We analyze the finite-blocklength performance of lossy joint source-channel codes (JSCC) in an unknown-channel framework, where the true channel is unknown but the source distribution is known. We establish achievability results for mismatched-design JSCC, where the code design is based on a channel $Q_{Y|X}$ but deployed over a different channel $P_{Y|X}$. Our mismatched-design achievability result allows nonstationary channel laws and arbitrary standard Borel alphabets for the source, reproduction, channel input and channel output. The achievability bound is given in terms of the rate-distortion and rate-dispersion functions, as well as two channel-dependent quantities that we call the mismatched-design rate and mismatched-design rate-dispersion. For block erasure channels, our result shows that channel mismatch incurs no penalty. We then show a second-order universal family of source-channel codes over the set of block erasure channels. Our code construction uses Poisson functional representations of suitable conditional probability measures to produce the encoder and decoder outputs. We use a parameterized family of Gibbs posteriors as the decoder-side kernels, whose envelope recovers the generalized mutual information.

The origin of pressure-induced superconductivity in MnB4 remains unclear. Here we show that it can be explained by electron-phonon coupling once the structural space is mapped using both volume and the Mn dimer distance as key structural parameters under compression. Minor changes in the dimer distance significantly affect electronic and phonon properties, bringing the calculated Tc into agreement with experiment. Our results suggest that MnB4 is a highly responsive system, providing a platform for probing the subtle interplay between structural instability, superconductivity and magnetism.

While previous versions of the Ai2 Climate Emulator (ACE) have been trained with CO$_2$ as a forcing, they are only accurate within a narrow range of scenarios, for example climate over the last 80 years forced by observed sea surface temperature (SST), sea ice, and CO$_2$ (AMIP), or equilibrium or near-equilibrium climates with CO$_2$ concentrations ranging from 1x to 4x that of the present day. Attempting to simulate climate forced by AMIP SST perturbed by +4 K or the response to an abrupt quadrupling of CO$_2$, results in unphysical behavior. We attribute this to these models being trained on datasets where the SST and CO$_2$ are correlated, limiting their ability to accurately learn their separate effects. In this study we introduce a new class of "random-CO$_2$" reference simulations where the SST and CO$_2$ are prescribed to vary independently. Trained on a balance of AMIP, equilibrium-climate, and random-CO$_2$ data, and including a total energy conservation constraint for improved interpretability, we present a more data-efficient model that not only accurately emulates its reference model in scenarios in which previous models excelled, but also scenarios like AMIP +4 K and slab-ocean-coupled abrupt 4xCO$_2$ where they did not. Limitations are that it has simplified or prescribed representations of other Earth system components like the ocean, land, and sea ice; does not expose other known climate drivers as forcings; and relies solely on physics-based model output for training data, inheriting the biases relative to observations thereof. Each of these represent opportunities for future work.

Inorganic structural chemistry leads naturally to a theory for crystal structure prediction formalized by a generalized disjunctive programming (GDP), which is formulated using continuous and Boolean variables to involve the algebraic equations, disjunctions, and logic propositions. Since the feasibilities of continuous variables change drastically depending on Boolean variables and vice versa, iterative optimization of continuous and Boolean variables efficiently transforms a randomly generated initial structure into an optimal solution. Boolean variables are introduced to elucidate the ``combinatorial backbone'' of the original continuous optimization problem, which corresponds to the graphs describing crystal structures with clear chemical meanings. Since many subgraphs are discovered in numerous graphs generated through structural optimizations, on-the-fly learning of the feasibilities of them accelerates the discovery of the optimal solutions. This theory enables designing a wide variety of crystal structures with small computations based on only the atomic radii and feasible coordination numbers of each atom.

