Much of the Outgoing Longwave Radiation (OLR) emitted to space is best described as random variability, or the ``Earth's Infrared Background''. A rigorous characterization of this background provides an objective null hypothesis and enables the isolation of atmospheric phenomena -- such as waves, storms, and other coherent structures -- within OLR observations. To this end, we identify the background as isotropic fluctuations implied by the fluctuation-dissipation theorem in response to internal atmospheric variability on small spatiotemporal scales. We use a stochastically forced energy balance climate model, which has a broad sense red spectrum consistent with observations, a first-order process in time, and a second-order process in space. By fitting the model to OLR data from satellite observations, we find that the background fluctuations have an upper bound of about 400~km and 2.5~days on their spatiotemporal (de)correlations, between meso-scale and synoptic-scale weather.

Multiple polylogarithms are equipped with rich algebraic structures including the motivic coaction and the single-valued map which both found fruitful applications in high-energy physics. In recent work arXiv:2312.00697, the current authors presented a conjectural reformulation of the motivic coaction and the single-valued map via zeta generators, certain operations on non-commuting variables in suitable generating series of multiple polylogarithms. In this work, the conjectures of the reference will be proven for multiple polylogarithms that depend on any number of variables on the Riemann sphere.

Given a graph $G$ and a set $S \subseteq V(G)$, we say that $S$ is $Δ$-convex if the neighborhood of every vertex not in $S$ is an independent set. A collection ${\cal V} = (V_1, V_2, \ldots , V_p)$ of convex sets of $G$ is a convex $p$-cover if $V(G) = \underset{1 \leq i \leq p}{\bigcup} V_i$ and $V_i \nsubseteq {\underset{1 \leq j \leq p, j\ne i}{\bigcup}} V_j$ for $i \in \{1, \ldots, p\}$. If the convex sets of ${\cal V}$ are pairwise disjoint, ${\cal V}$ is a convex $p$-partition of $V(G)$. The convex cover number $ϕ_c(G)$ (the convex partition number $Θ_c(G)$) of a graph $G$ is the least integer $p \geq 2$ for which $G$ has a convex $p$-cover (convex $p$-partition). In this work, we prove that the {\sc Convex p-cover} and {\sc Convex p-Partition} problems are \NP-complete for any fixed $p \ge 4$ in $Δ$-convexity. Furthermore, for the three standard graph products, namely, the Cartesian, strong and lexicographic products, we determine these parameters for some cases and present bounds for others.

Teleportation of quantum information over long distances requires robust entanglement on the macroscopic scale. The construction of highly energetic eigenstates with tunable long-range entanglement can provide a new medium for information transmission. Using a symmetric superposition of the antipodal triplet states, we construct polynomially many exact zero-energy eigenstates for a class of non-integrable spin-1/2 Hamiltonians with two-body interactions. These states exhibit non-thermal correlations, hence, are genuine quantum many-body scars. By tuning the distribution of triplets we induce extensive, logarithmic, or area-law entanglement, and can observe a second-order entanglement phase transition. Quasiparticle excitations in this manifold converge to be exact quantum many-body scars in the thermodynamic limit. This framework has a natural extension to higher dimensions, where entangled states controlled by lattice geometry and internal symmetries can result in new classes of correlated out-of-equilibrium quantum matter. Our results provide a new avenue for entanglement control and quantum state constructions.

We begin by giving a derived characterization of rational singularities for pairs in the sense of Schwede--Takagi. This characterization extends a characterization of rational singularities due to Lank--Venkatesh to pairs on normal varieties over fields of characteristic zero. As an application, we introduce a categorical invariant that measures the failure of rationality for pairs on affine varieties that are locally complete intersections.

Computed ultrasound tomography in echo mode generates maps of tissue speed of sound (SoS) from the shift of echoes when detected under varying steering angles. It solves a linearized inverse problem that requires regularization to complement the echo shift data with a priori constraints. Spatial gradient regularization has been used to enforce smooth solutions, but SoS estimates were found to be biased depending on tissue layer geometry. Here, we propose to train a linear operator to minimize SoS errors on average over a large number of random tissue models that sample the distribution of geometries and SoS values expected in vivo. In an extensive simulation study on liver imaging, we demonstrate that biases are strongly reduced, with residual biases being the result of a partial non-linearity in the actual physical problem. This approach can either be applied directly to echo-shift data or to the SoS maps estimated with gradient regularization, where the former shows slightly better performance, but the latter is computationally more efficient. Experimental phantom results confirm the transferability of our results to real ultrasound data.

