Carnevale, Schein and Voll proved self-reciprocity of the generalized Igusa functions, and Maglione and Voll did the same for the Hall-Littlewood-Schubert series. We introduce a simultaneous generalization and refinement of these two rational functions, and prove that it satisfies a self-reciprocity property. This answers a problem posed by Maglione and Voll. Our method of proof is elementary, avoiding the use of $p$-adic integration.

Over the past decade, gravitational-wave astronomy has opened a new window onto the extreme states of matter inside compact stars. At some point during the inspiral of a binary system, each star starts to experience adiabatic tides, characterized by tidal deformabilities. The dominant tidal deformability, first measured with the GW170817 event, has already constrained the dense-matter equation of state. With the advent of third-generation detectors, tidal deformabilities are expected to be inferred with much higher precision, potentially revealing subleading tidal contributions. This motivates the development of more accurate compact-star models that incorporate richer microphysics. With this in mind, we move beyond the commonly adopted perfect-fluid approximation and model compact stars through a multifluid framework. In this work, we present the fully general-relativistic description of adiabatic tidal deformations of compact stars composed of an arbitrary number of interacting fluids, using Carter's multifluid variational formalism. A distinctive feature of this approach is the presence of nondissipative mutual entrainment between fluid species. We derive the hydrostatic equilibrium equations for multifluid configurations, along with the perturbed equations governing stationary gravitoelectric and gravitomagnetic tidal responses of arbitrary order. We then investigate how entrainment modifies the corresponding tidal deformabilities. Using an analytical representation of the multifluid equation of state, we show that entrainment leaves adiabatic tidal responses unchanged and therefore produces no measurable effect on the gravitational-wave signal emitted during the inspiral long before the excitation of internal mode resonances. We subsequently discuss two specific applications: superfluid neutron stars and dark matter admixed compact stars.

To reduce the cost of estimating the probability of a rare event involving a very large number of random parameters, we propose a new strategy for dimension reduction coupled with a surrogate model for the expensive part of the algorithm. To this end, we extend the Ordinary Kriging Active Subspace (OK-AS) method into a sequential version. Our approach consists of iteratively re-estimating the active subspace using a Kriging surrogate trained in a rotated coordinate system until the active subspace stabilises. This method allows for a reduction in prediction error and a better approximation of the active subspace on a benchmark of test problems. Furthermore, we integrate our algorithm into an efficient pre-existing approach for estimating the probability of a rare event. This approach is based on learning the active subspace associated with the random event whose probability is to be estimated. The sequential learning of an importance sampling density is necessary and corresponds to the expensive part of this strategy. To circumvent this issue, we integrate our sequential OK-AS version into the estimation of the importance sampling density. The numerical results indicate that our method allows for reducing the cost required to obtain a precise estimate of the rare event probability.

This study investigates the interconnectivity of firms and Environmental Justice Organizations (EJOs) involved in socio-environmental conflicts worldwide, using data from the Environmental Justice Atlas (EJAtlas). By constructing a multilayer network that links firms, conflicts, and EJOs, the research applies social network analysis to evaluate the simultaneous involvement of these actors across multiple disputes. Both projected networks of firms and EJOs have been analysed by aggregating nodes by categories and countries to reveal structural differences. Findings reveal a stark contrast between the interconnectedness of firms and EJOs. Multinational corporations form a cohesive global network, enabling them to coordinate strategies and exert influence across regions. Conversely, EJOs are fragmented, often operating in isolated clusters with limited interconnection but forming a robust, decentralized and self-organized global network. Firms network present a strong dependence on pertaining conflict category while EJOs network does not depend on conflict category. This structural difference suggests a risk of systemic and structural coordination for firms towards exploitative expansion while EJOs dynamics seems to be led by a white blood cells defense-like mechanism. While fragmentation may represents a critical challenge for social movements, decentralization and self-organization show a more diffuse global networks supported by a limited number of central hub able to build stronger global alliances to effectively counter the power dynamics of transnational corporations. By providing robust evidence of these networks, this research contributes to discuss how structural differences in global coordination for companies and EJOs directly derives as emergent properties depending on the purpose of the network itself, sectorial expansion for firms while ecosystem preservation for EJOs.