We study the finite-lattice statistical-mechanical model whose nearest-neighbor bond potential is the reciprocal cost $J(e^\varepsilon)=\cosh\varepsilon-1$, selected by the d'Alembert functional equation under the stated regularity and calibration assumptions. The structural inputs are stated explicitly; once they are fixed, the analysis is rigorous mathematics about the bond action $V(Δϕ)=\cosh(Δϕ)-1$ on finite boxes in $\mathbb Z^3\times\mathbb Z/8\mathbb Z$. Our main result pairs a negative and a positive statement about reflection positivity. For the continuous noncompact model the natural temporal kernel $K(u)=\exp[-(\cosh u-1)]$ fails the Bochner positive-definiteness test: an interval-certified quadrature gives $\widetilde K(3)<0$. Thus the standard Bochner route to Osterwalder-Schrader reflection positivity is obstructed. For a finite-alphabet variant, with field values restricted to a finite symmetric set $Φ=v_0\{-N,\ldots,N\}$, reflection positivity holds whenever the finite crossing-bond Toeplitz matrix $(K_{Φ(v_0,N)})_{a,b}:=K(b-a), a,b\inΦ$, is positive semidefinite. For $v_0\in\{1.2,1.5,2.5\}$, this is discharged by a rigorous diagonal-dominance certificate uniform in $N$, and the associated one-step transfer operator is then positive and self-adjoint in an explicit reflection-positivity inner product. These finite-volume results do not provide a continuum Wightman theory, Osterwalder-Schrader reconstruction, LSZ scattering, or a continuum mass gap.

Weyl fermions in inversion-symmetric Weyl semimetals occur in pairs of opposite chirality, leading to symmetric optical responses under circularly-polarised light and a vanishing net photocurrent. Here, we show that tailored two-colour light fields break this symmetry and enable selective excitation of individual Weyl nodes. The interference between a circularly-polarised $ω$ field and a phase-locked linearly-polarised $2ω$ field generates a chirality-dependent redistribution of carriers in momentum space, resulting in a nonzero controllable photocurrent. We demonstrate that both the magnitude and sign of the photocurrent can be tuned via the relative phase and field strength of the two colours, and identify an optimal regime in which chiral selectivity is maximised. Our results establish a general route to optically-controlled chiral charge dynamics in Weyl semimetals using polarisation-structured light.

We present a broadband spectro-polarimetric analysis of the extragalactic radio source \texttt{RACS\_0900-28\_7036} using SPICE-RACS DR2 observations with the Australian Square Kilometre Array Pathfinder (ASKAP). The source was selected for its large rotation measure (${\rm RM}=345.7\pm0.2~{\rm rad~m^{-2}}$), substantial excess relative to the local foreground ($Δ{\rm RM}\approx171~{\rm rad~m^{-2}}$), and strong evidence of Faraday complexity ($σ_{\rm add}/δσ_{\rm add}\approx8.6$). Observations span 803--1083~MHz in 36 spectral channels, enabling detailed characterization of Faraday rotation and wavelength-dependent depolarization. One-dimensional $q$-$u$ fitting and Bayesian model selection identify a multi-component model comprising one Burn-slab component and two external Faraday dispersion components (1 Slab + 2 EFD) as the preferred description. The dominant astrophysical component exhibits ${\rm RM}\approx345.5~{\rm rad~m^{-2}}$ with modest Faraday dispersion ($σ_{\rm RM}\approx3~{\rm rad~m^{-2}}$), while a secondary broader component at ${\rm RM}\approx131.5~{\rm rad~m^{-2}}$ shows strong depolarization ($σ_{\rm RM}\approx19.5~{\rm rad~m^{-2}}$). The fractional polarization spectrum and $q$--$u$ plane evolution further confirm multiple Faraday-active regions along the line of sight. These results demonstrate that ASKAP broadband spectropolarimetry can resolve complex Faraday structures and probe turbulent magnetized environments, providing a framework for systematic depolarization studies across the full SPICE-RACS catalog and enabling statistical investigations of Faraday complexity in diverse extragalactic radio sources.

Green asked the following question concerning structures in sumsets: Suppose that $\mathbb{F}_2^n$ is partitioned into sets $A_1, \dots, A_K$. Does $A_i+A_i$ contain a coset of codimension $O_K(1)$ for some $i$? An answer is not known even in the case of $K = 3$. We resolve this question in the affirmative in two special cases: (1) when $A_1, A_2$ are Hamming balls of radius $r < n/2 - 7$ relative to different bases, and (2) when $A_1$ is a Hamming ball of sufficiently small constant density.

