In fields ranging from business to systems biology, directed graphs with edges labeled by signs are used to model systems in a simple way: the nodes represent entities of some sort, and an edge indicates that one entity directly affects another either positively or negatively. Multiplying the signs along a directed path of edges lets us determine indirect positive or negative effects, and if the path is a loop we call this a positive or negative feedback loop. Here we generalize this to graphs with edges labeled by a monoid, whose elements represent `polarities' possibly more general than simply "positive" or "negative". We study three notions of morphism between graphs with labeled edges, each with its own distinctive application: to refine a simple graph into a complicated one, to transform a complicated graph into a simple one, and to find recurring patterns called "motifs". We construct three corresponding symmetric monoidal double categories of "open" graphs. We also study feedback loops using a generalization of the homology of a graph to homology with coefficients in a commutative monoid. In particular, we describe the emergence of new feedback loops when we compose open graphs using a variant of the Mayer-Vietoris exact sequence for homology with coefficients in a commutative monoid.

Populations of cells regulate gene expression in response to external signals, but their ability to make reliable collective decisions is limited by both intrinsic noise in molecular signaling and variability between individual cells. In this work, we use optogenetic control of the canonical Wnt pathway as an example to study how reliably information about an external signal is transmitted to a population of cells, and determine an optimal encoding strategy to maximize information transmission from Wnt signals to gene expression. We find that it is possible to reach an information capacity beyond 1 bit only through an appropriate, discrete encoding of signals: using either no Wnt, a short Wnt pulse, or a sustained Wnt signal. By averaging over an increasing number of outputs, we systematically vary the effective noise in the pathway. As the effective noise decreases, the optimal encoding comprises more discrete input signals. These signals do not need to be fine-tuned to achieve near-optimal information transmission. The optimal code transitions into a continuous code in the small-noise limit, which can be shown to be consistent with the Jeffreys prior. We visualize the performance of different signal encodings using decoding maps. Our results suggest optogenetic Wnt signaling allows for regulatory control beyond a simple binary switch, and provides a framework to apply ideas from information processing to single-cell in vitro experiments.

The observation of neutron star mergers with gravitational waves (GWs) has provided a new method to constrain the dense-matter equation of state (EOS) and to better understand its nuclear physics. However, inferring nuclear microphysics from GW observations necessitates the sampling of EOS model parameters that serve as input for each EOS used during the GW data analysis. The sampling of the EOS parameters requires solving the Tolman-Oppenheimer-Volkoff (TOV) equations a large number of times -- a process that slows down each likelihood evaluation in the analysis on the order of a few seconds. Here, we employ emulators for the TOV equations built using multilayer perceptron neural networks to enable direct inference of nuclear EOS parameters from GW strain data. Our emulators allow us to rapidly solve the TOV equations, taking in EOS parameters and outputting the associated tidal deformability of a neutron star in only a few tens of milliseconds. We implement these emulators in \texttt{PyCBC} to directly infer the EOS parameters using the event GW170817, providing posteriors on these parameters informed solely by GWs. We benchmark these runs against analyses performed using the full TOV solver and find that the emulators achieve speed ups of nearly \emph{two orders of magnitude}, with negligible differences in the recovered posteriors. Additionally, we constrain the slope and curvature of the symmetry energy at the 90\% upper credible interval to be $L_{\rm sym}\lesssim106$ MeV and $K_{\rm sym}\lesssim26$ MeV.

Achieving a sustainable electricity infrastructure requires the explicit integration of carbon emissions into power system modeling and optimization. However, existing open-source test cases for power system research lack generator-level carbon profiling, preventing the benchmark of carbon-aware operational strategies. To address this gap, this work introduces PGLib-CO2, an open-source extension to the PGLib-OPF test case library. The proposed PGLib-CO2 enriches standard grid test cases with CO2 and CO2-equivalent emission intensity factors to achieve realistic, generator-level carbon profiling with an expanded list of fuel types. Using the standardized data, PGLib-CO2 allows us to enhance the algorithms for computing key carbon emission metrics. We first utilize the differentiable programming paradigm for computing LMCE by treating the OPF-based grid dispatch as a differentiable layer. This method provides a rigorous marginal sensitivity for general convex cost functions, eliminating the need of using a small incremental change in numerical perturbation. Moreover, to accelerate the real-time LMCE computation, we develop an MPP-based approach that shifts the optimization burden to offline phase of identifying the OPF critical regions. Since each critical region is characterized by a pre-computed affine dispatch function, the online phase reduces to identifying the region followed by efficiently evaluating the region-specific LMCE values. Numerical evaluations on IEEE test systems demonstrate that the differentiable LMCE computation attains the precise sensitivity information, and the MPP-based approach retrieves the LMCE signals faster than the direct optimization approach. By bridging high-fidelity data with advanced parametric computation, PGLib-CO2 provides a reproducible and computationally efficient foundation for future research in sustainable power system operations.

