In this paper we study an optimization problem in which the control is information, more precisely, the control is a $σ$-algebra or a filtration. In a dynamic setting, we establish the dynamic programming principle and the law invariance of the value function. The latter requires a condition slightly stronger than the (H)-hypothesis for the admissible filtration, and enables us to define the value function on $\mathcal P_2(\mathcal P_2(\mathbb R^d))$, the space of laws of random probability measures. By using a new Itô's formula for smooth functions on $\mathcal P_2(\mathcal P_2(\mathbb R^d))$, we characterize the value function of the information control problem by an Hamilton-Jacobi-Bellman equation on this space.

Deep Neural Networks (DNNs) are vulnerable to backdoor attacks. Due to the nature of Machine Learning as a Service (MLaaS) applications, black-box defenses are more practical than white-box methods, yet existing purification techniques suffer from key limitations: a lack of justification for specific transformations, dataset dependency, high computational overhead, and a neglect of frequency-domain transformations. This paper conducts a preliminary study on various image transformations, identifying down-upscaling as the most effective backdoor trigger disruption technique. We subsequently propose \texttt{Lite-BD}, a lightweight two-stage blackbox backdoor defense. \texttt{Lite-BD} first employs a super-resolution-based down-upscaling stage to neutralize spatial triggers. A secondary stage utilizes query-based band-by-band frequency filtering to remove triggers hidden in specific bands. Extensive experiments against state-of-the-art attacks demonstrate that \texttt{Lite-BD} provides robust and efficient protection. Codes can be found at https://github.com/SiSL-URI/Lite-BD.

Topological superconductors (TSCs) provide a promising route to fault-tolerant quantum information processing. However, the canonical Majorana platform based on $2e$ TSCs remains computationally constrained. In this work, we find a $4e$ TSC that overcomes these constraints by combining a charge-$4e$ condensate with an Abelian chiral $\mathbb{Z}_3$ topological order in an intertwined fashion. Remarkably, this $4e$ TSC can be obtained by proliferating vortex-antivortex pairs in a stack of two $2e$ $p+ip$ TSCs, or by melting a $ν=2/3$ quantum Hall state. Specific to this TSC, the $hc/(4e)$ fluxes act as charge-conjugation defects in the topological order, whose braiding with anyons transmutes anyons into their antiparticles. This symmetry enrichment leads to $\mathbb{Z}_3$ parafermion zero modes trapped in the elementary vortex cores, which naturally encode qutrits. Braiding the parafermion defects alone generates the full many-qutrit Clifford group. We further show that a single-probe interferometric measurement enables topologically protected magic-state preparation, promoting Clifford operations to a universal gate set. Because the non-Abelian modes are bound to flux defects, they can, in principle, be externally controlled using superconducting circuit-based technology. More broadly, our results highlight hierarchical electron aggregation, the formation and condensation of higher-charge electron clusters, as a design principle for topological quantum matter with increased computational capability.

Addressing real-world optimization challenges requires not only advanced metaheuristics but also continuous refinement of their internal mechanisms. This paper explores the integration of machine learning in the form of neural surrogate models into metaheuristics through a recent lens: energy consumption. While surrogates are widely used to reduce the computational cost of expensive objective functions, their combined impact on energy efficiency, algorithmic performance, and solution accuracy remains largely unquantified. We provide a critical investigation into this intersection, aiming to advance the design of energy-aware, surrogate-assisted search algorithms. Our experiments reveal substantial benefits: employing a state-of-the-art pre-trained surrogate can reduce energy consumption by up to 98\%, execution time by approximately 98%, and memory usage by around 99\%. Moreover, increasing the training dataset size further enhances these gains by lowering the per-use computational cost, while static pre-training versus continuous (iterative) retraining have relatively different advantages depending on whether we aim at time/energy or accuracy and general cost across problems, respectively. Surrogates also have a negative impact on costs and accuracy at times, and then they cannot be blindly adopted. These findings support a more holistic approach to surrogate-assisted optimization, integrating energy with time and predictive accuracy into performance assessments.