The couplings between hadrons encode the dynamics of quantum chromodynamics. While many couplings can be calculated from decay widths, in some cases the decays are kinematically forbidden and hence are not directly accessible. We use a Regge framework to determine these couplings from high-energy polarized scattering processes. We apply this to the $πΔ$ photoproduction that was recently studied at GlueX and provide the first determination of the complete set of $NΔ$ couplings to $ρ$, $b_1$, and $a_2$.

We characterize finite-type $\mathbb{G}$-principal $\mathbb{U}$-equivariant bundles on normal $\mathbb{U}$-spaces for compact Lie groups $\mathbb{U}$ and $\mathbb{G}$, in several ways, including (a) their extensibility across the $\mathbb{U}$-equivariant compactification $β_{\mathbb{U}}X$ and (b) their becoming finite-type upon extending the structure group along at least one $\mathbb{U}$-equivariant compact-Lie-group embedding $\mathbb{G}\le \mathbb{K}$. This generalizes non-equivariant results of Phillips and the author's characterizing finite-type matrix-algebra bundles, upon specializing $\mathbb{G}$ to projective unitary groups. When the $\mathbb{U}$-action on $X$ has virtually abelian isotropy, matrix-algebra equivariant bundles are also finite-type precisely when, locally over a finite open $\mathbb{U}$-cover, they are tensor factors of trivial matrix bundles. In a $K$-theoretic offshoot we prove that for $\mathbb{U}$-actions with finite isotropy groups on compact Hausdorff spaces $X$ equivariant vector bundles $\mathcal{E}\to X$ are factors of trivial bundles $K$-theoretically: there is a class $a\in K_{\mathbb{U}}(X)$ with $[\mathcal{E}]a$ the class of a bundle induced by a $\mathbb{U}$-representation (which furthermore can be chosen so as to restrict to isotropy groups to multiples of the regular representations). This generalizes a result of Donovan and Karoubi.

Polynomial chaos expansions provide surrogate models for stochastic systems, with coefficients typically derived using Galerkin projection, stochastic collocation, or least squares approximation. These traditional approaches often fail to accurately capture statistical moments without resorting to high-order approximations. We propose a constrained optimization framework that modifies standard techniques to determine polynomial chaos coefficients that precisely recover the first two statistical moments. The effectiveness of our approach is demonstrated on several candidate algebraic functions of random variables, showing significant improvements in statistical accuracy even with low-order approximations.

This paper provides a data-driven design guaranteeing parameter convergence in model reference adaptive control (MRAC) when the to-be-controlled system is subject to process noise. In the context of MRAC, parameter convergence refers to ensuring convergence of the adaptive gains to a solution of the matching equations, or to an approximate solution when noise is present. In classical MRAC, even small noise may induce parameter drift, thus lacking robustness to noise. Meanwhile, existing robust MRAC methods cannot ensure parameter convergence without imposing excitation conditions on data. A key feature of the proposed framework is to ensure convergence of the adaptive gains to an approximate solution of the matching equations without relying on persistently exciting signals. Furthermore, the matching error can be explicitly characterized as a function of the noise. This explicit characterization allows to establish a necessary and sufficient condition on the noise characteristics under which the limit closed-loop system matrix is Hurwitz. In the noise-free case, the proposed framework results in exact parameter convergence. Notably, as compared to existing methods achieving exact parameter convergence in the noise-free case, the condition on data in the proposed framework is weaker.

Permanent Magnet Synchronous Machines (PMSMs) have become one of the preferred forms of electromechanical energy converters, attributing to their high efficiency, torque density, and other unique advantages. However, given the need for proper rotor position measurement for commutation and field orientation, accurate rotor position sensing is of paramount importance. In sensing motor rotor position with a sensor, harmonic errors that arise in the sensing subsystem lead to undesirable torque ripple. Thus, this paper presents an adaptive, extremum seeking control based approach capable of mitigating position signal harmonics in PMSMs. The proposed approach is experimentally validated under varying torque, speed, and harmonic conditions. Its harmonic compensation performance is comparatively evaluated against the look-up table based method. Furthermore, the accuracy of the proposed approach is analyzed, highlighting its effectiveness.

