This paper considers systems in which two or more ligands bind independently to a common scaffold. Such systems arise in a range of applications, including immunotherapy and synthetic biology. We show that each stoichiometric compatibility class contains a unique steady state, and that this steady state is asymptotically stable. The main result gives a rigorous proof that the steady-state concentration of the fully bound complex, viewed as a function of the total scaffold concentration, has a unique maximum. This biphasic dose response is a characteristic feature of scaffolding systems and, in the special case of two ligands, plays an important role in the design and analysis of bispecific antibody drugs.

Spatially resolved observations of the Sun and the astronomical sample size of stellar bodies are the respective key strengths of solar and stellar observations. However, the large difference in object brightness between the Sun and other stars has led to distinctly different instrumentation and methodologies between the two fields. We produce and analyze synthetic full-disk spectra derived from 19 small area field-of-view optical observations of solar flares acquired by the Swedish 1-m Solar Telescope (SST) between 2011 and 2024. These are used to investigate what can and cannot be inferred about physical processes on the Sun from Sun-as-a-star observations. The recently released Numerical Empirical Sun-as-a-Star Integrator (NESSI) code provides synthetic full-disk integrated spectral line emission based on smaller field-of-view input, accounting for center-to-limb variations and differential rotation. We use this code to generate pseudo-Sun-as-a-star spectra from the SST observations. ...

Hybrid Analog and Digital (HAD) architectures significantly reduce hardware overhead but introduce severe dimensionality compression, which strips the Spatial Covariance Matrix (SCM) of the degrees of freedom required for high-resolution Direction-of-Arrival (DoA) estimation. This challenge is further compounded by passive Butler-matrix implementations of Discrete Fourier Transform (DFT) analog beamforming, which avoid active phase shifters and amplifiers. In this paper, we propose a Generalized Least Squares (GLS) framework that exploits the Cauchy-like displacement structure that arises after DFT beamforming. By leveraging this structure, we develop a highly efficient numerical technique to recover the SCM for uniform linear arrays with a complexity of $\mathcal{O}(N_{\text{RF}}^2 N_x)$, where $N_x$ is the number of antennas and $N_{\text{RF}}$ the number of RF-chains. Simulations demonstrate that our estimator approaches the Cramér-Rao Bound (CRB) while outperforming state-of-the-art methods.

The bulk photovoltaic effect (BPVE), a manifestation of broken centrosymmetry, has attracted interest as a probe of the symmetry and quantum geometry of materials, and for use in photovoltaic and optoelectronic devices. However, so far the effect has not been captured directly in space and time. Here, we use contactless pump-probe microscopy to visualize the spatiotemporal evolution of photoexcited carriers in single-crystal, mono-domain $BiFeO_{3}$, a prototypical ferroelectric material. We observe asymmetric carrier transport along the polar axis, which confirms the intrinsic bulk- and symmetry-driven nature of the BPVE. Remarkably, this asymmetric transport persists for several nanoseconds after photoexcitation, which cannot be explained by conventional short-lived shift or phonon ballistic current BPVE mechanisms. Our Monte Carlo simulations show that asymmetric momentum scattering by defects, such as oxygen vacancies, leads to long-lived asymmetric carrier transport, as observed experimentally. Beyond fundamental insights, this paves the way towards controlling symmetry- and defect-driven photoresponses.

[Working Paper] Survey research has a long-standing history of being a human-powered field, but one that embraces various technologies for the collection, processing, and analysis of various behavioral, political, and social outcomes of interest, among others. At the same time, Large Language Models (LLMs) bring new technological challenges and prerequisites in order to fully harness their potential. In this paper, we report work-in-progress on a systematic literature review based on keyword searches from multiple large-scale databases as well as citation networks that assesses how LLMs are currently being applied within the survey research process. We synthesize and organize our findings according to the survey research process to include examples of LLM usage across three broad phases: pre-data collection, data collection, and post-data collection. We discuss selected examples of potential use cases for LLMs as well as its pitfalls based on examples from existing literature. Considering survey research has rich experience and history regarding data quality, we discuss some opportunities and describe future outlooks for survey research to contribute to the continued development and refinement of LLMs.