Radiation impacts are a current challenge with computing on superconducting-based quantum devices because they can lead to widespread correlated errors across the device. Such errors can be problematic for quantum error correction (QEC) codes, which are generally designed to correct independent errors. To address this, we have developed a computational model to simulate the effects of radiation impacts on QEC performance. This is achieved by building from recently developed models of quasiparticle density, mapping radiation-induced qubit error rates onto a quantum error channel and simulation of a simple surface code. We also provide a performance metric to quantify the resilience of a QEC code to radiation impacts. Additionally, we sweep various parameters of chip design to test mitigation strategies for improved QEC performance. Our model approach is holistic, allowing for modular performance testing of error mitigation strategies and chip and code designs.

We present an analytical study of the transport coefficients associated with the shear sector of gravitational perturbations around asymptotically anti-de Sitter black branes. In the long-wavelength, low-frequency limit, the wave solutions admit a structure that is fully described in terms of multiple polylogarithms in several variables. We focus primarily on computing the transport coefficients for $\mathcal{N}=4$ SYM, by performing a bulk computation in the five-dimensional black hole background up to order $\mathfrak{q}^{10}$, which extends the results previously available in the literature. We then generalise the procedure to $d+1$ dimensions, characterising the mathematical structure of the resulting transport coefficient expressions.

Large language models (LLMs) have achieved strong performance on code generation. However, most prior evaluations focus on snippet-level outputs, such as function generation or repository completion. These settings do not fully evaluate application-level code generation, where the goal is to produce a runnable repository with coherent multi-file structure, dependency support, and end-to-end executability. In addition, real-world software quality depends not only on functional correctness but also on non-functional quality attributes, such as maintainability and security. In this paper, we present RAL-Bench, a benchmark and evaluation framework for application-level code generation. For each task, RAL-Bench derives a concise natural-language requirement from a high-quality reference project, constructs black-box system tests for both functional correctness and non-functional quality attributes. It also retains only the candidate tests that pass on the reference repository. Under this unified evaluation protocol, functional correctness is measured by the system test pass rate, while non-functional quality is evaluated along five ISO/IEC 25010-inspired dimensions, with per-dimension diagnostics and reference-normalized scoring.We evaluate 16 frontier LLMs under a controlled zero-shot setting with greedy decoding. The results show that functional correctness remains the primary bottleneck in application-level code generation, while non-functional quality also remains challenging. Under our evaluation protocol, no model exceeds a 45\% functional score. These findings suggest that strong performance on existing code generation benchmarks does not yet translate to strong performance on application-level repository generation. This result highlights the need for evaluation settings that directly assess end-to-end repository generation rather than relying only on snippet-level success.

We generalize neutrino energy density content in the early universe near BBN era $T\simeq1$ MeV within Tsallis nonextensive statistics. By using Curado-Tsallis constraints we obtain generalized distribution functions $f_q(E)$. We compute the generalized thermodynamic integral for the energy density $ρ_q$. We define a reescaling $R^{(ξ= +1)}_ρ(q) = ρ_q/ρ^{\rm std}$ which is a ratio between the deformed energy density and the standard extensive case. The last was used to directly map and deform neutrino content via the effective number of neutrinos $N_{\rm eff}$. The deformation prediction was confronted against CMB$+$BAO and BBN data for $N_{\rm eff}$ by a joint/combined $χ^2$ type-fit. We obtained the constraints $|q-1|\le 1.09\times 10^{-2}$ (95\% CL) and $|q-1|\le 1.32\times 10^{-2}$ (99\% CL) from the combined analysis by numerically calculating the best value of the Tsallis parameter $q_{\rm best}$.

High-quality feedback is essential for effective human-AI interaction. It bridges knowledge gaps, corrects digressions, and shapes system behavior; both during interaction and throughout model development. Yet despite its importance, human feedback to AI is often infrequent and low quality. This gap motivates a critical examination of human feedback during interactions with AIs. To understand and overcome the challenges preventing users from giving high-quality feedback, we conducted two studies examining feedback dynamics between humans and conversational agents (CAs). Our formative study, through the lens of Grice's maxims, identified four Feedback Barriers -- Common Ground, Verifiability, Communication, and Informativeness -- that prevent high-quality feedback by users. Building on these findings, we derive three design desiderata and show that systems incorporating scaffolds aligned with these desiderata enabled users to provide higher-quality feedback. Finally, we detail a call for action to the broader AI community for advances in Large Language Models capabilities to overcome Feedback Barriers.