While Third Generation Partnership Project (3GPP) has confirmed orthogonal frequency division multiplexing (OFDM) as the baseline waveform for sixth-generation (6G), its performance is severely compromised in the high-mobility scenarios envisioned for 6G. Building upon the GEARBOX-PHY vision, we present gear-switching OFDM (GS-OFDM): a unified framework in which the base station (BS) adaptively selects among three gears, ranging from legacy OFDM to delay-Doppler domain processing based on the channel mobility conditions experienced by the user equipments (UEs). We illustrate the benefit of adaptive gear switching for communication throughput and, finally, we conclude with an outlook on research challenges and opportunities.

Using only continuous partitions of unity, we provide equivalent definitions for the metric, topological and topological tail entropies and pressures of a continuous self-map of a compact set, as well as their conditional versions. A tail variational principle for these new definitions is proved. We extend Downarowicz's notions of candidates and entropy structures to account for almost-increasing sequences of functions arising from the new definitions. Finally, we deduce a partial answer to a question raised by Newhouse.

In this paper, we propose an adaptive multilevel preconditioned Helmholtz-Jacobi-Davidson (PHJD) method for the Maxwell eigenvalue problem with singularities. The key idea in this work is to employ the local multilevel method for preconditioning the Jacobi-Davidson correction equation. It is shown that our convergence factor is quasi-optimal, which means the convergence factor is independent of mesh sizes and mesh levels provided the coarse mesh is sufficiently fine. Numerical experiments on complex domains are carried out to confirm the theoretical results and demonstrate the efficiency of the proposed method.

This paper proposes an $α$-fair multistatic integrated sensing and communication (ISAC) framework for multi-user multi-input multi-output (MIMO)-orthogonal frequency division multiplexing (OFDM) systems, where communication users act as passive bistatic receivers to enable multistatic sensing. Unlike existing works that optimize aggregate sensing metrics and thus favor geometrically advantageous targets, we minimize the $α$-fairness utility over per-target Cramér--Rao lower bounds (CRLBs) subject to per-user minimum data rate and transmit power constraints. The resulting non-convex problem is solved via the Riemannian conjugate gradient (RCG) method with a smooth penalty reformulation. Simulation results validate the effectiveness of the proposed scheme in achieving a favorable sensing fairness--communication trade-off.

The coupling between electronic excitations and collective bosonic modes is fundamental to the emergence of high-temperature superconductivity in cuprates. Despite extensive effort, conventional equilibrium and pump-probe optical spectroscopies still struggle to disentangle couplings to different bosonic modes when their energy scales overlap. Here we overcome this limitation using ultrafast two-dimensional electronic spectroscopy (2DES), which correlates coherent excitation and detection photon energies with femtosecond time resolution. Applied to optimally doped Bi$_2$Sr$_2$Ca$_{0.92}$Y$_{0.08}$Cu$_2$O$_{8+δ}$, 2DES reveals a pronounced off-diagonal resonance arising from the ultrafast generation of non-thermal bosons with energy $\hbarΩ_\mathbf{q}\simeq200$ meV. By comparing the measured spectra with a theoretical framework that explicitly includes the interaction between charge-transfer and magnetic excitations, we identify these bosons as paramagnons with momenta centered near $(π/2,π/2)$ and extending toward $(0,π)$ and $(π,0)$. The resonance persists across a large range of temperatures and doping concentrations, demonstrating that high-energy paramagnons are ubiquitously and strongly coupled to electronic excitations throughout the cuprate phase diagram. Time-domain analysis constrains the build-up of the paramagnon population to $\lesssim 10$ fs, placing a lower bound $λ\gtrsim 0.7$ on the coupling strength. More broadly, our results establish 2DES as a powerful approach for disentangling mode-selective electron-boson interactions and addressing decoherence dynamics, thereby establishing a new avenue for investigating strongly correlated quantum materials. These findings also provide a direct framework for future time-resolved resonant inelastic X-ray scattering experiments aimed at tracking the ultrafast dynamics of magnetic excitations.

Pulse charging can be used to boost up charging speed for lithium-ion batteries and delay battery capacity fading by periodically pausing the current during charging. However, this technique introduces intermittence for current and may thus challenge the electric stability of charger as well as its energy supply source. To deal with this challenge, a coordination method for multiple loads simultaneously being charged has been proposed in this paper. The method exploits the off-time intervals of pulse current to charge other loads. By properly grouping and coordinating the charging loads, the fluctuation and amplitude of the charging current can be mitigated. To optimally schedule all charging loads, mathematical models are formulated to help find out the best scheduling scheme for the loads. Two scenarios have been considered as well as two mathematical models have been proposed and elucidated in the paper. In one scenario all loads are charged using PCs with the same frequency, while in the other scenario PCs with various frequencies are considered. In addition, a procedure of scheduling the charging process considering power limit is developed. The proposed method has been applied to and quantitatively evaluated in two application scenarios. Compared to randomly charging, both fluctuation and amplitude of the total current for multiple loads simultaneously being charged have been mitigated after properly scheduled. Using the proposed method, the merits of pulse charging for batteries can be utilized while the stability issue can be alleviated.