Let $K$ be a number field, let $S$ be a finite set of primes of $K$ containing all archimedean primes, and let $G_{K,S}$ denote the Galois group of the maximal extension of $K$ unramified outside $S$. In this paper, we study the second partial Euler--Poincaré characteristic $χ_{2}(G_{K,S},M)$ for a finite $G_{K,S}$-module $M$, without imposing the condition that the order of $M$ is an $S$-unit. By adjoining a further finite set of primes of $K$, which can be chosen to be disjoint from any prescribed set of primes of density zero, we obtain an explicit formula for the corresponding second partial Euler--Poincaré characteristic. As an application, we investigate the presentation of the Galois group $G_{K,S}$. Furthermore, for any number field, we construct counterexamples to the dimension conjecture for Galois deformation rings.

We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov-Witten theory of the projective line and is dictated by $\mathbb{Z}_2$-equivariant topological recursion.

As data science emerges as a distinct academic discipline, introductory data science (IDS) courses play a key role in shaping students foundational understanding. Often taught by instructors without formal training in data science or pedagogy, these courses present a unique and globally relevant context for examining pedagogical content knowledge (PCK). Drawing on semi-structured interviews with 14 IDS instructors and their course syllabi, this study explores how IDS instructors describe and make sense of their teaching practices, which are analyzed through the lens of PCK. The findings highlight key components of PCK about IDS and offer insights into supporting instructor development. This work contributes to expanding the scope of PCK research into new interdisciplinary domains and ongoing global efforts to build capacity in data science education. It could serve as a starting point for developing a PCK framework specific to IDS.

The design of communication systems has traditionally prioritized the reliable and timely delivery of data. However, the scalability challenges faced by the evolution towards a data-driven hyper-connected society and economy demand new communication paradigms that carefully curate the content being transmitted. This paper proposes a joint semantic and task-oriented communication paradigm where connected devices transmit only the information necessary to convey the desired meaning that is relevant to the intended receivers, based on their context. We qualitatively and quantitatively analyze the potential benefits of the proposed semantic and task-oriented communication paradigm in the Vehicle-to-Everything (V2X) domain. The V2X domain offers a unique environment for the development and deployment of semantic and task-oriented V2X communications, as it is rich in contextual information and Connected and Autonomous Vehicles (CAVs) are native semantic devices. The qualitative analysis focuses on a cooperative perception use case and shows how semantic and task-oriented V2X communications can reduce the amount of information transmitted by each vehicle without compromising the situational awareness of its intended receivers. The quantitative analysis numerically demonstrates that semantic and task-oriented V2X communications can achieve a two-fold improvement in communication efficiency which can significantly benefit the scalability of future V2X networks.

Alzheimer's disease (AD) manifests as a continuous progression from normal cognition (NC) through mild cognitive impairment (MCI) to dementia. However, most deep learning approaches reduce this continuum to disjointed classification tasks, largely ignoring dynamic stage transitions. To decode this complex progression, we propose M$^3$AD, a unified framework that jointly addresses three-class diagnosis classification and diagnosis stage transition prediction using only T1-weighted sMRI. M$^3$AD leverages an interpretable multi-gate mixture of experts architecture, employing specialized routing mechanisms to dynamically capture both diagnosis-specific pathological patterns and shared structural features across the continuum. It further integrates clinical priors (age, sex, eTIV) via adaptive attention fusion to enhance generalization. M$^3$AD achieves 95.13% accuracy, compared to 90.44% reported by MCLNC under its original experimental setting, and 94.87% for transition prediction. Crucially, analyzing the multi-gate routing reveals distinct expert activation signatures distinguishing stable from progressive MCI, providing a mechanistic basis for individual-level progression risk stratification. Code is available at https://github.com/csyfjiang/M3AD.