There is increasing interest in combining information from experimental studies, including randomized and single-group trials, with information from external experimental or observational data sources. Such efforts are usually motivated by the desire to compare treatments evaluated in different studies -- for instance, by constructing external comparator groups for some index study -- or to estimate treatment effects with greater precision. Proposals to combine experimental studies with external data were made at least as early as the 1970s, but in recent years have come under increasing consideration within clinical practice and by regulatory agencies involved in drug and device evaluation, particularly with the increasing availability of trial and observational data. In this paper, we describe basic study templates that combine information from experimental studies with external data, and use the potential (counterfactual) outcomes framework to elaborate identification strategies for potential outcome means and average treatment effects. We argue that these identification strategies inherit ideas relevant to the study of causation in single-source studies and the related literature on combining information (e.g., generalizability and transportability methods), but merit consideration as a separate class of causal problems because they differ in terms of their scientific motivations, definitions of the target population, sampling, data structures, and identifiability conditions. In formalizing identification strategies for the analyses described herein, we hope to provide a conceptual foundation to support the systematic use and evaluation of such efforts.

This work introduces a new method for selecting the number of components in finite mixture models (FMMs) using variational Bayes, inspired by the large-sample properties of the Evidence Lower Bound (ELBO) derived from mean-field (MF) variational approximation. Specifically, we establish matching upper and lower bounds for the ELBO without assuming conjugate priors, suggesting the consistency of model selection for FMMs based on maximizing the ELBO. As a by-product of our proof, we demonstrate that the MF approximation inherits the stable behavior (benefited from model singularity) of the posterior distribution, which tends to eliminate the extra components under model misspecification where the number of mixture components is over-specified. This stable behavior also leads to the $n^{-1/2}$ convergence rate for parameter estimation, up to a logarithmic factor, under this model overspecification. Empirical experiments are conducted to validate our theoretical findings and compare with other state-of-the-art methods for selecting the number of components in FMMs.

We study noncommutative rings whose proper subrings all satisfy the same chain condition. We show that if every proper subring of a ring $R$ is right Noetherian, then $R$ is either right Noetherian or the trivial extension of $\mathbb{Z}$ by the Prüfer $p$-group for a prime $p$. We also prove that if every proper subring of $R$ is right Artinian, then $R$ is either right Artinian or $\mathbb{Z}$. For commutative rings, both results were proved by Gilmer and Heinzer in 1992. Our result for right Artinian subrings only generalises the absolute case of their commutative result. We generalise the full result (when only certain subrings are right Artinian) in the context of PI rings.

In recent years, the Fiat-Naor function inversion scheme has been used to disprove conjectures in fine-grained complexity theory and design state of the art data structures for a number of combinatorial problems. We pursue this line of research by considering its application to data structures for searching in implicit sets, defined as the image of a function. We show that, if $f$ is of the form $[N]\to [2^{w}]^d$ for some $w=polylog(N)$ and is computable in constant time, then, for any $0<α<1$, we can obtain a data structure using $Õ(N^{1-α/3})$ space such that, for a given $d$-dimensional axis-aligned box $B$, we can search for some $x\in [N]$ such that $f(x) \in B$ in time $Õ(N^α)$. (Here the $Õ(.)$ notation omits polylogarithmic factors.) Using similar techniques, we further obtain - data structures for range counting and reporting, predecessor, selection, ranking queries, and combinations thereof, on the set $f([N])$, - data structures for preimage size and preimage selection queries for a given value of $f$, and - data structures for selection and ranking queries on geometric quantities computed from tuples of points in $d$-space. These results unify and generalize previously known results on 3SUM-indexing and string searching, and are widely applicable as a black box to a variety of problems. In particular, we give a data structure for a generalized version of gapped string indexing, and show how to preprocess a set of points on an integer grid in order to efficiently compute (in sublinear time), for points contained in a given axis-aligned box, their Theil-Sen estimator, the $k$th largest area triangle, or the induced hyperplane that is the $k$th furthest from the origin.