We establish strong Feller property and irreducibility for the transition semigroup associated to a class of nonlinear stochastic partial differential equations with multiplicative degenerate noise. As a by-product, we prove uniqueness of the invariant measure under no strong-dissipativity assumptions. The drift of the equation diverges exactly where the noise coefficient vanishes, resulting in a competition between the dissipative effects and the degeneracy of the noise. We propose a method to measure the accumulation of the solution towards the potential barriers, allowing to give rigorous meaning to the inverse of the degenerate noise coefficient. From the mathematical perspective, this is one of the first contributions in the literature establishing strong Feller properties and irreducibility in the multiplicative degenerate case, and opens up novel investigation paths in the direction of regularisation effects and ergodicity in the degenerate-noise framework. From the application perspective, the models cover interesting scenarios in physics, in the context of evolution of relative concentrations of mixtures, under the influence of thermodynamically-relevant potentials of Flory-Huggins type.

We establish the existence and uniqueness of distributed equilibria to possibly nonsymmetric $N$ player differential games with interactions through controls under displacement semimonotonicity assumptions. Surprisingly, the nonseparable framework of the running cost combined with the character of distributed equilibria leads to a set of consistency relations different in nature from the ones for open and closed loop equilibria investigated in a recent work of Jackson and the second author. In the symmetric setting, we establish quantitative convergence results for the $N$ player games toward the corresponding Mean Field Games of Controls (MFGC), when $N\to+\infty$. Our approach applies to both idiosyncratic noise driven models and fully deterministic frameworks. In particular, for deterministic models distributed equilibria correspond to open loop equilibria, and our work seems to be the first in the literature to provide existence and uniqueness of these equilibria and prove the large $N$ convergence in the MFGC setting. The sharpness of the imposed assumptions is discussed via a set of explicitly computable examples in the linear quadratic setting.

Generative recommendation commonly adopts a two-stage pipeline in which a learnable tokenizer maps items to discrete token sequences (i.e. identifiers) and an autoregressive generative recommender model (GRM) performs prediction based on these identifiers. Recent tokenizers further incorporate collaborative signals so that items with similar user-behavior patterns receive similar codes, substantially improving recommendation quality. However, real-world environments evolve continuously: new items cause identifier collision and shifts, while new interactions induce collaborative drift in existing items (e.g., changing co-occurrence patterns and popularity). Fully retraining both tokenizer and GRM is often prohibitively expensive, yet naively fine-tuning the tokenizer can alter token sequences for the majority of existing items, undermining the GRM's learned token-embedding alignment. To balance plasticity and stability for collaborative tokenizers, we propose DACT, a Drift-Aware Continual Tokenization framework with two stages: (i) tokenizer fine-tuning, augmented with a jointly trained Collaborative Drift Identification Module (CDIM) that outputs item-level drift confidence and enables differentiated optimization for drifting and stationary items; and (ii) hierarchical code reassignment using a relaxed-to-strict strategy to update token sequences while limiting unnecessary changes. Experiments on three real-world datasets with two representative GRMs show that DACT consistently achieves better performance than baselines, demonstrating effective adaptation to collaborative evolution with reduced disruption to prior knowledge. Our implementation is publicly available at https://github.com/HomesAmaranta/DACT for reproducibility.

In this work, we investigate the relation between bound states and quasinormal modes within black hole perturbation theory in the context of spectral instability. Our analysis indicates that the reliability of such spectral mapping stretches beyond the domain of validity of the analytic continuation employed to connect the perturbative bound-state problem to the corresponding open-system dynamics. However, for the numerical scheme proposed by Völkel to work, the transformations of the metric parameters must be carried out in a region where the underlying Taylor expansion is convergent. As analytically accessible explicit examples, we explore the perturbed delta-function and Pöschl-Teller potential barriers. For the latter, we construct two distinct perturbative setups for which the convergence of the series expansion involved in the perturbation theory can be rigorously controlled. When the deformation is placed near the potential's extremum, the resulting corrections to the bound-state energies can be analytically continued to yield perturbed quasinormal frequencies, in agreement with known semi-analytic results. In contrast, when the perturbation is localized asymptotically far from the compact object, the bound states are only mildly modified and are accurately described by a perturbative expansion to the first order. However, the associated analytic continuation yields a strongly deformed spectrum that shows no clear connection to the quasinormal modes. These findings contribute to the effort to scrutinize the conditions under which bound states faithfully encode quasinormal spectra and to shed light on the underlying physics of black hole spectral instability.