The emergence of neutral collective modes is a hallmark of correlated quantum phases but is often challenging to probe experimentally. In two-dimensional flatband systems, charge responses have been intensively investigated yet neutral excitations remain largely unexplored. In particular, intervalley coherent state (IVC) features a neutral Goldstone mode due to spontaneously broken valley U(1) symmetry. While IVC state has been proposed as a unifying theme across graphene and semiconductor based systems, its defining feature, the neutral Goldstone mode, remains elusive in experiment. Here we investigate space and time resolved transport of neutral modes in twisted WSe2 moire superlattices through a novel ultrafast imaging technique. We uncover two new propagating collective modes with very different velocities, which emerge near the van Hove singularity (VHS) in both intermediate (3.5 to 4 degree) and large (around 5 degree) angle twisted WSe2. The fast-propagating mode has a large speed of about 3 km/s and is consistent with a Goldstone mode for an IVC state, while the slow-moving mode is likely a gapped amplitude mode. They can be understood as the spin-valley analogues of collective modes of a superfluid, whose propagation is imaged for the first time in a condensed matter system. Our study demonstrates a powerful new approach for probing charge-neutral modes in quantum materials and offers key insights into the interplay between charge and spin-valley physics in moire superlattices.

We investigate the problem of finding the minimum number of pieces necessary for dividing a three-dimensional sphere or a ball and reassembling it to form $n$ congruent copies of the original object, generalising a known result by Raphael Robinson.

The maximum entropy principle, as applied to quantum systems, is a fundamental prescript positing that for a quantum system for which we only have partial knowledge, the maximum entropy state consistent with the partial knowledge is a valuable choice as the system's state. An intriguing result is that in case the only prior knowledge is of a fixed energy, the maximum entropy state turns out to be the thermal state, a ubiquitous state in several arenas, especially in statistical mechanics. We extend the consequences of this principle from static quantum states to dynamic quantum processes. We establish that a quantum channel attains maximal output entropy under a fixed energy constraint if and only if it is an absolutely thermalizing channel, where the fixed output is the thermal state corresponding to that energy. Our results have potential implications for understanding the informational and thermodynamic utility of quantum channels under physical constraints. As an application, we examine the consequences for private randomness distillation from fixed energy constrained quantum processes.

In this paper we study the spectral analysis of Bochner-Kodaira Laplacians on an Abelian variety, complex projective space $\mathbb{P}^{n}$ and a Grassmannian with a holomorphic line bundle. By imitating the method of creation and annihilation operators in physics, we convert those eigensections (of the \textquotedblleft higher energy" level) into holomorphic sections (of the \textquotedblleft lowest energy" level). This enables us to endow these spectral bundles, which are defined over the dual Abelian variety, with natural holomorphic structure. Using this conversion expressed in a concrete way, all the higher eigensections are explicitly expressible using holomorphic sections formed by theta functions. Moreover, we give an explicit formula for the dimension of the space of higher-level eigensections on $\mathbb{P}^{n}$ through vanishing theorems and the Hirzebruch-Riemann-Roch theorem. These give a theoretical study related to some problems newly discussed by string theorists using numerical analysis. Some partial results on Grassmannians are proved and some directions for future research are indicated.

We investigate the global structure of the states becoming light at perturbative limits of 4d $\mathcal{N}=1$ string and M-theory compactifications, identifying the different duality frames that emerge asymptotically and how they fit together in moduli space. These limits are characterized by the presence of EFT strings - a special class of axionic BPS strings whose tension, derived from the IR Kähler potential, vanishes in Planck units at infinite field distance. An intriguing integer scaling relation, $m \sim \mathcal{T}^w$ with $w = \{1,2,3\}$ in Planck units, connects the tension $\mathcal{T}$ of these strings to the mass scale $m$ of the leading tower of states along the string flow. We show that this relation also holds for the subleading towers below the species scale that generate the tower convex hull, implying that their associated $\vecζ= -\vec{\nabla} \log m$ vectors lie in a lattice generated by those of the EFT strings. This reveals a striking UV/IR interplay and offers organizing principles for the parametric hierarchies among the relevant UV scales in a given perturbative limit and the web of dualities governing 4d string vacua.