We present a technique for high-precision absolute measurements of gamma-ray production cross sections (n,xg) induced by 14 MeV neutrons. The technique is based on the Associated Particle Imaging (API) method, which tags individual neutrons emitted from a deuterium-tritium source with their associated alpha-particles, enabling coincidence-based suppression of lower-energy neutrons and room background signals, while also providing neutron flux measurements with uncertainties on the order of 1%. This compact, laboratory-scale technique has the potential to address gaps and discrepancies in existing cross section libraries at a fraction of the cost of large-scale dedicated facilities, with direct applications in active neutron interrogation, detector calibration, nuclear fusion science, and Monte Carlo simulations, among others. We demonstrate the technique through proof-of-concept experiments on thin and thick samples of natural Fe (1 mm, 8 mm) and natural C (2 mm, 10 mm). For Fe, gamma-ray production cross sections were measured for the 846.78 and 1238.33 keV transitions from the first and second excited states of 56Fe. For C, the (n,n'g) cross section was measured for the 4438.91 keV transition from the first excited state of 12C. Measurements were performed at 110 and 48 degrees relative to the neutron beam to characterize gamma-ray anisotropy. For the thin samples, the measured cross sections are 723 +/- 70 mb (56Fe, 846.78 keV, 110 deg), 303 +/- 42 mb (56Fe, 1238.33 keV, 110 deg), 755 +/- 106 mb (56Fe, 846.78 keV, 48 deg), 321 +/- 149 mb (56Fe, 1238.33 keV, 48 deg), 141 +/- 16 mb (12C, 4438.91 keV, 110 deg), and 279 +/- 105 mb (12C, 4438.91 keV, 48 deg). Uncertainties are dominated by counting statistics and detector efficiency calibration, both of which can be reduced in future experiments to achieve overall uncertainties of 5% or better.

Electrical transport and magnetic measurements have been made on UTe2 under pressure P up to approximately 16 GPa to determine the superconducting transition temperature Tc vs P phase diagram in the high-pressure tetragonal phase. Superconductivity emerges near 5 GPa, coincident with the orthorhombic to tetragonal phase transition; in the tetragonal phase, Tc reaches a maximum value of approximately 4 K at 6 GPa and then decreases with P and appears to vanish near 18 GPa. Tetragonal UTe2 has a relatively small upper critical field Hc2(0) $\approx$ 1.2 T at 5.3 GPa, smaller than the Pauli paramagnetic limit, and is orbitally limited with a coherence length $ξ$tetra $\approx$ 16.5 nm. This small value of Hc2(0) favors more conventional superconductivity; in contrast, the large values of Hc2(T) for orthorhombic UTe2 exceed the Pauli paramagnetic limit in all three crystallographic directions and have been attributed to unconventional superconductivity, widely believed to involve spin-triplet pairing. The temperature-pressure phase diagram of UTe2 shows a striking dichotomy: a narrow, fragile, unconventional superconducting region in the orthorhombic phase vs a broad, robust, and more conventional superconducting dome in the tetragonal phase. This dichotomy is consistent with the proposal that U-dimers, present (absent) in the orthorhombic (tetragonal) phase, may play a role in spin-triplet superconductivity of orthorhombic UTe2. In the tetragonal phase, the normal-state electrical resistivity $ρ$(T) exhibits metallic behavior with a knee between 200 and 240 K that depends weakly on P and most likely marks the onset of a transition to a magnetically ordered phase that coexists with superconductivity.

We begin by presenting the mathematical rationale underlying classical deductive inference. We then introduce the foundational ideas of the Bayesian inference framework. Results lying at the interface of Statistics and Ergodic Theory are outlined, providing a theoretical framework applicable to the prediction and analysis of real-world phenomena from random data. This text is expository in nature - no new results are presented; rather, recently published results are described in a didactic manner. Throughout, we work with Hölder equilibrium measures, which encompass a substantially more general class of processes than i.i.d. ones.