In the present paper, a systematic study is made of quantitative semicontinuity (a.k.a. Lipschitzian) properties of certain multifunctions, which are defined as a solution map associated to a family of parameterized ``split" feasibility problems. The latter are a particular class of convex feasibility problems with well recognized applications to several areas of engineering and systems biology. As a part of a perturbation analysis of variational systems, this study falls within the framework of a line of research pursued by several authors. It is performed by means of techniques of variational analysis, which lead to establish sufficient conditions for the Lipschitz lower semicontinuity, calmness, isolated calmness, Lipschitz upper semicontinuity and Aubin property of the solution map. Along with each of these properties, a quantitative estimate of the related exact bound is also provided. The key elements emerging on the way to achieving the main results are dual regularity conditions qualifying the problem behaviour, which are expressed in terms of convex analysis constructions involving problem data. The approach here proposed tries to unify the study of the aforementioned properties.

We present novel randomized approximation schemes for the Edit Distance (ED) problem and the Longest Common Subsequence (LCS) problem that, for any constant $ε>0$, compute a $(1+ε)$-approximation for ED and a $(1-ε)$-approximation for LCS in time $n^2 / 2^{\log^{Ω(1)}(n)}$ for two strings of total length at most $n$. This running time improves upon the classical quadratic-time dynamic programming algorithms by a quasi-polynomial factor. Our results yield significant insights into fine-grained complexity: Firstly, for ED, prior work indicates that any exact algorithm cannot be improved beyond a few logarithmic factors without refuting established complexity assumptions [Abboud, Hansen, Vassilevska Williams, Williams, 2016]; our quasi-polynomial speed-up shows a separation the complexity of approximate ED from that of exact ED, even for approximation factor arbitrarily close to $1$. Secondly, for LCS, obtaining similar approximation-time tradeoffs via deterministic algorithms would imply breakthrough circuit lower bounds [Chen, Goldwasser, Lyu, Rothblum, Rubinstein, 2019]; our randomized algorithm demonstrates derandomization hardness for LCS approximation.

Discrete quantum groups were introduced as duals of compact quantum groups by Podleś and Woronowicz in 1990. They have been studied intrinsically by Effros and Ruan (1994) and by the author (1996). In a more recent note (2025), we have given a slightly updated treatment, viewing the duality between discrete and compact quantum groups as a special case of the more general duality of algebraic quantum groups. Along these lines, we start in this paper with the discrete quantum group $su_q(2)$, not constructed as the dual of the compact quantum group $SU_q(2)$ but rather from the Hopf algebra deformation of the enveloping algebra of the Lie algebra of $SU(2)$, as given by Jimbo (1985). The passage to the discrete quantum group as studied in earlier papers is not completely trivial as we will see. This is a known phenomenon. We consider the dual of this discrete quantum group in the sense of duality of algebraic quantum groups and see that this indeed is the compact quantum group $SU_q(2)$.

We report the first unambiguous detection of cannabinoid molecules in an exoplanetary atmosphere. Using 420 hours of JWST observations combining NIRSpec and MIRI instruments, we identify spectroscopic signatures of tetrahydrocannabinol (THC; $Δ^9$-C$_{21}$H$_{30}$O$_2$) and cannabidiol (CBD; C$_{21}$H$_{30}$O$_2$) in the transmission spectrum of the temperate sub-Neptune K2-18b. The THC feature at 2.42~$μ$m is detected at 9.2$σ$ significance, while CBD absorption at 3.69~$μ$m reaches 7.8$σ$. We additionally report a mysterious feature at exactly 4.20~$μ$m detected at 4.20$σ$ (the probability of this coincidence is discussed extensively). Our atmospheric retrievals using the novel \texttt{TerpeneRetrieval} code indicate a CBD-to-THC ratio of 0.40$\pm$0.08, classifying K2-18b as a ``balanced hybrid'' world according to standard terrestrial cannabis taxonomy. We introduce the Cannabis Habitable Zone (``Green Zone'') framework and demonstrate that K2-18b lies squarely within it. We explore multiple production mechanisms including biogenic synthesis, abiotic photochemistry, exogenous delivery via ``space nuggets,'' and deliberate atmospheric engineering by an advanced civilization. These findings suggest that K2-18b may host conditions suitable for advanced photochemistry, atmospheric relaxation processes, and possibly the most chill civilization in the galaxy. If confirmed by independent observations, this represents a paradigm shift in our understanding of biosignatures and the prevalence of recreational organic chemistry in the cosmos.

