A radio antenna is primarily designed to convert electromagnetic waves into electrical current and vice versa. However, a part of the incident wavefield is scattered due to structural effects andreflection at the antenna's electrical port. Because the reflected power depends on the load impedance, an antenna can also be referred to as a loaded scatterer. Its interaction with electromagnetic waves is characterized by absorption and scattering cross-sections (ACS and SCS). When immersed in a diffuse field, such as the one generated within a reverberation chamber (RC), the impact of the loaded antenna is determined by averaging these properties over incident angles. Of particular interest is the averaged ACS from which one can derive the antenna contribution to the RC quality factor (Q-factor). Current formulations rely on different power budget analyses which do not account for wave interferences between the ingoing and outgoing fields. Moreover, existing formulations consistently neglect the structural component. In this paper, we introduce a rigorous formulation of the antenna contribution to the RC Q-factor which takes into account the aforementioned effects. The antenna is modeled using the scattering-matrix theory, which linearly links the ingoing and outgoing waves in terms of spherical harmonics expansion. The derived theory is validated using several numerical simulations based on a Method-of-Moment code. The model's ability to retrieve antenna properties from multiple Q-factor estimations in an RC is then demonstrated. All results are compared with existing formulations.

The interior of mature neutron stars is expected to contain superfluid neutrons and superconducting protons. The influence of temperature and currents on superfluid properties is studied within the self-consistent time-dependent nuclear energy-density functional theory. We find that this theory predicts the existence of a regime in which nucleons are superfluid (the order parameter remains finite) even though the energy spectrum of quasiparticle excitations exhibits no gap. We show that the disappearance of the gap leads to a specific heat that is not exponentially suppressed at low temperatures as in the BCS regime but can be comparable to that in the normal phase. Introducing some dimensionless effective superfluid velocity, we show that the behavior of the specific heat is essentially universal and we derive general approximate analytical formulas for applications to neutron-star cooling simulations.

The current interpretation of the observed late time cooling of transiently accreting neutron stars in low-mass X-ray binaries during quiescence requires the suppression of neutron superfluidity in their crust at variance with recent ab initio many-body calculations of dense matter. Focusing on the two emblematic sources KS~1731$-$260 and MXB~1659$-$29, we show that their thermal evolution can be naturally explained by considering the existence of a neutron superflow driven by the pinning of quantized vortices. Under such circumstances, we find that the neutron superfluid can be in a gapless state in which the specific heat is dramatically increased compared to that in the classical BCS state assumed so far, thus delaying the thermal relaxation of the crust. We have performed neutron-star cooling simulations taking into account gapless superfluidity and we have obtained excellent fits to the data thus reconciling astrophysical observations with microscopic theories. The imprint of gapless superfluidity on other observable phenomena is briefly discussed.

We explore the connection of positivity of the imaginary part of forward elastic amplitudes for perturbative scattering with consistency of the entanglement generated by the S-matrix, for states with arbitrary internal quantum numbers such as flavor. We also analyze "disentanglers," certain highly entangled initial states for which the action of the S-matrix is to decrease subsystem entanglement. As a by-product, we develop a framework based on wave packets to regularize the spacetime divergences that appear in the plane-wave derivation of the $2\to2$ entanglement expression.

Given a lattice path $ν$, the alt $ν$-Tamari lattice is a partial order recently introduced by Ceballos and Chenevière, which generalizes the $ν$-Tamari lattice and the $ν$-Dyck lattice. All these posets are defined on the set of lattice paths that lie weakly above $ν$, and posses a rich combinatorial structure. In this paper, we study the geometric structure of these posets. We show that their Hasse diagram is the edge graph of a polytopal complex induced by a tropical hyperplane arrangement, which we call the alt $ν$-associahedron. This generalizes the realization of $ν$-associahedra by Ceballos, Padrol and Sarmiento. Our approach leads to an elegant construction, in terms of areas below lattice paths, which we call the canonical realization. Surprisingly, in the case of the classical associahedron, our canonical realization magically recovers Loday's ubiquitous realization, via a simple affine transformation.

The Witten effect implies the dynamics of axion and magnetic monopole. The Cho-Maison monopole is a realistic electroweak monopole arisen in the Weinberg-Salam theory. This monopole of TeV scale mass motivates the dedicated search for electroweak monopole at colliders. In this work we investigate the implication of KSVZ axion for the electroweak magnetic monopole. We use the spherically symmetric ansatz for the electroweak dyon and introduce the spherically symmetric function for the axion field. The effective Lagrangian is then shown in terms of the electroweak monopole part, the axion kinetic energy as well as the axion interaction term. We derive the consequent equations of motion in the presence of the axion-photon coupling and show the numerical results of the topological solutions. We then calculate the changed characteristics of the electroweak monopole such as the monopole mass and the electromagnetic charges, as well as the axion potential energy.

