham, arXiv:XXXX.XXXX] addresses the complementary case of control via a time-dependent Hamiltonian. Our work shows how the dynamics of the environment of an open quantum system can be controlled to design effective quantum processes in non-Markovian systems.

Catch bonds are interactions whose lifetimes increase under mechanical load, a counterintuitive behaviour that underlies diverse biological processes. Translating this mechanism to synthetic materials offers the potential to create systems that are compliant at low stress but stiffen under applied force, with applications ranging from impact-responsive materials to dynamic tissue scaffolds. However, engineering materials with tunable, force-dependent interactions remains challenging, and existing conceptual designs are limited. Here, we present a minimal synthetic framework for catch bond behaviour in dynamic hydrogels, based on reversible ring-forming polymers. Using coarse-grained molecular dynamics simulations, we show that hydrogels with such a chemistry undergo fewer bond-breaking reactions as the stress increases and can even display a non-monotonic dependence of the strain rate on the applied stress. Our results highlight the potential of reversible ring formation as a versatile platform for designing mechanically adaptive materials with tunable durability and responsiveness.

Role classification involves grouping hosts into related roles. It exposes the logical structure of a network, simplifies network management tasks such as policy checking and network segmentation, and can be used to improve the accuracy of network monitoring and analysis algorithms such as intrusion detection. This paper defines the role classification problem and introduces two practical algorithms that group hosts based on observed connection patterns while dealing with changes in these patterns over time. The algorithms have been implemented in a commercial network monitoring and analysis product for enterprise networks. Results from grouping two enterprise networks show that the number of groups identified by our algorithms can be two orders of magnitude smaller than the number of hosts and that the way our algorithms group hosts highly reflects the logical structure of the networks.

Entanglement in many-body quantum systems is distributed across spatial regions, where its structure often dictates the information-processing capabilities of the state. Yet, characterizing the entanglement structure, especially for mixed states, remains a challenge. In this work, we propose hysteretic squashed entanglement $T_{sq}$, a conditional entanglement monotone that measures the genuine quantum correlations between two subregions, conditioned on a third region, in a many-body quantum state. $T_{sq}$ is upper bounded by the convex-roof extension of quantum conditional mutual information and exhibits several desirable properties like monogamy, convexity, asymptotic continuity, faithfulness, and additivity for tensor-product states. We study the conditional entanglement generation in a one-dimensional transverse-field Ising model under quench, where we show that $T_{sq}$ effectively squashes classical contributions and can detect genuine quantum correlations across both adjacent and long-range subsystems. We elucidate the utility of this measure as a robust quantifier of topological entanglement entropy for mixed states. This opens new operational resource-theoretic avenues for probing topological order and criticality.

The One-hundred-deg^2 DECam Imaging in Narrowbands (ODIN) survey is conducting the widest-field deep narrow-band imaging of the equatorial and southern skies. ODIN uses three custom-built narrow-band (NB) filters that sample Lya-emitting galaxies (LAEs) within thin cosmic slices centered at z=2.4, 3.1, and 4.5. In this work, we utilize extensive DESI spectroscopy of ODIN-selected galaxies in the COSMOS and XMM-LSS fields to validate our LAE selection. 2-4 hr exposures with DESI yielded redshift confirmation of 3,075 ODIN LAE candidates with NB magnitudes brighter than 26~mag. Restricting to objects that yield high-confidence redshifts, the confirmation rates are (93, 96, 92)% at z=(2.4, 3.1, 4.5). The primary contaminants consist of active galactic nuclei at the expected Lya redshift range and lower redshifts (C IV, C III]), with the remainder being star-forming galaxies ([O II] and [O III]). We find minimal contamination from [O II] emitters in our sample (<~1%), implying that our REW>20 A narrow-band excess photometry requirement is sufficient to remove them.

A privacy-preserving dynamic average consensus (DAC) algorithm is proposed that achieves consensus while preventing external eavesdroppers from inferring the reference signals and their derivatives. During the initialization phase, each agent generates a set of sinusoidal signals with randomly selected frequencies and exchanges them with its neighboring agents to construct a masking signal. Each agent masks its reference signals using this composite masking signal before executing the DAC update rule. It is shown that the developed scheme preserves the convergence properties of the conventional DAC framework while preventing information leakage to external eavesdroppers. Furthermore, the developed algorithm is applied to state-of-charge (SoC) balancing in a networked battery energy storage system to demonstrate its practical applicability. Simulation results validate the theoretical findings.

Wireless local area networks (WLANs) based on the family of 802.11 technologies are becoming ubiquitous. These technologies support multiple data transmission rates. Transmitting at a lower data rate (by using a more resilient modulation scheme) increases the frame transmission time but reduces the bit error rate. In non-cooperative environments such as public hot-spots or WLANs operated by different enterprises that are physically close to each other, individual nodes attempt to maximize their achieved throughput by adjusting the data rate or frame size used, irrespective of the impact of this on overall system performance. In this paper, we show both analytically using a game theoretic model and through simulation that the existing 802.11 distributed MAC protocol, DCF (for Distributed Coordination Function), as well as its enhanced version, which is being standardized as part of 802.11e, can lead non-cooperative nodes to undesirable Nash equilibriums in which the wireless channel is inefficiently used. We show that by establishing independence between the allocation of the shared channel resource and the transmission strategies used by individual nodes, an ideal MAC protocol can lead rational nodes to arrive at equilibriums in which all competing nodes achieve higher throughputs than with DCF.