The theory of gravitational wave turbulence describes the long-term statistical behaviour of a set of weakly nonlinear interacting waves. In this paper, we aim to study aspects of gravitational turbulence within the framework of general relativity using the Hadad-Zakharov (HZ) metric. The latter is parameterised by four functions (the coefficients of a diagonal metric) that must satisfy seven non-trivial Einstein equations, six of which are independent. The issue of their mutual compatibility is therefore essential, yet it has so far been overlooked. In this work, we argue that these equations can be compatible in the weakly nonlinear regime under specific conditions. Our analytical investigation is complemented by direct numerical simulations performed with a new GPU-based code, TIGER. A comparative analysis of the evolution of the Ricci and Kretschmann scalars indicates that gravitational wave turbulence corresponds to the propagation of a genuine physical degree of freedom. These numerical findings, however, must be interpreted with caution, given the difficulty of satisfying all seven Einstein equations simultaneously with sufficient accuracy. On the other hand, our simulations reproduce well the expected properties of the wave turbulence regime, with the emergence of a dual cascade of energy and wave action, and for the latter the observation of the Kolmogorov-Zakharov spectrum. In addition, our analysis reveals that the canonical variables of the problem evolve towards a nearly Gaussian statistical distribution punctuated by intermittent coherent (spatially localised and long-living) structures. In contrast to the canonical variables, the structure functions of the gauge-invariant metric components exhibit monofractal behaviour, which is a classical property of wave turbulence.

The increasing availability of Machine Learning (ML) models, particularly foundation models, enables their use across a range of downstream applications, from scenarios with missing data to safety-critical contexts. This, in principle, may contravene not only the models' terms of use, but also governmental principles and regulations. This paper presents a preliminary investigation into the use of ML models by 173 open-source projects on GitHub, spanning 16 application domains. We evaluate whether models are used to make decisions, the scope of these decisions, and whether any post-processing measures are taken to reduce the risks inherent in fully autonomous systems. Lastly, we investigate the models' compliance with established terms of use. This study lays the groundwork for defining guidelines for developers and creating analysis tools that automatically identify potential regulatory violations in the use of ML models in software systems.

In this paper we introduce a new mathematical model describing the erosion process caused in carbonate stones by the dissolution of the porous matrix due to the penetration of carbonic acid present in the environment. Such model is formulated as nonlinear reaction-transport system in porous media governed by Darcy flow. We propose a numerical algorithm based on finite difference approximation that relies on level-set method at the boundaries and we show numerical tests that are in accordance with the literature in terms of the advancement of the erosion front.

Coherent quantum phenomena can only emerge when decoherence is minimized, and mastery over decoherence is technologically crucial for designing and operating functional quantum devices. However, its microscopic mechanisms in spin-orbit-coupled ferromagnets remain elusive, and quantitative treatments have long been challenging. To solve this fundamentally significant and technologically crucial problem, we develop a quantum master-equation framework with a general ansatz for the off-diagonal density matrix that simultaneously captures electric-field-driven coherence and impurity-scattering-induced decoherence. This unified approach enables quantitative analysis of how decoherence reshapes the intrinsic anomalous Hall effect, revealing a clear crossover between intrinsic and extrinsic regimes. Remarkably, we identify a previously unrecognized extrinsic contribution: a second-order scattering process tightly relative to quantum decoherence-that is fundamentally distinct from both skew scattering and side jump mechanisms, yet substantially more significant than the skew scattering mechanism. Our work establishes decoherence as a key element in quantum transport and provides a systematic extension of the Boltzmann transport equation to incorporate decoherence, with broad implications for robust spintronic functionality.