Medical "Crisis Standards of Care" call for a utilitarian allocation of scarce resources in emergencies, while favoring the worst-off under normal conditions. Inspired by such triage rules, we introduce social welfare functions whose distributive tradeoffs depend on the prevailing level of aggregate welfare. These functions are inherently self-referential: they take the welfare level as an input, even though that level is itself determined by the function. In our formulation, inequality aversion varies with welfare and is therefore self-referential. We provide an axiomatic foundation for a family of social welfare functions that move from Rawlsian to utilitarian criteria as overall welfare falls, thereby formalizing triage guidelines. We also derive the converse case, in which the social objective shifts from Rawlsianism toward utilitarianism as welfare increases.

We numerically solve the conjectured Quantum Spectral Curve for strings on AdS$_3\times$S$^3\times$T$^4$ with R--R charge from weak to strong coupling. At strong coupling, the spectrum organises into flat-space string mass levels with universal square-root scaling in the string tension at leading order, and additional Kaluza-Klein fine-splitting at subleading order. At weak coupling, the energies are determined by a nearest-neighbour Bethe Ansatz, with universal subleading corrections that are suppressed at large volume.

We clarify why spin-singlet superconductivity persists in monolayer transition-metal dichalcogenides even in high magnetic fields beyond the Pauli limit. The phenomenon called Ising protection is caused by two magnetically active potentials: a Zeeman field and an Ising spin-orbit interaction. These potentials induce two spin-triplet pairing correlations in a spin-singlet superconductor. One belonging to odd-frequency symmetry class arises solely from a Zeeman field and always makes the superconducting state unstable. The other belonging to even-frequency symmetry class arise from the interaction between the two magnetic potentials and eliminate the instability caused by odd-frequency pairs. The presence or absence of even-frequency spin-triplet pairs explains the anisotropy of the Ising protection. The analytical expression of the superfluid weight enables us to conclude that even-frequency spin-triplet Cooper pairs support spin-singlet superconductivity in high Zeeman fields.

This work investigates the propagation of elastic waves in periodic Kelvin-cell chains, focusing on symmetry-breaking geometric modifications induced by twisting the cell's faces. By imposing such twists, the original lattice topology is preserved, while mirror symmetries are strategically broken through modifying a single geometric parameter, allowing wave characteristics to be adjusted without additional resonators or mass augmentation. The complex-valued Bloch-Floquet analysis reveals that twisting activates two distinct wave attenuation mechanisms: Bragg-type band gaps associated with periodicity-induced scattering, and polarization-dependent band gaps arising from longitudinal-torsional mode coupling and avoided crossings. To obtain qualitative and quantitative insight into these mechanisms, a simplified analytical model with coupled translational and rotational degrees of freedom is considered. The finite-element wave transmission calculations are experimentally validated on SLA-printed three-cell specimens, for which wave attenuation reaches up to 20 dB within the predicted band-gap frequencies. Note that high prediction accuracy requires accounting for viscoelastic material behavior, underscoring the importance of material behavior on the wave propagation characteristics. Overall, the findings show that modest geometric modifications to a classical Kelvin-cell lattice can enhance wave-filtering behavior, offering a tractable design strategy for vibration control in lightweight architected lattices.

In this paper, we find Kerr solution accompanied with a nontrivial vector field as a solution to one of the simplest vector-tensor theories of gravity, namely the bumblebee model with an intriguing coupling constant between the Ricci curvature tensor and the vector field. We also demonstrate that the accompanied vector field can be generated via the Newman-Janis algorithm from a simple spherical vector field, which together with the Schwarzschild metric constitutes a solution to the same bumblebee model. It is probably the simplest example of a theory and its black-hole solutions for the Newman-Janis algorithm to hold except for general relativity.