We prove a rate of convergence for finite element approximations of stationary, second-order mean field games with nondifferentiable Hamiltonians posed in general bounded polytopal Lipschitz domains with strongly monotone running costs. In particular, we obtain a rate of convergence in the $H^1$-norm for the value function approximations and in the $L^2$-norm for the approximations of the density. We also establish a rate of convergence for the error between the exact solution of the MFG system with a nondifferentiable Hamiltonian and the finite element discretizations of the corresponding MFG system with a regularized Hamiltonian.

In cloud-scale systems, failures are the norm. A distributed computing cluster exhibits hundreds of machine failures and thousands of disk failures; software bugs and misconfigurations are reported to be more frequent. The demand for autonomous, AI-driven reliability engineering continues to grow, as existing humanin-the-loop practices can hardly keep up with the scale of modern clouds. This paper presents STRATUS, an LLM-based multi-agent system for realizing autonomous Site Reliability Engineering (SRE) of cloud services. STRATUS consists of multiple specialized agents (e.g., for failure detection, diagnosis, mitigation), organized in a state machine to assist system-level safety reasoning and enforcement. We formalize a key safety specification of agentic SRE systems like STRATUS, termed Transactional No-Regression (TNR), which enables safe exploration and iteration. We show that TNR can effectively improve autonomous failure mitigation. STRATUS significantly outperforms state-of-the-art SRE agents in terms of success rate of failure mitigation problems in AIOpsLab and ITBench (two SRE benchmark suites), by at least 1.5 times across various models. STRATUS shows a promising path toward practical deployment of agentic systems for cloud reliability.

We propose a novel modeling framework for time-evolving networks allowing for long-term dependence in network features that update in continuous time. Dynamic network growth is functionally parameterized via the conditional intensity of a marked point process. This characterization enables flexible, joint modeling of both update timing and the network updates themselves, dependent on the entire left-continuous sample path. We propose a path dependent nonlinear marked Hawkes process as an expressive platform for modeling such data; its dynamic mark space embeds the time-evolving network. We prove well-posedness and establish sufficient stability conditions, demonstrate simulation and subsequent feasible likelihood-based inference through numerical study, and illustrate the methodology with an application to conference attendee social network data. The proposed formulation provides a flexible and principled foundation for statistical inference on complex network evolution in continuous time.

Crystal structures can be viewed as assemblies of space-filling polyhedra, which play a critical role in determining material properties such as ionic conductivity and dielectric constant. However, most conventional crystal structure prediction methods rely on random structure generation and do not explicitly incorporate polyhedral tiling, limiting their efficiency and interpretability. In this highlight, we introduced a novel crystal structure generation method based on discrete geometric analysis of polyhedral information. The geometry and topology of space-filling polyhedra are encoded as a dual periodic graph, and the corresponding crystal structure is obtained via the standard realization of this graph. We demonstrate the effectiveness of our approach by reconstructing face-centered cubic (FCC), hexagonal close-packed (HCP), and body-centered cubic (BCC) structures from their dual periodic graphs. This method offers a new pathway for systematically generating crystal structures based on target polyhedra, potentially accelerating the discovery of novel materials for applications in electronics, energy storage, and beyond.

Although the $λ$I-calculus is a natural fragment of the $λ$-calculus, obtained by forbidding the erasure of arguments, its equational theories did not receive much attention. The reason is that all proper denotational models studied in the literature equate all non-normalizable $λ$I-terms, whence the associated theory is not very informative. The goal of this paper is to introduce a previously unknown theory of the $λ$I-calculus, induced by a notion of evaluation trees that we call "Ohana trees". The Ohana tree of a $λ$I-term is an annotated version of its Böhm tree, remembering all free variables that are hidden within its meaningless subtrees, or pushed into infinity along its infinite branches. We develop the associated theories of program approximation: the first approach -- more classic -- is based on finite trees and continuity, the second adapts Ehrhard and Regnier's Taylor expansion. We then prove a Commutation Theorem stating that the normal form of the Taylor expansion of a $λ$I-term coincides with the Taylor expansion of its Ohana tree. As a corollary, we obtain that the equality induced by Ohana trees is compatible with abstraction and application. Subsequently, we introduce a denotational model designed to capture the equality induced by Ohana trees. Although presented as a non-idempotent type system, our model is based on a suitably modified version of the relational semantics of the $λ$-calculus, which is known to yield proper models of the $λ$I-calculus when restricted to non-empty finite multisets. To track variables occurring in subterms that are hidden or pushed to infinity in the evaluation trees, we generalize the system in two ways: first, we reintroduce annotated versions of the empty multiset indexed by sets of variables; second, (...)