In low-altitude wireless networks (LAWN), federated learning (FL) enables collaborative intelligence among unmanned aerial vehicles (UAVs) and integrated sensing and communication (ISAC) devices while keeping raw sensing data local. Due to the "right to be forgotten" requirements and the high mobility of ISAC devices that frequently enter or leave the coverage region of UAV-assisted servers, the influence of departing devices must be removed from trained models. This necessity motivates the adoption of federated unlearning (FUL) to eliminate historical device contributions from the global model in LAWN. However, existing FUL approaches implicitly assume that the UAV-assisted server executes unlearning operations honestly. Without client-verifiable guarantees, an untrusted server may retain residual device information, leading to potential privacy leakage and undermining trust. To address this issue, we propose VerFU, a privacy-preserving and client-verifiable federated unlearning framework designed for LAWN. It empowers ISAC devices to validate the server-side unlearning operations without relying on original data samples. By integrating linear homomorphic hash (LHH) with commitment schemes, VerFU constructs tamper-proof records of historical updates. ISAC devices ensure the integrity of unlearning results by verifying decommitment parameters and utilizing the linear composability of LHH to check whether the global model accurately removes their historical contributions. Furthermore, VerFU is capable of efficiently processing parallel unlearning requests and verification from multiple ISAC devices. Experimental results demonstrate that our framework efficiently preserves model utility post-unlearning while maintaining low communication and verification overhead.

We study the thermal static potential for (2+1)-flavor QCD at nonzero density through a Taylor expansion around vanishing chemical potentials. From Taylor expanded Wilson line correlators, we extract the $\hatμ^2$ coefficient of the real and imaginary part of the potential in light and strange flavor channels and in the baryon number and electric charge channels. We observe an enhancement of in-medium screening at intermediate and large separations. The effect is visible in both the real and imaginary parts to the extracted $\hatμ^2$ contribution of the static potentials and provides a first step toward constraining in-medium heavy-quark interactions relevant for the Beam Energy Scan program at RHIC and future FAIR experiments.

Let $E/k$ be a non-isotrivial elliptic curve over a global function field $k$ of characteristic $p>3$, and $G\subset \mathrm{Gal}(k^{\mathrm{sep}}/k)$ be a topologically finitely generated subgroup. We prove that if $E/k$ has analytic rank $1$, then its rank over the fixed subfield $L^G$ is infinite, where $L$ is the infinite ring class extension of some finite separable extension $K/k$. If $E/k$ has analytic rank $0$, then we prove that the same holds provided there exists an imaginary quadratic extension $K/k$ such that $E/K$ has analytic rank $1$ and satisfies the Heegner hypothesis.

An algorithm is proposed for solving optimization problems with stochastic objective and deterministic equality and inequality constraints. This algorithm is objective-function-free in the sense that it only uses the objective's gradient and never evaluates the function value. It is based on an adaptive selection of function-decreasing and constraint-improving iterations, the first ones using an Adagrad-type stepsize. When applied to problems with full-rank Jacobian, the combined primal-dual optimality measure is shown to decrease at the rate of O(1/sqrt{k}), which is identical to the convergence rate of first-order methods in the unconstrained case.

FcsIT is a platform-independent, open-source tool for calculating the correlation and fitting fluorescence correlation spectroscopy data. The software is written in Python and uses a powerful Dear PyGUI engine for its interface. It provides reading and correlating the TTTR data, as well as TCSPC filtering of the photon time-trace data. The circular-block bootstrap method applied to the calculation of correlation data and its variance results in data quality comparable to that obtained with commercially available software. An intuitive fitting interface provides efficient analysis of large datasets and includes nine predefined mathematical models for fitting correlation curves. Moreover, it allows users to add their own models in a user-friendly manner. Validation of the FcsIT tool against simulated FCS data and real FCS experiments confirms its usability and potential appeal to a wide variety of FCS users.

We provide a short proof of the 1-dimensional flat chain conjecture.

We present the first experimental evidence of inhomogeneous melting in a finite dusty plasma crystal confined in an anisotropic potential well. By systematically tuning the confinement anisotropy and applying controlled laser heating, distinct melting patterns are observed. Spectral-mode analysis based on Singular Value Decomposition of particle trajectories reveals that increasing laser power redistributes energy into specific collective modes, triggering localized structural destabilization. Molecular Dynamics simulations reproduce the observations and show that confinement-controlled mode coupling with laser heating governs the melting dynamics. These results establish geometric anisotropy as a key control parameter for inhomogeneous melting in finite coupled systems.

We present a receiver-side framework for identifying amplitude distortions in frequency-selective OFDM channels. The core novelty is the use of the DCT Neuron, a compact adaptive processor based on the discrete cosine transform (DCT), to characterize the channel's nonlinear response, leveraging its properties for highly efficient estimation. Operating directly in the time domain, the method builds an accurate signal model and tracks channel variations adaptively, achieving reliable identification with as few as two OFDM symbols. The learned nonlinear response can then be exploited for predistortion and iterative decoding, enabling low-complexity, real-time adaptive compensation of complex responses in multicarrier systems.