Future wireless networks demand capabilities beyond traditional communication, driving the development of Integrated Sensing and Communication (ISAC) for environmental awareness, localization, and tracking. Ubiquitous cellular deployment allows ISAC to maximize spectral efficiency, lower costs, and expand sensing coverage. However, sub-6 GHz research has heavily favored communication, leaving sensing capabilities largely underexplored. To bridge this gap, we introduce CellSense, a novel sub-6 GHz ISAC architecture natively integrated into the 5G cellular protocol stack for real-world target tracking. We validate the system via Sionna-based orthogonal frequency-division multiplexing (OFDM) link-level simulations and an experimental USRP hardware prototype using the OpenAirInterface (OAI) stack. Furthermore, we analyze the communication-sensing tradeoff by quantifying how pilot symbol density impacts throughput versus sensing accuracy. Simulations show that CellSense achieves a 74 percent detection probability with a 1.43 m localization error in indoor warehouse environment, which improves to 94 percent detection and a sub-meter error of 0.33 m in the outdoor environment of Oval area at the NCSU Centennial campus. Hardware experiments in a highly cluttered indoor laboratory confirm a 1.28 m localization accuracy and 76 percent detection probability, proving its efficacy for practical ISAC deployments.

Negatively charged boron vacancy ($V_B^-$) centers in hexagonal boron nitride ($h$-BN) have attracted wide-range interests owing to their van der Waals lattice and their potentials for $in$-$situ$ quantum sensing. Here we propose and experimentally demonstrate an all-optical strategy for wide-field magnetometry based on $V_B^-$ centers. This strategy exploits the magnetically sensitive ground-state level anti-crossing (GSLAC) of $V_B^-$ centers, which induces a strong electron spin transition between $m_S = 0$ and $m_S = -1$ states, enabling microwave-free magnetic field measurement. By monitoring the shift of GSLAC feature, the external magnetic field can be precisely determined. Using this technique, we demonstrate all-optical wide-field imaging of near-field DC magnetic field distribution from current-carrying circuits over an area of around 42 $\times$ 21 $μ$m$^2$. An estimated photon shot-noise-limited sensitivity of 67.1 $μ$T/$\sqrt{\text{Hz}}$ is achieved for a single pixel, which is an approximately threefold improvement over the ODMR method, along with a spatial resolution of about 1 $μ$m per pixel. Our approach expands the applicability of $V_B^-$ centers in quantum sensing, paving the way for robust and convenient magnetometry under extreme conditions.

Multi-party chat often contains interleaved dialogues because multiple participants can discuss different topics at the same time. Dialogue disentanglement addresses this problem by separating an entangled utterance sequence into coherent dialogues. While large language models (LLMs) are promising for this task, they still struggle with dialogue disentanglement and achieve low accuracy. This paper proposes an automatic prompt optimization for LLM based dialogue disentanglement. We decompose the prompt into three components: task instruction, utterance representation, and output instruction, and optimize them using GEPA, an optimization method for compound AI systems. Experiments on benchmark datasets show that the optimized prompts improve dialogue disentanglement accuracy over the original prompts and can surpass hand crafted prompts.

Control Barrier Functions (CBFs) have been proposed to ensure safety of autonomous systems. This paper considers control policies that switch between CBF constraints. Under this approach, we represent a complex non-convex safe region as a union of sets that are computationally tractable to verify. We denote this framework as union-CBFs and make the following contributions. First, considering switching CBF-QP controllers, we propose a sufficient condition that ensures (i) the system undergoes a finite number of switches in any finite time interval and ensures (ii) the forward invariance of the closed-loop system in between switches. Second, we consider two types of switching strategies and propose union-CBFs conditions for each strategy to satisfy (i) and (ii). Third, we formulate Sum-of-Squares (SOS) algorithms to verify the conditions. The experiments show that our union-CBFs framework results in a larger safe region compared to high-degree polynomial CBFs. We also show the efficiency of the verification algorithms using a polynomial system model.