In this paper, we address the well-known challenge in the numerical solution of time-fractional partial differential equations (TFPDEs), namely, that the dependence on all previous time levels leads to storage requirements that grow linearly with the number of time steps. To overcome this difficulty, we develop an efficient algorithm based on incremental singular value decomposition (ISVD), which avoids the excessive memory demands associated with storing the full solution history. A rigorous error analysis is established, and numerical experiments are presented to validate the theoretical results. Comparisons with the direct method and a representative fast evaluation method show that the proposed ISVD approach dramatically reduces memory usage relative to the direct method and remains competitive with the fast method over the tested parameter regimes.

For $S=S_{g,n}$ a closed orientable differentiable surface of genus $g$ from which $n$ points have been removed, such that $χ(S)=2-2g-n<0$, let $\mathrm{P}Γ(S)$ be the pure mapping class group of $S$ and $\mathrm{P}\widehatΓ(S)$ and $\mathrm{P}\checkΓ(S)$ be, respectively, its profinite and its congruence completions, the latter being identified with the image of the natural representation $\mathrm{P}\widehatΓ(S)\to\operatorname{Out}({\widehatπ}_1(S))$ (where ${\widehatπ}_1(S)$ is the profinite completion of the fundamental group of $S$). We determine the automorphism groups of procongruence completions under a natural rigidity condition, and show that the profinite Grothendieck-Teichmüller group embeds into the outer automorphism group of the profinite completion. Let $\operatorname{Out}^{\mathbb{I}_0}(\mathrm{P}\widehatΓ(S))$ and $\operatorname{Out}^{\mathbb{I}_0}(\mathrm{P}\checkΓ(S))$ be the groups of outer automorphisms which preserve the conjugacy class of a procyclic subgroup generated by a nonseparating Dehn twist (a condition trivially satisfied for $g=0$). Our main result gives that, for $χ(S)<g-2$ and $(g,n)\neq (1,2)$, there is a natural isomorphism: \[\operatorname{Out}^{\mathbb{I}_0}(\mathrm{P}\checkΓ(S))\congΣ_n\times\widehat{\operatorname{GT}},\] where $Σ_{n}$ is the symmetric group on $n$ letters and $\widehat{\operatorname{GT}}$ denotes the profinite Grothendieck-Teichmüller group. We also prove that, for $χ(S)<g-2$, there is a natural faithful representation $\widehat{\operatorname{GT}}\hookrightarrow\operatorname{Out}^{\mathbb{I}_0}(\mathrm{P}\widehatΓ(S))$.

The relative arbitrage portfolio outperforms a benchmark portfolio over a given time-horizon with probability one. With market price of risk processes depending on the market portfolio and investors, this paper analyzes the multi-agent optimization of relative arbitrage opportunities in the coupled system of market and wealth dynamics. We construct a well-posed market dynamical system of McKean-Vlasov type under an empirical measure of investors, where each investor seeks for relative arbitrage with respect to a benchmark dependent on market and all the agents. We show the conditions to guaranty relative arbitrage opportunities among competitive investors through the Fichera drift. Under mild conditions, we derive the optimal strategies for investors and the unique Nash equilibrium that depends on the smallest nonnegative solution of a Cauchy problem.