We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures. Through the introduction of the $α$-$z$-Rényi relative entropies, which comprise known relevant quantities such as the Rényi relative entropy and the sandwiched Rényi relative entropy, we establish the Holevo-Rényi inequality. This result leads to a quantum bound for the $α$-mutual information, suggesting new insights into communication channel performance and the fundamental limits for reliability functions in memoryless multi-letter communication channels.

We prove that the set of matchings with a fixed number of unmatched vertices is Schur-positive with respect to the set of short chords. Two proofs are presented. The first proof applies a new combinatorial criterion for Schur-positivity, while the second is bijective. The coefficients in the Schur expansion are derived, and interpreted in terms of Bessel polynomials. We present a Knuth-like equivalence relation on matchings, and show that every equivalence class corresponds to an irreducible representation. We proceed to find various refined Schur-positive sets, including the set of matchings with a prescribed crossing number and the set of matchings with a given number of pairs of intersecting chords. Finally, we characterize all the matchings $m$ such that the set of matchings avoiding $m$ is Schur-positive.

Noise-shaping quantization techniques are widely used for converting bandlimited signals from the analog to the digital domain. They work by ``shaping" the quantization noise so that it falls close to the reconstruction operator's null space. We investigate the compatibility of two such schemes, specifically $ΣΔ$ quantization and distributed noise-shaping quantization, with random samples of bandlimited functions. Suppose $R>1$ is a real number and assume that $\{x_i\}_{i=1}^m$ is a sequence of i.i.d random variables uniformly distributed on $[-\tilde{R},\tilde{R}]$, where $\tilde{R}>R$ is appropriately chosen. We show that by using a noise-shaping quantizer to quantize the (randomly sign flipped) values of a real-valued $π$-bandlimited function $f$ at $\{x_i\}_{i=1}^m$, a function $f^{\sharp}$ can be reconstructed from these quantized values such that $\|f-f^{\sharp}\|_{L^2[-R, R]}$ decays with high probability as $m$ and $\tilde{R}$ increase. This decay holds uniformly over all bandlimited $f$. We emphasize that the sample points $\{x_i\}_{i=1}^m$ are completely random, that is, they have no predefined structure, which makes our findings the first of their kind.

The paper examines the effects of stringent land use regulations, measured using the Wharton Residential Land Use Regulatory Index (WRLURI), on employment growth during the period 2010-2020 in the Retail, Professional, and Information sectors across 878 local jurisdictions in the United States. All the local jurisdictions exist in both (2006 and 2018) waves of the WRLURI surveys and hence constitute a unique panel data. We apply a mediation analytical framework to decompose the direct and indirect effects of land use regulation stringency on sectoral employment growth and specialization. Our analysis suggests a fully mediated pattern in the relationship between excessive land use regulations and employment growth, with housing cost burden as the mediator. Specifically, a one standard deviation increase in the WRLURI index is associated with an approximate increase of 0.8 percentage point in the proportion of cost burdened renters. Relatedly, higher prevalence of cost-burdened renters has moderate adverse effects on employment growth in two sectors. A one percentage point increase in the proportion of cost burdened renters is associated with 0.04 and 0.017 percentage point decreases in the Professional and Information sectors, respectively.

Skyrmions are topological solitons in two-dimensional systems and have been observed in various physical systems. Generating and controlling skyrmions in artificial resonator arrays lead to novel acoustic, photonic, and electric devices, but it is a challenge to implement a vector variable with the chiral exchange interaction. Here, we propose to use quadrature variables, where their parametric coupling enables skyrmions to be stabilized. A finite-element simulation indicates that a acoustic skyrmion would exist in a realistic structure consisting of a piezoelectric membrane array.

A set $S\subseteq V$ of vertices of a graph $G$ is a $c$-clustered set if it induces a subgraph with components of order at most $c$ each, and $α_c(G)$ denotes the size of a largest $c$-clustered set. For any graph $G$ on $n$ vertices and treewidth $k$, we show that $α_c(G) \geq \frac{c}{c+k+1}n$, which improves a result of Dvoř{á}k and Wood [Innov.\ Graph Theory, 2025], while we construct $n$-vertex graphs $G$ of treewidth $k$ with $α_c(G)\leq \frac{c}{c+k}n$. In the case $c\leq 2$ or $k=1$ we prove the better lower bound $α_c(G) \geq \frac{c}{c+k}n$, which settles a conjecture of Chappell and Pelsmajer [Electron.\ J.\ Comb., 2013] and is best-possible. Finally, in the case $c=3$ and $k=2$, we show $α_c(G) \geq \frac{5}{9}n$ which is best-possible.