For two subspaces $U,V\subseteq\RR^n$, the circumcentered--reflection method (CRM) of Behling, Bello-Cruz, and Santos~\cite{BBS2018} computes the projection onto $U\cap V$ using only the reflections across $U$ and $V$, with known linear-convergence rate $c_F$, the cosine of the Friedrichs angle. We prove that, when CRM is initialized in $V$, it contracts at the strictly smaller rate $ρ_V=(\sin^2θ_p-\sin^2θ_F)/(\sin^2θ_p+\sin^2θ_F)$, where $θ_F\in(0,π/2]$ is the Friedrichs angle and $θ_p\in[θ_F,π/2]$ the largest principal angle between $U$ and $V$. The bound is sharp, attained on an explicit ray in $V$, and optimal among parameter-free single-step iterations. The constant itself is not new: Bauschke, Bello-Cruz, Nghia, Phan, and Wang~\cite{BBNPW2016} identified it as the optimal rate of the relaxed alternating-projection family and of their adaptive linesearch map $B_T$. Our contribution is that the parameter-free geometric circumcenter attains it as well, via Kantorovich's inequality applied to a single self-adjoint operator on $V$. Restricted to $V$, CRM coincides pointwise with the linesearch maps $A_T$ and $B_T$ from the Gubin--Polyak--Raik framework~\cite{GPR1967}. We further prove $ρ_V<c_F^2$ whenever $θ_F<π/2$, with one-step convergence exactly when $θ_F=θ_p$. Over-reflecting either or both of $R_U$, $R_V$ inside the circumcenter does not help. Going faster than $ρ_V$ universally requires memory: Chebyshev semi-iteration applied to $P_VP_U$ attains a strictly smaller rate, beating $ρ_V$ by a factor at most $2$, attained in the limit $θ_F\toθ_p$.

The classical Rogers--Shephard inequalities were extended to the Firey $L_p$-summation by Bianchini and Colesanti in the plane and by Zvavitch and the second and fourth authors for locally anti-blocking convex bodies in $\mathbb{R}^n$, leaving open the equality cases. We characterize the equality cases of these inequalities: in both cases, for $p>1$, equality holds if and only if the convex body is a simplex with one vertex at the origin.

Yttrium Iron Garnet YIG (Y3Fe5O12), is a commonly used material for magnonic devices due to its crystal and chemical structure, which makes the material highly ferromagnetic and enables long-range magnon propagation. Magnonic devices were fabricated by depositing a 390 nm thick thin film of YIG, using low vacuum RF sputtering, on Si substrates with a 240 nm buffer layer of SiO2. Two sets of devices were used to study the effect of the Si/SiO2 interface on the YIG. The first set features patterned hole pairs on the SiO2, which was created using fluorine etching. Patterned samples were used as seed nucleation points to study the crystallization behavior. The second set was a non-patterned Si/SiO2 with YIG deposited uniformly on the top. Post-deposition recrystallization of the YIG film was accomplished in a horizontal furnace under O2 atmosphere, between 750 degrees C and 850 degrees C. By patterning devices with a SiO2 buffer layer, depositing YIG via RF sputtering, and subsequently crystallizing the films in a furnace, we establish a fabrication route toward devices that can be suspended. Although further optimization of stoichiometry is required, achieving precise compositional control would enable the realization of fully suspended and released YIG devices that can be transferred onto alternative substrates.

We establish new polynomial-weighted recursions for Andrews' smallest parts function. Our results use the generating series for the spt function, a harmonic Maass form of weight 3/2, paired with the Dedekind eta function. Unlike previous work, we use the Rankin-Cohen bracket to obtain modular forms of weight larger than 2. This introduces a nontrivial quasimodular component, which we determine for the relevant weights. We apply the holomorphic projection operator and the vanishing of cusp form spaces of small enough weight to obtain our results.

This paper presents a finite modal semantics where truth is closed under admissible continuation, then refined by discounted value, and finally certified by residual tests. The admissibility kernel is the classical greatest fixed point of a one-step predecessor expressing that some choice cell has all compatible successors inside a set. Certified choices are exactly local witnesses; the discounted value transformer is defined only over those witnesses; value-refined modal bisimulation is the coarsest local equivalence preserving formulas, kernel, certified choices, Bellman values, greedy sets, residual certificates, and public release certificates. A canonical pseudometric refines this equivalence: it is the unique fixed point of a Hausdorff-lifted choice-matching transformer over certified choices; its zero set is the value-refined bisimulation, and the optimal discounted value is one-Lipschitz with respect to it. Any approximate quotient incurs only a distance-bounded value error. Branching choice-cell and locus presentations place choice inside the model; the transition presentation is a conservative retraction. The same engine is applied to a public share-alike release fragment: attribution as label preservation, same-license propagation as derivative closure, no downstream restriction as admissibility, and the BY-SA witness as a residual-stable certificate. Finite examples show that altering the order of truth, admissibility, value, quotienting, public derivation, and certification changes the semantics.