Moderation and blocking behavior, both closely related to the mitigation of abuse and misinformation on social platforms, are fundamental mechanisms for maintaining healthy online communities. However, while centralized platforms typically employ top-down moderation, decentralized networks rely on users to self-regulate through mechanisms like blocking actions to safeguard their online experience. Given the novelty of the decentralized paradigm, addressing self-moderation is critical for understanding how community safety and user autonomy can be effectively balanced. This study examines user blocking on Bluesky, a decentralized social networking platform, providing a comprehensive analysis of over three months of user activity through the lens of blocking behaviour. We define profiles based on 86 features that describe user activity, content characteristics, and network interactions, addressing two primary questions: (1) Is the likelihood of a user being blocked inferable from their online behavior? and (2) What behavioral features are associated with an increased likelihood of being blocked? Our findings offer valuable insights and contribute with a robust analytical framework to advance research in moderation on decentralized social networks.

This paper presents a study of nonlinear superpositions of Riemann wave solutions admitted by quasilinear hyperbolic first-order systems of partial differential equations. In particular, we focus on the Euler system and non-elastic wave superpositions that cannot be decomposed into pairwise independent interactions of waves. A crucial tool for this analysis is the property of quasi-rectifiability of the families of vector fields determined by this system. It imposes certain conditions to be satisfied by the commutators of these vector fields. They enable us to find a parametrization of the region of superpositions of Riemann waves which leads to a simplification of the initial system of equations. In order to identify non-elastic superpositions we prove that a class of Lie modules associated with them can be uniquely transformed into a real Lie algebra through an angle-preserving transformation. We are then able to select a particular basis of vector fields associated with a given module which ensures the property of quasi-rectifiability. That, in turn, allows us to construct the reduced form of the Euler system for which a non-elastic superposition of two Riemann waves is then derived analytically. A study of the geometry of the manifold of non-elastic wave superpositions in terms of deformations of submanifolds corresponding to the Lie algebras is performed. Finally, we adapt the described approach to the general form of a hydrodynamic-type system i.e., to arbitrary Lie modules of vector fields associated with such a system, providing the criteria for their quasi-rectifiability. A geometric interpretation of non-elastic wave superpositions in this system is given.

Coordinated missions involving Unmanned Aerial Vehicles (UAVs) in dynamic environments pose significant challenges in maintaining both coordination and agility. In this paper, relying on the cooperative path following framework and using a game-theoretic formulation, we introduce a novel and scalable approach in which each UAV acts autonomously in different mission conditions. This formulation naturally accommodates heterogeneous and time-varying objectives across the system. In our setting, each UAV optimizes a cost function that incorporates temporal and mission-specific constraints. The optimization is performed within a one-dimensional domain, significantly reducing the computational cost and enabling real-time application to complex and dynamic scenarios. The framework is distributed in structure, enabling global, system-wide coordination (a Nash equilibrium) by using only local information. For ideal systems, we prove the existence and the Nash equilibrium exhibits exponential convergence. Furthermore, we invoke model predictive control (MPC) for non-ideal scenarios. In particular, we propose a discrete-time optimization approach that tackles path-following errors and communication failures, ensuring reliable and agile performance in dynamic and uncertain environments. Simulation results demonstrate the effectiveness and agility of the approach in ensuring successful mission execution across diverse realistic scenarios.

DESI has reported a dynamical dark energy (DE) signal based on the $w_0 w_a$CDM model that is in conflict with Hubble tension. Recalling that the combination of DESI DR1 BAO and DR1 full-shape (FS) modeling are consistent with $Λ$CDM, in this letter we comment on the status of fluctuations in DR1 BAO documented in \cite{DESI:2024mwx, Colgain:2024xqj} in the DR2 update. In particular, we note that neither DR1 BAO nor DR2 BAO nor DR2 BAO+CMB confronted to the $w_0 w_a$CDM model with relaxed model parameter priors confirm late-time accelerated expansion today. Translating DESI BAO constraints into flat $Λ$CDM constraints, we observe that the LRG1 constraint remains the most prominent outlier, a distinction now held jointly with ELG1, LRG2 switches from smaller to larger $Ω_m$ values relative to Planck-$Λ$CDM, and ELG data drive the relatively low $Ω_m$ in the full DR2 BAO. We observe that one cannot restore $w_0 = -1$ within one $1 σ$ by removing either LRG1 or ELG1 or LRG2, but LRG2 in DR2, in contrast to LRG1 in DR1, now has the greatest bearing on $w_0 > -1$. We conclude that BAO has yet to stabilise, but the general trend is towards greater consistency with DESI DR1 FS modeling results, where there may be no dynamical DE signal in DESI data alone.