This paper addresses the problem of distributed resilient state estimation and control for linear time-invariant systems in the presence of malicious false data injection sensor attacks and bounded noise. We consider a system operator (defender) capable of deploying cybersecurity measures to counteract the sensor compromises. Although such measures enhance resilience against adversarial attacks, they may incur substantial costs; hence, it is crucial to select countermeasures to balance resilience gains and cost efficiency strategically. We first demonstrate that the system's resilience against attacks is maximized through the appropriate implementation of security measures, implying that no attacker can execute undetectable sensor attacks. Building on this analysis, we propose an algorithm that identifies the optimal security measure. While determining this measure is NP-hard in general, we also derive sufficient conditions under which efficient computation is feasible. Furthermore, we develop a distributed resilient state estimation and control scheme informed by the optimal security measure and establish conditions that guarantee bounded estimation and control errors. Finally, we validate the efficacy of our approach via numerical simulations of a vehicle platooning scenario.

Andréka and Maddux classified the relation algebras with at most 3 atoms, and in particular they showed that all of them are representable. Hirsch and Cristiani showed that the network satisfaction problem (NSP) for each of these algebras is in P or NP-hard. The literature contains many results on representations of relation algebras; in particular, some relation algebras with four atoms are not representable. We extend the result of Cristiani and Hirsch to relation algebras with at most 4 atoms: the NSP is always either in P or NP-hard. To this end, we construct universal, fully universal, or even normal representations for these algebras, whenever possible.

We conduct a computability-theoretic study of Ramsey-like theorems of the form "Every coloring of the edges of an infinite clique admits an infinite sub-clique avoiding some pattern", with a particular focus on transitive patterns. As it turns out, the patterns corresponding to separable permutations play an important role in the computational features of the statement. We prove that the avoidance of any separable permutation is equivalent to the existence of an infinite homogeneous set in standard models, while this property fails for any other pattern. For this, we develop a novel argument for relativized diagonal non-computation.

In the past two decades, enormous efforts have been made to search for possible platforms and schemes to implement topological quantum computation (TQC). In exploring the Fu-Kane scheme of TQC based on Josephson trijunctions constructed on topological insulators, the predicted Majorana phase diagram of an individual trijunction has already been verified experimentally. If Majorana zero modes indeed exist in this kind of trijunction, coupling between them in multiple trijunction devices should be further expected. In this study, we fabricated Josephson devices containing two adjacent Josephson trijunctions on the surface of Sn-(Bi, Sb)2(Te, S)3 and observed a possible signature of the coupling effect manifesting as the reopening of a minigap in both trijunctions where a closure would otherwise be expected if the trijunctions existed individually. While alternative interpretations cannot be fully ruled out, our findings provide experimental support for the validity of the Fu-Kane theory and provide further motivation for advancing the TQC scheme proposed by Fu and Kane.

As a key component of low-altitude wireless networks, aerial base stations (AeBSs) provide flexible and reliable wireless coverage to support 6G ultra-reliable and low-latency communication (URLLC) services. However, limited spectrum resources and severe co-channel interference pose significant challenges to the deployment and resource allocation of AeBSs. To address these limitations, this paper proposes a novel rate-splitting multiple access (RSMA)-enabled transmission design to manage interference and enhance URLLC services in spectrum-constrained multi-AeBS networks. We formulate a joint optimization problem involving AeBS deployment, user association, and resource allocation to maximize the sum rate and coverage of system. Given the NP-hard nature of the problem, we propose a novel alternating optimization framework based on the generative graph diffusion models. Specifically, we model AeBSs and ground users as graph nodes, then we employ a discrete graph generation process solved via denoising diffusion to explore the combinatorial space of deployment and association strategies. Moreover, the successive convex approximation (SCA) is adopted to optimize AeBS beamforming and RSMA rate allocation under finite blocklength constraints. Extensive simulations demonstrate that the proposed algorithm outperforms existing methods in terms of convergence speed, sum rate, and coverage, while also exhibiting robust performance under varying network densities and interference levels.