Integrated Sensing and Communication (ISAC) systems require efficient beamforming architectures to jointly support communication and sensing functionalities. To reduce hardware overhead, Hybrid Beamforming (HBF) has been widely studied and shown to achieve performance close to fully digital beamforming under practical hardware constraints. As a promising evolution, Reconfigurable Antenna (RA) technologies have recently emerged to further enhance beamforming Degrees of Freedom (DoFs) by dynamically reconfiguring antenna Electromagnetic(EM) characteristics, yet their integration into ISAC systems remains largely unexplored. In this paper, we investigate an RA-assisted ISAC system and develop a decoupled Triple-Hybrid Beamforming (Tri-HBF) framework that alternatively optimizes digital, analog, and EM beamformers to maximize the communication rate and sensing Signal-to-Clutter-plus-NoiseRatio (SCNR). For both Single-user Single-target (SUST) and Multiple-user Multiple-target (MUMT) scenarios, we first transform the original fractional objectives into fraction-free ones via methods tailored to their respective structures. The resulting problems are then solved via alternating optimization over different variable blocks. Closed-form updates are derived for all variables except the EM beamforming subproblem in the MUMT scenario. To further reduce the complexity introduced by Semidefinite Relaxation (SDR) in EM beamforming, we propose a low-complexity iterative approach across antennas with closed-form updates. Simulation results demonstrate that the proposed scheme significantly outperforms benchmark designs with conventional omnidirectional and directional antennas, achievingalmost 100% improvement in spectrum efficiency and 62.5% reduction in antenna overhead, thereby unveiling the

We study the instanton counting in four dimensional $\mathcal{N}=2$ supersymmetric gauge theories on the blow-up of $\mathbb{C}^2$: we start by formulating the instanton moduli space as a quiver variety, which we regularise by introducing two stability parameters, thus endowing it with a structure of infinitely many chambers separated by walls. Within a given chamber, we formulate the instanton partition function as a contour integral, which can be evaluated using the Jeffrey-Kirwan residue prescription. We characterise the physically relevant contributions in terms of bipartite oriented graphs and show that they can more efficiently be classified in terms of combinatorial objects called super-partitions. Within a given chamber, only certain types of super-partitions contribute and we show that the corresponding selection criteria are equivalent to stability conditions that have previously been proposed in the literature. We use this formalism to compare how the instanton counting changes when moving across walls between neighbouring chambers and provide explicit expressions for the corresponding partition functions. In a limiting chamber and using our approach, we show how to reproduce the Nakajima-Yoshioka blow-up formula.

Submovements are ballistic components of human motion constituting a large part of motor interaction and arising from the cyclical and overlapping cognitive processes of perception, motor planning, and motor execution. Extracting submovements is challenging as the motions tend to overlap, or start before the previous ends. We propose and evaluate use of a wavelet-inspired technique to accurately locate and parameterize submovements from one-dimensional speed time series. Our method employs a self-weighted loss refinement step to identify and improve regions of poor quality of fit, a challenge for simpler wavelet transforms. We demonstrate the accuracy of our method by presenting analysis of ~6,400 1-2s trials of synthetic egocentric camera (first-person shooter) aim data for which we know ground truth, modeled from a similarly sized real data set of 13 users. We compare our method to dual-threshold and the persistence 1D segmentation techniques and note challenges and opportunities for future improvements.

Ultrafast strong-field laser--plasma physics is shown to offer a promising framework for relativistic nonlinear quantum electrodynamics (QED). As one of its key advantages, this approach to relativistic nonlinear QED does not require an external beam of relativistic particles. Instead, high-energy electrons are produced in this setting as a part of ultrafast strong-field laser--plasma interactions. An intense ultrashort laser pulse generates and accelerates dense electron bunches to relativistic energies, giving rise to photon-pair emission confined to the nanometer scale in space and the attosecond scale in time. As a lowest-order nonlinear QED process, relativistic electrons in laser-driven plasmas are shown to give rise to attosecond bursts of two-photon emission, providing an ultrabroadband source of correlated photon pairs. As a physically insightful estimate, the rate of this two-photon emission is expressed via a product $ α^2 γω_{turn}$, where $α$ is the fine-structure constant, $γ$ is the Lorentz factor, and $ ω_{turn}$ is the local relativistic curvature frequency. Photon pairs with strongest correlations, providing a resource for photon entanglement, are emitted at a much lower rate, estimated as $ α^2 γ^2 ω_{turn} E_{\perp} /E_S$, where $E_{\perp}$ is the laser electromagnetic field, determining the transverse Lorentz force, and $E_S$ is the Schwinger critical field. Our study offers a clear guidance on how quantum aspects of laser-driven relativistic plasma electrodynamics can be isolated from their classical counterparts, enabling a physically justifiable approach to the analysis of nonlinear QED phenomena in complex laser--plasma interactions driven by ultrashort high-intensity laser pulses.