We extend the classical ideas of the Partial Information Decomposition (PID) to the quantum domain and quantify unique, redundant, and synergistic quantum information. We show that unique information plays the central role in quantum error correction codes: any erasure-correctable subset of encoding qubits must contain zero unique information. Synergistic information between two disjoint subsets of encoding qubits appears when a logical operation is supported on the whole set but not on the subsets separately. In a different application of our PID, we show that redundant quantum information is the crucial feature of the decoherence mechanism proposed by Zurek \textit{et al.} to explain how the classical world emerges out of the quantum world.

Selecting the active space for multireference electronic-structure calculations is a long-standing bottleneck that often requires expert chemical intuition and costly trial-and-error. We introduce RLEASE (Reinforcement Learning Efficient Active Space Engine), a low-cost method for automatic, geometry-dependent active-space selection. A neural network predicts per-orbital diagnostic scores ($\hat{s}_{1}$) from inexpensive Hartree-Fock orbital descriptors, and a learned threshold partitions orbitals into active and inactive sets. The threshold policy is optimized with proximal policy optimization, using the discrepancy between sc-NEVPT2 energies computed with the selected active space and DMRG reference energies as the reward. After training, the same RLEASE-selected active spaces can be used with multireference perturbation theory or composite coupled-cluster energy estimators. Despite being trained on a small set of molecules and geometries, RLEASE transfers to chemically diverse test systems, producing compact active spaces and competitive potential-energy surfaces relative to established entropy-based selectors. Because deployment requires only inexpensive orbital descriptors and neural-network inference, RLEASE enables high-throughput multireference workflows without molecule-specific retraining or target-system pilot DMRG calculations.

Graph signal processing has opened new avenues to the canonical denoising problem in interesting settings. Specifically, here we propose a Wiener-filter solution for graph signals on directed graphs. Under various stationarity assumptions combining uncorrelated and correlated noise conditions, we show optimal solutions, including a successful proof-of-concept for temperature graph.

We prove a singular-endpoint reduction for the three-dimensional incompressible Navier--Stokes large-data regularity problem in the smooth finite-energy class. The result is a reduction theorem: any hypothetical first singularity of a general three-dimensional solution generates, after scale normalization, threshold selection, and endpoint extraction, a terminal singular endpoint in the axisymmetric-with-swirl class. Thus a proof of the companion axisymmetric-with-swirl endpoint theorem closes the corresponding full three-dimensional finite-energy regularity statement. The proof is organized around the scalar vorticity-amplitude identity. Let \(ω=\nabla\times u\), \(A=|ω|\), \(ξ=ω/|ω|\), and \(S=\sym\nabla u\). The regularized identity \[ (\partial_t+u\cdot\nabla-νΔ)A =A\bigl(ξ\cdot Sξ-ν|\nablaξ|^2\bigr) \] splits the endpoint into a zero-production branch and a positive-production branch. The zero-production branch is closed by a Nash--Liouville argument after the amplitude-tail alternatives are removed. In the positive-production branch, the vortex-stretching density is first rebased onto comparable active donors. The central point of the present formulation is that this rebase is signed and stable: positive-signed donor mass is selected by a Carleson procedure, rebased into an exact orthogonal solenoidal hull, and then either produces a nonzero finite-band hull energy or activates a routed output.

Vehicle-to-vehicle (V2V) communication is expected to improve road safety and reduce congestion. However, prior work shows that V2V information sharing under partial adoption may increase congestion and decrease safety. We study whether increasing V2V adoption itself affects road safety. We propose a corrected version of an existing model and analyze its behavior under varying adoption levels. We show that, in some cases, increased V2V adoption can increase accident probability. Moreover, under an optimal signaling policy, the system can ensure that accident probability is non-increasing in the adoption level.