This paper assumes a robust, in general not dominated, probabilistic framework and provides necessary and sufficient conditions for a bipolar representation of subsets of the set of all quasi-sure equivalence classes of non-negative random variables, without any further conditions on the underlying measure space. This generalizes and unifies existing bipolar theorems proved under stronger assumptions on the robust framework. Applications are in areas of robust financial modeling.

We seek to improve the restriction bounds of Neumann data of Laplace eigenfunctions $u_h$ by studying the $L^2$ restriction bounds of Neumann data and their $L^2$ concentration as measured by defect measures. Let $γ$ be a closed smooth curve with unit exterior normal $ν$. We can show that $\| h \partial_νu_{h} \|_{L^2(Γ)}=o(1)$ if $\{u_h\}$ is tangentially concentrated with respect to $γ$. As a key ingredient of the proof, we give a detailed analysis of the $L^2$ norms over $γ$ of the Neumann data $h\partial_νu_h$ when mircolocalized away the cotangential direction.

We find that Alexander polynomial of a ribbon knot in $ \mathbb{Z}HS^3 $ is determined by the intrinsic singularity information of its ribbon, and give a formula to calculate Alexander polynomial of a ribbon knot by that. We define half Alexander polynomial $ A_R (t) $, an invariant of oriented ribbons, and in fact the Alexander polynomial of the ribbon knot is $ A_R (t) A_R (t^{-1}) $. We give two useful simplified formulas for half Alexander polynomial. We characterize completely the polynomials arising as half Alexander polynomials of ribbons. The above study unexpectedly leads us to discover new formulas for Alexander polynomial of general knots and virtual knots in terms of Gauss diagrams.

We study a special class of (real or complex) robust Hadamard matrices, distinguished by the property that their projection onto a $2$-dimensional subspace forms a Hadamard matrix. It is shown that such a matrix of order $n$ exists, if there exists a skew Hadamard matrix of this size. This is the case for any even dimension $n\le 20$, and for these dimensions we demonstrate that a bistochastic matrix $B$ located at any ray of the Birkhoff polytope, (which joins the center of this body with any permutation matrix), is unistochastic. An explicit form of the corresponding unitary matrix $U$, such that $B_{ij}=|U_{ij}|^2$, is determined by a robust Hadamard matrix. These unitary matrices allow us to construct a family of orthogonal bases in the composed Hilbert space of order $n \times n$. Each basis consists of vectors with the same degree of entanglement and the constructed family interpolates between the product basis and the maximally entangled basis.

We argue that the possible new heavy boson resonance of 750 GeV is an ideal candidate as a twin particle of the 125 GeV scalar boson, both emerging from the large mixing of the scalar toponium and scalar gluonium. The twin pseudoscalar particles are expected to have smaller masses. The discovery of the 750 GeV resonance is possible only with a much more data than for the 125 GeV resonance since only the gluonium component is detectable above the toponium threshold. The similar type of the QCD resonances is expected in the bottomonium-gluonium system. If the LHC will discover all these heavy quarkonium-gluonium resonances, the absence of the Higgs scalar should not be considered an obstacle because the nonsingular theory with the UV cutoff fixed by the weak boson masses is superior to the Standard Model. Namely, it solves the basic problems for the SM such as: (1) the existence of light neutrinos, (2) dark matter particles to be the heavy Majorana neutrinos and (3) broken lepton and baryon numbers.

The object of this work is the systematical study of a certain type of generalized Cartan matrices associated with the Dynkin diagrams that characterize Cartan-Lie and affine Kac-Moody algebras. These generalized matrices are associated to graphs which arise in the study and classification of Calabi-Yau spaces through Toric Geometry. We focus in the study of what should be considered the generalization of the affine exceptional series $E_{6,7,8}^{(1)}$ Kac-Moody matrices. It has been conjectured that these generalized simply laced graphs and associated link matrices may characterize generalizations of Cartan-Lie and affine Kac-Moody algebras.

Cylindric Schur functions are a family of symmetric functions that generalize skew Schur functions. We give a short proof that skew cylindric Schur functions expand positively in terms of non-skew cylindric Schur functions. In particular, we show that the expansion coefficients are fusion coefficients.