We establish an exponentially decaying upper bound on the average energy that can be extracted in quantum energy teleportation (QET) protocols executed on finite-range {gapped} lattice systems possessing a unique ground state. Under mild regularity assumptions on the Hamiltonian and uniform operator-norm bounds on the local measurement operators, there exist positive constants $C$ and $μ$ (determined by the spectral gap, interaction range and local operator norms) such that for any local measurement performed in a region $A$ and any outcome-dependent local unitaries implemented in a disjoint region $B$ separated by distance $d=\operatorname{dist}(A,B)$ one has $|E_A-E_B|\le C\,e^{-μd}$. The bound is nonperturbative, explicit up to model-dependent constants, and follows from the variational characterization of the ground state combined with exponential clustering implied by the spectral gap. We emphasize that the constants deteriorate as the gap closes (equivalently, as the correlation length diverges), so the estimate is intended for the gapped regime.

In this work, we perform a comprehensive investigation of the production of high-spin $ω_J$ and $ρ_J$ mesons ($J=2,3,4,5$) in $π^- p$ reactions using an effective Lagrangian approach. By constructing the relevant $t$-channel processes and calibrating the model with a single adjustable parameter fitted to existing data, we successfully reproduce the measured total and differential cross sections for the $J=3$ states $ω_3(1670)$ and $ρ_3(1690)$. Within the same framework, we predict the production cross sections for their lower- and higher-spin partners: $ω_2(1975)$, $ρ_2(1940)$, $ω_4(2250)$, $ρ_4(2230)$, $ω_5(2350)$, and $ρ_5(2350)$. Our results show that these states exhibit measurable cross sections with characteristically forward-peaked angular distributions, underscoring their strong potential for observation in future $πp$ meson-beam experiments.

We investigate a dark sector coupled to the Standard Model (SM) through a kinetically mixed dark photon $U$ associated with a new $U(1)'$ gauge symmetry. Kinetic mixing $\varepsilon$ induces an effective coupling to the electromagnetic current, while $U$ interacts with stable dark matter (DM) $χ$ via a dark gauge coupling $g_χ$. Our analysis is based on the parton-hadron-string dynamics (PHSD) transport approach, extended to include dark photon production and decay into dileptons ($U\!\to e^+e^-$). In PHSD, dark photons are produced in high-energy collisions through Dalitz decays of light mesons ($π^0,η,η',ω$), Delta-resonances ($Δ\!\to N U$), direct vector meson decays ($ρ,ω,ϕ\!\to U$), kaon decays, and $q\bar q\!\to U$ annihilation. Building on previous PHSD benchmarks against dilepton data, we extract upper limits on $\varepsilon^2(m_U,m_χ,α_χ)$ in both the visible regime ($m_U<2m_χ$), where $U\!\to e^+e^-$ dominates, and the invisible regime ($m_U>2m_χ$), where $U\!\toχ\barχ$ is kinematically open. Cosmological and astrophysical constraints are incorporated in two complementary ways. First, we compute the velocity-dependent self-interaction cross section $σ/m_χ$ for Yukawa-mediated SIDM and confront it with bounds from dwarf galaxies, galaxy groups, and clusters. Second, we determine thermal relic target curves by computing the relic abundance and requiring $Ω_{\rm DM}h^2\simeq 0.12$, consistent with \textit{Planck} measurements of the cosmic microwave background. Combining PHSD limits on $\varepsilon^2$ with relic density and self-interaction requirements, we exclude regions of the $(m_χ,m_U)$ plane for each DM realization (Dirac, Majorana, or complex scalar) and identify benchmark scenarios in which heavy-ion, cosmological, and astrophysical constraints are simultaneously satisfied.

This paper considers submodular function minimization (SFM) restricted to a family of subsets. We show that SFM over complements of families with certain hierarchical structures can be solved in polynomial-time. This yields a polynomial-time algorithm for SFM over complements of various families, such as intersecting families, crossing families, and the unions of lattices. Moreover, this tractability result partially settles the open question posed by Nägele, Sudakov, and Zenklusen on polynomial-solvability of SFM over the intersection of parity families. Furthermore, our tractability result implies that for a constant positive integer $k$, the $k$-th smallest value of a submodular function can be obtained in polynomial-time.