In this paper, we consider the global spherically symmetric strong solution to the compressible Navier-Stokes equations with far-field vacuum and density-denpendent degenerate viscosity which is referenced from Bresch-Vasseur-Yu \cite{B-V-Y 2021}. For the 1D Navier-Stokes equations, Wen-Zhang \cite{W-Z SIAM 2025} have considered the Cauchy problem which established the dependence relationship $γ-δ-\frac{1}{p}\ge0$ within the $W^{2,p}(\mathbb{R})$ and $p\ge 2$. In contrast, the solution space of this paper is $H^2[a,+\infty)$, $a>0$ and $δ$ satisfies $1>δ\gtrsim0.7427$. This result can be regarded as the first one on spherically symmetric strong solutions to the 3D Navier-Stokes equations with the viscosity proposed in \cite{B-V-Y 2021} and far-field vacuum.

Randomized controlled trials (RCTs) are often underpowered to detect treatment heterogeneity in subgroups defined by cross-classifications of multiple covariates, due to sparse sample sizes in some strata. External RCT data can help, but typically provide treatment effect estimates at a coarser level (e.g., by sex or race) rather than for the finer subgroups of interest (e.g., race-by-sex). We propose a novel James-Stein (JS)-type estimator that borrows strength from such coarsened external estimates to improve estimation of finer subgroup-specific conditional average treatment effects (CATEs) in an internal study, while accommodating potential incompatibility in marginal CATEs across populations. Based on asymptotic theory, we derive a practical analytic variance estimator for the JS estimator that exhibits acceptable empirical performance. Under mild conditions, we show that the proposed estimator uniformly dominates the ordinary least squares (OLS) estimator based on internal data regarding a weighted quadratic loss. Simulation studies demonstrate favorable performance compared with existing shrinkage methods, including empirical Bayes and generalized ridge estimators. We illustrate our method by estimating race-by-sex subgroup CATEs in a tirzepatide weight-loss trial (SURMOUNT-1), borrowing sex-specific and race-specific estimates from two previous semaglutide trials (STEP 1 and STEP 2). The proposed method detects a significantly larger treatment effect on percentage weight loss in the female-White subgroup than in the female-Asian subgroup, a difference not detected using internal data alone.

BPS states in holographic CFTs are usually classified into supergravitons, namely BPS fluctuations around empty AdS, and black-hole microstates, which appear above an energy threshold. In AdS$_3$/CFT$_2$, however, this picture is incomplete because of additional degrees of freedom, called singletons, associated with boundary diffeomorphisms. We present a general procedure for extending the BPS spectrum of supergravitons by dressing them with singletons, thereby defining a generalized, gravity-sector Hilbert space that admits decomposition into affine multiplets of the full superconformal algebra. This extends the procedure previously proposed in arXiv:2505.14888 which was applicable only at low levels, by removing that limitation. We apply the new procedure to the D1-D5 CFT ${\rm Sym}^N(T^4)$ and explicitly construct affine multiplets in the gravity sector for the $N=2$ theory up to level $h=2$. We find that, at the free orbifold point, the gravity-sector spectrum agrees with the CFT up to $h=\frac12$. Upon turning on a deformation, however, states at $h=1$ lift and the agreement improves to $h=\frac32$. Interestingly, the lifting occurs between states in the gravity sector, involving mixtures of supergravitons and singletons, and stringy states. We conjecture that, upon deformation, the gravity-sector Hilbert space becomes the monotone Hilbert space while its complement becomes the fortuitous Hilbert space.