Flexible coupler antenna systems have recently received significant research interest due to their capability to intelligently reconfigure wireless channels by controlling coupler positions and/or rotations and dynamically exploiting mutual coupling. In this paper, we investigate a new type of flexible coupler antenna, termed rotatable coupler antenna (RCA), for enabling spectrum and energy efficient wireless communication cost-effectively. Specifically, an RCA consists of one fixed active antenna and multiple low-cost passive couplers, each of which can independently rotate in three-dimensional (3D) space, so as to collaboratively achieve mechanical beamforming without requiring additional radio-frequency (RF) chains for the couplers. We study an RCA-enhanced point-to-point communication system, where one RCA is deployed at the transmitter to serve a single user equipped with a fixed antenna. Based on multi-port circuit theory, we establish the channel model and characterize the mutual coupling coefficients as a function of coupler rotations. We formulate a new problem to maximize the received signal-to-noise ratio (SNR) at the user by optimizing the 3D rotations of all couplers, subject to practical coupler rotation constraints. To tackle this nonconvex problem, we develop a spherical-cap conditional-gradient-based algorithm with cross-entropy-method initialization. Simulation results demonstrate that the proposed RCA system can significantly improve communication performance in comparison with benchmark schemes, while requiring substantially fewer active antennas and RF chains.

Modern Portfolio Theory (MPT) prescribes how to maximise the return of an asset portfolio for a given level of risk. The optimal trade-off between return and variance defines the efficient frontier. Whether actual cryptoasset portfolios approximate this prescription and whether proximity to the frontier translates into realised performance remain difficult to test at large scale in traditional markets due to their opaque nature and the inaccessibility of data. As we show, public blockchains make these questions measurable: every token transfer is recorded, thus enabling complete portfolio reconstruction for every account at any point in time. We leverage this transparency to reconstruct cryptoasset portfolios for over 116M Ethereum accounts across the full chain history (2015-2025), measure their distance to the constrained efficient frontier, and quantify how deviations translate into realised performance. Here we show that market entry timing, not allocation choice, is the dominant predictor of realised cryptoasset returns. On-chain wealth is highly concentrated and portfolios are pervasively under-diversified, with single-asset holdings accounting for 83.35% of accounts. Two-asset portfolios sit closest to the efficient frontier defined by their held assets, a proximity that reflects the narrowness of their opportunity set rather than deliberate optimisation. Passive market-capitalisation weighting outperforms every MPT optimisation strategy in median realised return, and entry month alone explains 70-79% of the variance in returns, far exceeding the contribution of allocation choice. Mean-variance optimisation therefore appears neither descriptive of observed behaviour nor prescriptively useful in the cryptoasset domain, even if MPT retains its value as a normative benchmark.

We prove that the short-time Fourier transform with Gaussian window performs $L^2$-local stable phase retrieval at the constant function. The proof involved significant interplay between mathematicians and LLMs. An autoformalization in Lean 4 of an extension of our result to $L^2$-local stable phase retrieval for all Hermite windows and all elements in the finite span of the canonical basis vectors is also presented.

Broadcast domination assigns a nonnegative integer power to every vertex of a graph so that every vertex is within the assigned power of some broadcasting vertex, and the objective is to minimize the sum of the powers. Heggernes and Lokshtanov proved that the problem is polynomial-time solvable on arbitrary connected unweighted graphs by showing that some optimal efficient broadcast has a domination graph that is a path or a cycle, and by reducing the general case to an $O(n^6)$-time algorithm. This paper gives an efficient algorithm of the path-case. Instead of building one auxiliary acyclic graph for every possible left endpoint vertex, we build a single directed acyclic graph whose states are oriented broadcast balls together with their two possible residual sides. The resulting path-case algorithm runs in $O(n^3)$ time and $O(n^3)$ space on an $n$-vertex graph. Combining this routine with the same peel-one-ball reduction of Heggernes and Lokshtanov yields an exact $O(n^5)$-time algorithm for optimal broadcast domination on arbitrary connected unweighted graphs. This resolves the quintic-time conjecture for general graphs attributed to Heggernes and Sæther and recorded in subsequent surveys of broadcast domination.

In the standard geometric optics approximation, null rays propagating in a spherically symmetric black hole background follow planar geodesics. This picture changes, however, when the helicity-dependent effects of light are incorporated into the dynamics. Specifically, the interaction between the helicity of light and the spacetime curvature induces a significant angular deflection out of the geodesic plane. In this paper, we employ the spinoptics formalism to study light deflection due to the helicity-curvature interaction in two spherically symmetric geometries: the Rezzolla--Zhidenko (RZ) parametrized metric, and a hairy regular black hole solution obtained via gravitational decoupling. Our results reveal clear imprints of both the RZ parametrization coefficients and the hairy black hole parameter on the deflection angle. Furthermore, we assess the viability of using the RZ parametrization to mimic the regular hairy black hole, discussing the validity and limitations of such an approximation.