Quantum computational advantage was claimed for the first time in 2019 and several experiments since then have reinforced the claim. And yet, there is no consensus whether or not quantum advantage has actually been achieved. In this article, I address this question and argue that, in fact, it has. I also outline next steps for theory and experiments in quantum advantage.

Gödel's second incompleteness theorem is standardly understood as showing that no sufficiently strong, consistent theory of arithmetic can prove its own consistency, a result typically interpreted against a model-theoretic background in which arithmetical language is evaluated with respect to an independently given structure of natural numbers. This paper develops an alternative perspective grounded in proof-theoretic semantics. We distinguish between derivability and a semantic notion of consequence given by support, defined compositionally in terms of the inferential roles fixed by a theory. For suitable arithmetical theories A formulated in a finite signature (such as Robinson's Q and Peano Arithmetic), these two notions can diverge in a principled way: although A does not prove its own consistency, it nevertheless supports its formalized consistency statement, and more generally supports sentences not derivable within it. This does not conflict with Gödel's incompleteness theorem, but instead reframes incompleteness as a divergence between two internally determined notions of consequence associated with a single theory, rather than as a gap between syntactic provability and truth in a mind-independent structure. The result clarifies the relationship between reflection, consistency, and inferentialist approaches to meaning, and shows how substantial semantic determinacy may arise from the inferential structure of arithmetic itself.

We explore the use of level structures to generalize the SQIsign signature scheme. We give a general framework where, given the public key and the commitment, the challenge is to exhibit an isogeny between them with an additional requirement, namely to map a chosen level structure to another. We then instantiate the framework using 1-dimensional and 2-dimensional isogenies. In doing that we provide a new explicit Deuring correspondence for supersingular elliptic curves with level structures and solve new constrained norm equations.

This work summarizes the design, construction, initial performance evaluation and pilot clinical results of the IMAS system, a long axial field of view (FOV), also known as total-body (TB-), positron emission tomography (PET) prototype scanner. This PET enables for the first time in TB-PET imaging, simultaneously time-of-flight (TOF) and depth-of-interaction (DOI) capabilities. The IMAS detector block is based on LYSO semi monolithic scintillators, with individual slab sizes of 3 mm x 25 mm x 20 mm each. Arrays of 1x8 slabs are coupled to 8x8 Silicon Photomultiplier arrays. A proprietary readout reduces the 64 signals to only 16 outputs, preserving both 3D photon impact positioning and timing accuracy. IMAS has a total of 30,720 channels. PETsys electronics is used for data acquisition. The IMAS geometry is based on 5 rings of 10 cm each, with a 5 cm gap between them. It defines an axial FOV of 71 cm with a bore aperture of 82 cm. We report in this work the pilot tests of the system performance and the first clinical results. We found that the system spatial resolution remained below 4 mm across the entire FOV, even at the off-radial position of 30 cm. A coincidence time resolution with a small size 22Na source of 560 ps FWHM was measured. A sensitivity of 56.54 cps/kBq is in good agreement with previous simulation studies; however, the noise equivalent count rates performance (79 kcps at 3.26 kBq/mL) was significantly lower than expected, likely due to a data transfer bottleneck between the system and the acquisition workstation. Finally, a comparison of one of the imaged patients with a commercial TOF PET/CT scanner is also provided, pinpointing an improved tumor identification for IMAS, and the advantages of TOF and especially DOI capabilities.

Nonreciprocal interactions in active matter are known to generate exotic mechanical behaviors such as odd elasticity and odd viscosity. However, these phenomena have largely been studied in isolation, raising a fundamental question: Is there a single system that embodies these distinct regimes of odd matter and can transition between phases, establishing a unified phase diagram for nonreciprocal active matter? To address this, we introduce a tunable robotic active matter platform, the Magnetomechanically Augmented Spinning roBotic (MASBot) collective, in which particle-level control of chirality, activity, and pairwise interactions enables access to distinct phases of odd matter. By continuously increasing repulsive forces relative to attractive and transverse forces, we experimentally map a transition from an odd elastic crystal to an odd viscous liquid, and then to a chiral active gas. We find that this latter phase forms a non-space-filling, nonreciprocal active gas stabilized by long-range hydrodynamic attractive forces, whose statistical signatures are consistent with those of a two-dimensional self-gravitating point vortex gas. Within these phases, adjusting spinning frequency and introducing spatially patterned activity allows us to fine-tune odd mechanical responses and tailor power spectra. Further polar and rotational symmetry breaking at the particle scale leads to novel emergent states such as phase separation and collective translation. Together, our system provides a fundamental experimental testbed for nonequilibrium physics and establishes a blueprint for treating robotic swarms as programmable states of matter, enabling functions that range from resilient structures to adaptive swarm reconfiguration.

We model the phase transition of a superconductor as a U(1) lattice gauge system, and determine its critical behavior. For this, we perform Monte Carlo simulations, treating the order parameter field and the gauge field on equal footing, without additional approximations. As the defining correlation function, we determine the order parameter correlation function including a gauge string, thus achieving a gauge-invariant characterization of the long-range behavior explicitly. We obtain a critical exponent $β$ that is consistent with the exponent of the U(1) transition of neutral bosons, i.e. of Bose-Einstein condensation. We determine the critical behavior of the heat capacity, which displays a temperature depends consistent with an XY transition. These results clarify the universality class of the phase transition of this system.