The Chabauty--Coleman--Kim method, under favourable circumstances, describes the set of integral points of a hyperelliptic curve inside the $p$-adic zeroes of certain transcendental functions. For an elliptic curve of Mordell--Weil rank one, the Chabauty--Coleman--Kim set in depth 2 is given by the zeroes of a (finite union of) quadratic polynomial(s) in the $p$-adic logarithm of the elliptic curve and the local $p$-adic height at $p$. Here, we give an explicit formula for a finite set containing the Chabauty--Coleman--Kim set in depth 3 for an elliptic curve of rank at most 2 under an assumption on non-vanishing of a special value of a $p$-adic $L$-function. The finite set is given by the zeroes of a polynomial in $p$-adic elliptic polylogarithms. We use these formulas to verify new instances of Kim's conjecture.

We investigate timelike geodesics in asymptotically flat regular black holes supported by a phantom scalar field characterized by a scalar charge $A$. This parameter removes the central singularity and continuously deforms the Schwarzschild geometry while preserving asymptotic flatness. We derive the equations of motion for massive test particles and classify bounded and unbounded trajectories in terms of the conserved energy and angular momentum. We determine circular and critical orbits, including the innermost stable circular orbit (ISCO), and analyze the transition between capture and scattering. We show that the scalar charge modifies the location of the unstable and stable circular orbits, the ISCO, and the threshold angular momentum for scattering, exhibiting a nontrivial dependence on the radial coordinate. Their physical scales are naturally described in terms of the invariant areal radius $R(r)=\sqrt{r^2+A^2}$. In the weak-field regime, we compute the perihelion precession and obtain corrections proportional to the scalar charge, allowing us to constrain the scalar charge from Solar System observations. We also analyze the motion with vanishing angular momentum and show that, while the qualitative structure of the trajectories remains connected to the Schwarzschild limit $A\to 0$, the quantitative deviations encode the geometric effects of the scalar hair.

The interaction between a Nambu-Goto string and a Kerr black hole gives one of the methods of energy extraction from a rotating black hole. Although the properties of such processes have been well studied for rigidly rotating strings, little is known for non-rigidly rotating strings. In this paper, we study time evolution of a Nambu-Goto string on the equatorial plane of a Kerr spacetime, which sticks on the horizon and extends to spatial infinity. The time evolution is studied by the series expansion with respect to $t$ and the numerical simulations, which give reliable results for $t\lesssim 4M$ and $t\lesssim 38M$, respectively, where $M$ is the black hole mass. Since the angular velocity of the string on the horizon must coincide with the horizon angular velocity to keep the timelike property, the string is dragged into rotation and coils around the black hole. The negative energy is observed to fall into the black hole, but the positive energy follows after that, meaning that the energy extraction occurs for a short period of time. In the outside region, a wave is generated and propagates to the distant region carrying the extracted energy. After the propagation of the wave, the system approaches the time-independent configuration found by Boos and Frolov, and the total extracted energy is estimated as $E_{\rm ext}\lesssim μM$, where $μ$ is the tension of the string.

We introduce a graph-signal generalisation of Sample Entropy, denoted SampEn$_{G}$, to quantify irregularity of graph signals on a continuous state space, complementing existing methods on symbolic dynamics. Our approach replaces the temporal delay embedding of classical SampEn with a multi-hop graph-based embedding: for each node, we aggregate patterns from local walk-weighted neighbourhood averages computed via powers of the graph shift operator. We show empirically that SampEn$_{G}$ reduces to classical 1D SampEn on directed path graphs, and validate its nonlinear sensitivity using the logistic map. Experiments on directed Erdős--Rényi graph signals further characterise its behaviour with connectivity and pattern length $m$, with practical runtimes on the order of thousands of nodes. We expect SampEn$_{G}$ to open up new ways to analyse graph signals, generalising SampEn and the concept of conditional entropy to extending nonlinear analysis to a wide variety of network data.

We prove general sufficient conditions for zero velocity in position dependent one-dimensional quantum walks, and hence for the absence of ballistic transport. Our starting point is a general a priori upper bound on the velocity, formulated in terms of sparse bi-infinite sequences of sites, their gap structure, and the corresponding local coin parameters. This estimate yields several deterministic criteria for zero velocity that depend only on the behavior of suitable coin entries along selected subsequences and are independent of the values of the coins elsewhere. We also discuss the random case as an application of the general approach. All of our results remain valid in the CMV setting.