In this work the standard kinetic theory assumption of instantaneous collisions is lifted. As a continuation of of a previous paper by Kanzler, Schmeiser, and Tora [KRM, 2024], a model for higher order non-instantaneous alignment collisions is presented and studied in the asymptotic regime of short collision duration. A first order accurate approximative model is derived as a correction to the instantaneous limit. Rigorous results on its well-posedness and on the instantaneous limit are proven. The approximative model is a system of two equations. An equally accurate scalar approximation is suggested.

The neutrino telescopes have firmly established the existence of ultrahigh-energy neutrinos. Observations of these neutrinos offer a unique probe of neutrino self-interactions. This work investigates how the self-interacting neutrinos, mediated by scalar bosons, inject energy into the medium through radiative scattering with the cosmic neutrino background, leaving an imprint on the cosmic microwave background (CMB) spectrum. The energy injection into plasma in redshift ranges, $5\times10^4\lesssim z\lesssim2\times10^6$ and $ z\lesssim5\times10^4$, leads to $μ$-type and $y$-type CMB spectral distortions, respectively. Using observational constraints from Cosmic Background Explorer/Far Infrared Absolute Spectrophotometer (COBE/FIRAS) and projected sensitivities from Primordial Inflation Explorer (PIXIE) experiments for $μ$-type and $y$-type CMB distortions, we derive the stringent upper bounds on the self-interaction coupling strength as a function of mediator mass for neutrino interactions. We focus on flavor-specific self-interaction related to muon neutrinos and sub-GeV mass mediators ($m_ϕ$). We find the upper bound on the self-interaction coupling strength to be $\sim 2.8\times 10^{-4}$ for the muon neutrino, considering ultrahigh-energy muon neutrino energy to be 1 PeV and PIXIE projected upper bounds on $y$-type CMB spectral distortion. The bound remains constant till the mediator mass reaches the center-of-mass energy, and after that, it gets relaxed and becomes proportional to the mediator mass. We have also compared our results with existing bounds in the literature. Our findings indicate that CMB spectral distortion could play a decisive role in exploring neutrino physics beyond the standard model of particle physics, and future missions like PIXIE can provide valuable insights.

We prove that the $τ$-tilting graph of any quasi-silted algebra is connected and has the reachable-in-face property. Our approach utilizes $τ$-reduction and wall and chamber structures. In particular, we observe a sufficient condition on the wall and chamber structure under which the connectivity of $τ$-tilting graphs is preserved under taking quotients of algebras. As an immediate consequence, the connectivity of $τ$-tilting graphs is also established for several new classes of algebras.

Whether a variable is the cause of another, or simply associated with it, is often an important scientific question. Causal Inference is the name associated with the body of techniques for addressing that question in a statistical setting. Although assessing causality is relatively straightforward in the presence of temporal information, outside of that setting - the situation considered here - it is more difficult to assess causal effects. The development of the field of causal inference has involved concepts from a wide range of topics, thereby limiting its adoption across some fields, including meteorology. However, at its core, the requisite knowledge for causal inference involves little more than basic probability theory and regression, topics familiar to most meteorologists. By focusing on these core areas, this and a companion article provide a steppingstone for the meteorology community into the field of (non-temporal) causal inference. Although some theoretical foundations are presented, the main goal is the application of a specific method, called matching, to a problem in meteorology. The data for the application are in public domain, and R code is provided as well, forming an easy path for meteorology students and researchers to enter the field.

Non-relativistic QCD (NRQCD) is used to calculate the relativistic correction to the amplitude for exclusive photoproduction of vector Quarkonia in the near-threshold region within the generalized parton distribution (GPD) framework. The relativistic corrections are found to be large for $J/ψ$, and lead to a breakdown of the GPD moment expansion near threshold. Cross-sections for both $J/ψ$ and $Υ$ are calculated with the former being compared to the data. We also demonstrate the presence of endpoint divergences for the relativistic correction away from the near-threshold regime.