Nitinawarat and Narayan proposed a perfect secret key generation scheme for the so-called \emph{pairwise independent network (PIN) model} by exploiting the combinatorial properties of the underlying graph, namely the spanning tree packing rate. This work considers a generalization of the PIN model where the underlying graph is replaced with a hypergraph, and makes progress towards designing similar perfect secret key generation schemes by exploiting the combinatorial properties of the hypergraph. Our contributions are two-fold. We first provide a capacity achieving scheme for a complete $t$-uniform hypergraph on $m$ vertices by leveraging a packing of the complete $t$-uniform hypergraphs by what we refer to as star hypergraphs, and designing a scheme that gives $\binom{m-2}{t-2}$ bits of perfect secret key per star graph. Our second contribution is a 2-bit perfect secret key generation scheme for 3-uniform star hypergraphs whose projections are cycles. This scheme is then extended to a perfect secret key generation scheme for generic 3-uniform hypergraphs by exploiting star graph packing of 3-uniform hypergraphs and Hamiltonian packings of graphs. The scheme is then shown to be capacity achieving for certain classes of hypergraphs.

The scalable preparation of large photon-number (Fock) states is a long-standing frontier in quantum science, with direct implications for quantum metrology and bosonic quantum information processing. Despite substantial progress at small photon numbers, extending state generation to large photon numbers while maintaining high fidelity and operating deterministically remains a significant challenge. Here we demonstrate a scalable and experimentally accessible control protocol for generating large photon-number states using only native spin--oscillator operations. The protocol alternates Jaynes--Cummings interactions with phase-space displacements to imprint photon-number--dependent phases and convert them into selective interference in photon-number space. It already achieves high preparation fidelity unconditionally, while an optional final qubit projection removes residual qubit--field correlations and further enhances the fidelity. Conditioned on this final projection, photon-number state preparation with fidelities exceeding $0.95$ is achieved for photon numbers in the few-hundred regime, with a success probability exceeding $0.90$, placing the protocol in a near-deterministic operating regime. The resulting control sequences remain shallow and are robust against detuning, control noise, and experimentally relevant dissipation. Our results establish a practical route to scalable, high-fidelity photon-number state preparation at large photon numbers and provide a versatile interference-engineering toolbox for nonclassical bosonic state synthesis.

AI-powered coding assistants are rapidly becoming fixtures in professional IDEs, yet their sustained influence on everyday development remains poorly understood. Prior research has focused on short-term use or self-reported perceptions, leaving open questions about how sustained AI use reshapes actual daily coding practices in the long term. We address this gap with a mixed-method study of AI adoption in IDEs, combining longitudinal two-year fine-grained telemetry from 800 developers with a survey of 62 professionals. We analyze five dimensions of workflow change: productivity, code quality, code editing, code reuse, and context switching. Telemetry reveals that AI users produce substantially more code but also delete significantly more. Meanwhile, survey respondents report productivity gains and perceive minimal changes in other dimensions. Our results offer empirical insights into the silent restructuring of software workflows and provide implications for designing future AI-augmented tooling.

We report on a broadband search for axion-like-particle (ALP) interactions using a radio-frequency-operated $^{87}\mathrm{Rb}$ atomic magnetometer. The instrument provides wide spectral coverage and sensitivity to an oscillating pseudomagnetic field that may be generated by the gradient coupling of the ALP field to the constituent fermions of atoms. We search for an ALP-gradient signature in the mass range $2.40\times10^{-10}\,\mathrm{eV}/c^{2}$--$2.11\times10^{-9}\,\mathrm{eV}/c^{2}$. No statistically significant signatures of an oscillating magnetic field are observed, and we derive upper limits on the corresponding ALP-proton, -neutron and -electron couplings, $g_{αpp}$, $g_{αnn}$ and $g_{αee}$, respectively. The result on $g_{αpp}$ improves over previous laboratory searches, while the limits on $g_{αnn}$ and $g_{αee}$ complement earlier laboratory searches and astrophysical bounds. The work extends searches for ALP-fermion interactions into a mass region largely unexplored in a dark-matter context, demonstrating the potential of our method for broadband axion-like particle searches targeting the Galactic dark-matter halo.