Let $S$ be an $\mathbb N$-graded Koszul Artin-Schelter regular algebra and let $σ$ be a graded algebra automorphism of $S$. We study the stable category of graded maximal Cohen-Macaulay modules over the trivial extension algebra $S\ltimes S_σ(-1)$. We show that this category is triangle equivalent to the bounded derived category of finitely generated (ungraded) modules over the Koszul dual algebra of the Zhang twist $S^{σ^{-1}}$. In the connected graded case, we also obtain a criterion for when two such stable categories are triangle equivalent, and show that such an equivalence induces an equivalence between the categories of graded modules over the original algebras.

A celebrated result of Johansson in graph theory states that every triangle-free graph of maximum degree $Δ$ can be properly colored with $O(Δ/\lnΔ)$ colors, improving upon the "greedy bound" of $Δ+1$ coloring in general graphs. This coloring can also be found in polynomial time. We present an algorithm for maintaining an $O(Δ/\lnΔ)$ coloring of a dynamically changing triangle-free graph that undergoes edge insertions and deletions. The algorithm is randomized and on $n$-vertex graphs has amortized update time of $Δ^{o(1)}\log{n}$ per update with high probability, even against an adaptive adversary. A key to the analysis of our algorithm is an application of the entropy compression method that to our knowledge is new in the context of dynamic algorithms. This technique appears general and is likely to find other applications in dynamic problems and thus can be of its own independent interest.

Consider two parties who want to agree on a common frequency band for communication in the presence of independent jammers. Such jammers block a different subset of bands at each site, where each party can observe only its own set of unjammed bands. Yet, they must agree on a common band without communicating. We first establish the optimal classical strategy, maximizing the probability they output a common frequency band in a single shot. We proceed to show that sharing an entangled pair of local dimension d allows the parties to coordinate strictly better, provided both the number of safe bands d and the spectrum size n are sufficiently large. We study explicit quantum strategies offering a pathway to near-term demonstrations, including an explicit strategy for d = 2 that outperforms the classical optimum for all spectrum sizes, achieving a 5.4% advantage asymptotically (in n) with just one shared Bell pair. Our approach is based on a general framework for constructing quantum strategies from classical spreading sequences via symmetric orthonormalization that may be of independent interest, and opens the door to concrete applications of quantum networks for cognitive radio and spread-spectrum communication.

We extend some properties of a pair of ideals described in terms of Tor modules to any number of ideals, including the well-known rigidity property. Those extensions require the development of a homological theory for spectral sequences arising from multiple complexes. Out of this theory, two new complexes associated with quotients by sums and quotients by products of the given ideals emerge, and their homologies are related via the Tor-independence property. In the multigraded setting, we describe the support regions of Tor modules for quotients by sums and products of ideals generated by variables in terms of each other.

Co80Ir20 ferromagnetic thin films have recently been the focus of intensive research because the negative magnetocrystalline anisotropy adds to the shape anisotropy and favors a strong alignment of the magnetization in the film plane for [001] textured or epitaxial thin films. However, the role of magnetoelastic effects has not been properly considered in most published research. In this work we have performed a detailed analysis of 24 nm Co80Ir20 thin films deposited on Si/SiO2 with different underlayers (Ta, Pt) and overlayers in order to induce [001]-textured growth and different degrees of strain. Using x-ray diffraction measurements we have found that the c-axis lattice parameter depends on the underlayer material (larger negative strain for Ta), but the degree of texture and the average grain size remain essentially constant, except for one of the multilayers. Differences in the magnetic behavior according to the underlayer were also found in room temperature magnetization vs field loops and temperature dependent dc magnetization measurements. Anisotropy was quantified using ferromagnetic resonance which showed that the effective anisotropy field is also dependent on the underlayer. Ta underlayers show an anisotropy close to that expected for shape, while Pt underlayer induces an additional in-plane anisotropy field of the order of 7-9 kOe. A simple model of stress induced anisotropy gives anisotropy field values similar to those observed experimentally. The correlation between observed strain and anisotropy together with the similarity in microstructural properties strongly suggests that stress effects cannot be disregarded when analyzing the magnetic data for the estimation of the magnetocrystalline contribution.