One obstacle to ``elevating'' correlation to causation is the phenomenon of confounding, i.e., when a correlation between two variables exists because both variables are in fact caused by a third variable, called a confounder. The situation where the confounders are measured is examined in an earlier, accompanying article. Here, it is shown that even when the confounding variables are not measured, under certain conditions it is still possible to estimate the causal effect via a regression-based method that uses the notion of instrumental variables. Using a meteorological data set, similar to that in the sister article, a number of different estimates of the causal effect are compared and contrasted. It is shown that the instrumental-variable estimates of causal effect depend on the choice of the instrumental variable, and that meteorological considerations are important in resolving the ambiguity. R code is provided for generating all of the results, and numerous directions for future work are outlined.

The nature of the Higgs boson, whether it is elementary or composite, will be investigated through precision measurements at the collider experiments. In composite Higgs scenarios, the Higgs may manifest as a pseudo Nambu-Goldstone boson (pNGB) arising from a strongly interacting sector. The $SU(5)/SO(5)$ Composite Higgs Model features a rich scalar sector, with the decay patterns of the scalars being heavily influenced by the way fermions are embedded in various representations of $SU(5)$. We discuss how masses of the pNGB scalars and their couplings depend functionally on the compositeness scale and the parameters of the strong sector. Unique decay modes of the scalars emerge from the model when the mixing among the various pNGB scalars is non-negligible. We present a comprehensive and thorough analysis of the fermiophilic and fermiophobic decay modes of the pNGB scalars. Significant differences are observed in the decay patterns of the two singly charged scalars. Further, the decay of one pNGB to another on-shell pNGB when masses exceed about $1$ TeV presents a rich phenomenology, leading to distinctive signatures at the colliders. In this context, the future muon collider offers a promising avenue for detecting pNGB scalars with masses larger than $1$ TeV, especially in final states involving $W/Z$ fatjets.

Motivated by the discrete logarithmic Minkowski problem we study for a given matrix $U\in\mathbb{R}^{n\times m}$ its cone-volume set $C_{\tt cv}(U)$ consisting of all the cone-volume vectors of polytopes $P(U,b)=\{ x\in\mathbb{R}^n : U^\intercal x\leq b\}$, $b\in\mathbb{R}^n_{\geq 0}$. We will show that $C_{\tt cv}(U)$ is a path-connected semialgebraic set which extends former results in the planar case or for particular polytopes. Moreover, we define a subspace concentration polytope $P_{\tt scc}(U)$ which represents geometrically the subspace concentration conditions for a finite discrete Borel measure on the sphere. This is up to a scaling the basis matroid polytope of $U$, and these two sets, $P_{\tt scc}(U)$ and $C_{\tt cv}(U)$, also offer a new geometric point of view to the discrete logarithmic Minkowski problem.

We find identities involving differential operators in the generic artinian reduction of the Stanley-Reisner ring of a simplicial sphere in any positive characteristic. These identities generalize the characteristic 2 identities used by Papadakis and Petrotou to give a proof of the algebraic g-conjecture. We show that these identities are a shadow of an identity on the degree map, and we use them to prove the anisotropy of certain forms on the generic artinian reduction of the Stanley--Reisner ring and to prove weak Lefschetz results.

Graph symmetries identify structural regularities and reduce the computational complexity of network analysis. In weighted graphs, however, exact automorphisms are rare because real-valued weights seldom coincide. We introduce a general framework for detecting approximate symmetries by aggregating weights into discrete categories, generating a sequence of coarser graphs on which classical automorphism analysis applies. The approximation path is fully configurable, based on interaction magnitudes, and can be matched to the empirical weight distribution. Applied to 250 empirical food webs using logarithmic aggregation, the method reveals that automorphisms emerge even at low approximation levels and almost always form small orbits. Orbit sizes rarely exceed two or three vertices, reflecting the combinatorial fragility of larger symmetric sets. Even so, symmetric vertices occupy diverse structural positions in the network and high connectivity does not imply asymmetry. The observation of just local permutations confirms the conclusions of trophic species and niche analysis. A case study demonstrates that automorphisms can also recover latent ecological structure. The minimal aggregation level at which two vertices become substitutable provides a quantitative measure of role similarity. The framework offers a principled, automorphism-based approach for quantifying similarity and redundancy in weighted complex networks.