We characterize the fixed sets of automorphisms of an arbitrary countable, arithmetically saturated structure.

Instruments targeting 21~cm emission at high redshifts need a spectral dynamic range of better than ten thousand to distinguish the 21~cm background against bright foregrounds. Systematics arising from the antenna pattern are a leading limitation for current instruments and must be addressed in future experiments. Antenna pattern measurements could help reach this precision. Pattern measurements are complicated by the large scale of the instruments and interaction with the local environment. In-situ beam mapping methods have been investigated but the required accuracy remains ill defined. One consideration is whether the calibration source is in the far field. Near field measurements require more elaborate measurement and such an expense must be well motivated. The far field distance is set by the effective size of the antenna. Reflections and interactions with surroundings extend the effective size of the antenna to scales well beyond the physical aperture. Here we give a new, instrument-agnostic method for calculating beam calibration requirements. Using 21cm models and instrument noise we prescribe bounds on the geometric reflection size scales. These scales must be shown via measurement to be below noise. This prescription depends weakly on instrument-specific noise and for interferometers, on the characteristic baseline length, but is otherwise independent of any detailed simulation of antenna or analysis pipeline. Example calculations for HERA-like and EDGES-like instruments find cosmological structures map to reflection scales of 100~m. This far field distance puts ground-based transmitters close to the horizon and drone sources well above typical or legal operating heights. A near-field measurement approach is necessary. Phase-locked systems have been demonstrated with promising results but more work is necessary to validate an antenna pattern at the necessary dynamic range.

Manipulating materials properties with light drives advances in materials science and photonics. Hyperbolic metamaterials are promising candidates as next-generation quantum optical media. They support Bloch plasmon polaritons, which are characterized by potentially infinite wave-vectors and long lifetimes, but cannot be excited through direct light illumination due to momentum mismatch. Here, we experimentally show that a transient grating, formed via interference of fully coherent seeded free-electron laser pulses in a thin insulator film, enables the excitation of Bloch plasmon polaritons in an underlying hyperbolic metamaterial. Finite element simulations confirm the role of the transient grating in facilitating phase-matching and mode excitation. Our findings demonstrate a route to spatiotemporally excite Bloch plasmon polaritons modes, offering an alternative to permanently nanostructured gratings and potentially enabling ultrafast control of optical modes excitation.

Despite a global user base adopting large language models (LLMs) for daily writing tasks, model suggestions tend to align with Western values. Research has shown users commonly accept a high fraction of these AI suggestions, homogenizing writing styles and rendering outputs more ``Western'' than intended. While this suggests a need to reduce AI reliance, it remains unknown what kind of interventions could achieve this. Can framing the AI with specific values, and comparing it to one's own, make users less susceptible to overreliance and support more unique writing? We tested this hypothesis in a between-subjects online experiment with Indian and American participants (n=149) in which they were asked to perform AI-supported writing tasks, either 1) without an intervention, 2) after seeing an overview of the AI's framed values, or 3) after seeing an overview of the AI's framed values compared to their own. Our results show that seeing the AI's framed values reduces AI reliance, i.e., the proportion of the final essay generated by the AI, by an average of 20\%. Additionally, when participants saw an overview of the AI's framed values (without comparison to their own values), the final essays contain more unique text than without intervention. Our findings emphasize the importance of educating users about potential value biases in AI, showing that raising awareness with a simple overview of values encourages users to personalize their writing.

K-12 teachers employ Engineering Design Challenges to help students learn about the Engineering Design Process hands-on. They use techniques like hard scaffolding questions to guide the students as they think through the different stages of the engineering design process. While useful, the creation of these questions adds to the teacher's preparation time for their classes. Concept Catalyst uses Large Language Models to assist teachers with the rapid creation of scaffold questions for engineering design challenges. Unlike open-ended chat, Concept Catalyst uses LLMs to summarize and decompose an engineering design challenge into the concepts that students will engage with, allow the teacher to visually manipulate and link related concepts, and to propose scaffolding questions for the teacher to modify or accept.

This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data to compute rigorous upper and lower bounds on the target observable. Statistical uncertainties, including correlations, are incorporated through compatibility regions using the covariance matrix. The bounds are equivalent, via Lagrange duality, to certified bounds on the target smearing kernel. For polynomial, rational, and piecewise rational kernels, the resulting dual problems can be reduced to finite-dimensional semidefinite programs using techniques familiar, e.g., in the numerical conformal bootstrap. The present formulation clarifies the relation to moment problems, Nevanlinna--Pick interpolation, and linear kernel-reconstruction methods. Numerical examples demonstrate the method.