We develop a geometric and microlocal framework for the Navier-Stokes equations by lifting the dynamics to the cosphere bundle of a Riemannian manifold. In this formulation, velocity and vorticity are microlocal distributions governed by a linear, non-autonomous transport-dissipation system generated by a canonical vector field on the compact phase space. We introduce microlocal amplitude and directional entropy functionals, alongside monotone invariants quantifying angular concentration and alignment tied to potential regularity loss. Viscosity induces an effective geometric diffusion, yielding closed intrinsic differential inequalities. To capture fluid-geometry interactions, we define an effective connection and curvature tensor encoding the symmetric velocity gradient. This yields a Ricci-type microlocal evolution that constrains directional stretching. Our framework establishes a necessary and sufficient geometric equivalence criterion: finite-time singularity occurs if and only if at least one of three microlocal controls fails-deformation integrability, entropy boundedness, or lifted energy boundedness. Furthermore, a dimensional reduction mechanism emerges: as effective fiber dimension increases, a symmetry lock forces microlocal distributions toward isotropy, topologically obstructing angular singularities. While not resolving the global regularity problem, this reformulates it as a question of dissipative stability and spectral control on a compact, symmetry-constrained system, severely restricting admissible blow-up scenarios.

Large language models (LLMs) are a type of machine learning tool that economists have started to apply in their empirical research. One such application is macroeconomic forecasting with backtesting of LLMs, even though they are trained on the same data that is used to estimate their forecasting performance. Can these in-sample accuracy results be extrapolated to the model's out-of-sample performance? To answer this question, we developed a family of prompt sensitivity tests and two members of this family, which we call the fake date tests. These tests aim to detect two types of biases in LLMs' in-sample forecasts: lookahead bias and context bias. According to the empirical results, none of the modern LLMs tested in this study passed our first test, signaling the presence of lookahead bias in their in-sample forecasts.

Germanium quantum dot hole spin qubits are compatible with fully electrical control and are progressing toward multi-qubit operations. However, their coherence is limited by charge noise and driving field induced frequency shifts, and the resulting ensemble $1/f$ dephasing. Here we theoretically demonstrate that a bichromatic driving scheme cancels the second order frequency shift from the control field without sacrificing the electric dipole spin resonance (EDSR) rate, and without additional gate design or microwave engineering. Based on this property, we further demonstrate that bichromatic control creates a wide operating window that reduces sensitivity to quasi-static charge noise and thus enhances single qubit gate fidelity. This method provides a low-power route to a stabler frequency operation in germanium hole spin qubits and is readily transferable to other semiconductor spin qubit platforms.

This contribution presents studies of differential top-quark measurements at the Future Circular Collider in its proton-proton stage (FCC-hh). The analyses target the leptonic final states of the $\bar{t}tZ$ and $\bar{t}t\bar{t}t$ production processes. Particular focus is given to the high-$Q^2$ regime, where sensitivity to new physics, as encoded in an Effective Field Theory framework, is enhanced. The dataset corresponds to an integrated luminosity of 30 $\text{ab}^{-1}$ at $\sqrt{s} = 84$ TeV. The reconstructed transverse momentum $\text{p}_\text{T}(Z_{\ell\ell})$ distribution is shown to be measurable up to approximately 2 TeV with a precision of 20% in the high energy region ($\text{p}_\text{T}(Z_{\ell\ell})$ >1.8 TeV). The scalar transverse momentum $\text{H}_\text{T}$ of the four-top production reaches 3.5 TeV with a precision of 35%. Additionally, a dedicated study of the lepton reconstruction efficiency shows that redefining the isolation variable to account for the highly boosted objects at FCC-hh improves the total signal yield in $\bar{t}tZ$ by a factor of 1.5.

We study inflationary dynamics within the framework of fractal cosmology, where space is characterized by an effective non-integer dimension $D$. In our work, fractal effects are sourced through thermodynamic modifications at the cosmological horizon. Using the modified Friedmann and continuity equations, we then derive the modified slow roll parameter and their evolution for linear, cubic, Starobinsky ($R+R^2$) and Natural inflationary potentials, showing that the slow roll parameters get suppressed for $D<3$. We further derive a fractal extension of the Mukhanov-Sasaki equation by introducing an effective momentum $k_{\text{eff}}$, which captures the modification of spatial Laplacian due to fractality. This leads to explicit corrections to the scalar power spectrum and the spectral index $n_s$, depending on both $D$ and a fractional length scale $L$. Confrontation with Planck 2018 data constrains the effective dimension to a best-fit range of $2.7\lesssim D \lesssim 3$ for the Starobinsky model. Furthermore, in the case of Natural Inflation, fractal corrections relax the usual requirement of super-Planckian axion decay constants, opening a phenomenologically viable parameter space inaccessible in the standard $3+1$ dimensional cosmology.

We investigate the relativistic dynamics of quantum entanglement in a four-qubit cluster ($CL_4$) state using a fully operational Unruh-DeWitt detector framework. Contrary to the widely held expectation that the Unruh effect inevitably degrades initially maximal entanglement, we demonstrate that the $1-3$ bipartite entanglement of the $CL_4$ state remains strictly maximal for all accelerations, including the infinite-acceleration limit. This result uncovers a previously unexplored phenomenon, namely the ``complete freezing of initially maximal entanglement" under relativistic motion. To the best of our knowledge, this is the first identification and systematic characterization of such a phenomenon within a relativistic framework. These findings overturn the conventional view that acceleration universally diminishes maximal entanglement and establish the $CL_4$ state as a promising resource for quantum information processing in non-inertial or curved-spacetime settings.

We suggest a formation scenario of black holes with intermediate mass $\sim 10^3 M_\odot$, by post recombination Bondi-Hoyle-Lyttleton accretion into ultra dense dark matter halos (UDMH) of $\sim 10^5 M_\odot$, which have formed around the recombination epoch. Such UDMH can result from rare curvature fluctuations on small scales whose amplitude is still well below the current Cosmic Microwave Background (CMB) spectral distortion limits. Gas accreted by the UDMH is heated to virial temperatures above which atomic cooling is efficient, cools rapidly to about $\sim 8000$ K and collapses on the free fall time of few $10^4$ yr to the halo core, until supported by rotation. Further fragmentation due to molecular cooling is prevented by the suppression of $H_2$ molecule formation by the CMB photons at redshifts $z> 200-400$. We find that the rotationally supported gas disk will be compact and massive enough to undergo self-gravitational instability in some cases, plausibly where accretion is into a nearly spherical UDMH which has formed from a rare peak in the density field. This results in a further, rapid transfer of mass inwards due to viscous forces and gravitational torques leading to the formation of a supermassive star and/or black hole of about $10^3 M_\odot$ at redshifts of a few hundred. Such intermediate mass black holes formed at high redshifts can have a large-enough abundance to seed the first super massive black holes and help explain the abundance of active galaxies detected now at increasingly larger redshifts by the James Webb Space Telescope.

Systemic financial risk refers to the simultaneous failure or destabilization of multiple financial institutions, often triggered by contagion mechanisms or common exposures to shocks. In this paper, we present a dynamical model of bank leverage (the ratio of asset holdings to equity) a quantity that both reflects and drives risk dynamics. We model how banks, constrained by Value-at-Risk (VaR) regulations, adjust their leverage in response to changes in the price of a single asset, assumed to be held in fixed proportion across banks. This leverage-targeting behavior introduces a procyclical feedback loop between asset prices and leverage. In the dynamics, this can manifest as logistic-like behavior with a rich bifurcation structure across model parameters. By analyzing these coupled dynamics in both isolated and interconnected bank models, we outline a framework for understanding how systemic risk can emerge from seemingly rational micro-level behavior.