Bandeira et al. (2017) show that the eigenvalues of the Kendall correlation matrix of $n$ i.i.d. random vectors in $\mathbb{R}^p$ are asymptotically distributed like $1/3 + (2/3)Y_q$, where $Y_q$ has a Marčenko-Pastur law with parameter $q=\lim(p/n)$ if $p, n\to\infty$ proportionately to one another. Here we show that another Marčenko-Pastur law emerges in the "ultra-high dimensional" scaling limit where $p\sim q'\, n^2/2$ for some $q'>0$: in this quadratic scaling regime, Kendall correlation eigenvalues converge weakly almost surely to $(1/3)Y_{q'}$.

We introduce achievement positional games, a convention for positional games which encompasses the Maker-Maker and Maker-Breaker conventions. We consider two hypergraphs, one red and one blue, on the same vertex set. Two players, Left and Right, take turns picking a previously unpicked vertex. Whoever first fills an edge of their color, blue for Left or red for Right, wins the game (draws are possible). We establish general properties of such games. In particular, we show that a lot of principles which hold for Maker-Maker games generalize to achievement positional games. We also study the algorithmic complexity of deciding whether Left has a winning strategy as the first player when blue edges and red edges have respective sizes at most $p$ and $q$. This problem is in P for $p,q \leq 2$, but it is NP-hard for $p \geq 3$ and $q=2$, coNP-complete for $p=2$ and $q \geq 3$, and PSPACE-complete for $p,q \geq 3$ even when the 3-edges are the same for both colors. That last result has an interesting consequence on the Maker-Maker convention: for 3-uniform hypergraphs, which is the only case whose complexity is currently open (for starting positions of the game), we show PSPACE-completeness for positions obtained after one round of play.

We present a new careful and comprehensive analysis the observations of the satellites of Jupiter from the Sidereus Nuncius that extends and complements previous similar studies. Each observation is compared to the predictions obtained using a modern sky simulator, verifying and trying to understand them individually. The work considers both the information that can be extracted from the sketches and the angular measurements reported by Galilei. Angular measurements allow assessing the absolute accuracy in relation to modern ephemerides. We evaluate the performances of the telescope in terms of separation power of close-by satellites and the inefficiency in the detection connected to the proximity to the disk. A sinusoidal fit of the data, allows measuring the relative major semi-axes of the satellites' orbits and their periods with a statistical precision of 2-4\% and 0.1-0.3\% respectively. The posterior fit error is used to estimate the measurements precision. We show that with this data one can infer in a convincing way the third law of Kepler for the Jupiter system. The 1:2:4 orbital resonance between the periods of Io and Europa/Ganymede can be determined with \% precision. In order to obtain these results it is important to separate the four datasets. This operation was an extremely difficult task for Galilei. Nevertheless we show how some indication on the periods emerge from the using the modern Lomb-Scargle technique on the full data-set. We briefly extend the use of the simulator to verify the accuracy in the seven observations of the Moon and the performance in reproducing the Pleiades, the Orion belt, the Orion head and the Beehive cluster. Finally we present images obtained with a replica of the telescope that highlights the challenges of these observations thus confirming the excellence underlying this amazing set of early scientific data.

Millimeter-wave (mmWave) communication has been widely accepted as an enabler of 6G and other next-generation wireless networks, though high path loss strains link budgets, and difficult channel conditions have limited the deployment of mmWave within the 5G NR radio access network (RAN) primarily to dense urban environments. In this paper, we seek to demystify aspects of RAN planning and design for these environments by providing a set of empirical models of the mmWave channel at 28 GHz, alongside a methodology to develop spectrum consumption models (SCMs), which illustrate constraints on spectrum allocation by the RAN. We report on an extensive 28 GHz measurement campaign within the PAWR COSMOS testbed in New York City. This campaign resulted in over 46 million power measurements, collected from over 3,000 links across 24 street sidewalks at four different sites. Using these measurements, we study the effects of the setup and environments, such as TX height and seasonal effects. We then derive a series of channel models for path loss and the azimuth beamforming gain loss, and use them to derive distributions of the link SNR values achievable by UEs on the measured sidewalks. We show, among other results, that 100% of UEs on a given city block can achieve 10 dB SNR at locations with a strong street canyon effect. Finally, we develop a process to generate SCMs based on the IEEE 1900.5.2 standard using the empirical channel models. The generated SCMs facilitate the evaluation of spectrum sharing and interference management scenarios since they capture all directional propagation effects reflected in the measurements and provide a way to easily share the main propagation characterization results derived from the measurements. We believe that the models, methods, and results in this paper will help inform the future of mmWave wireless network deployments within dense urban areas.

Vector-boson fusion production of new Higgs bosons decaying into pairs of electroweak gauge bosons ($W^\pm W^\pm$, $WZ$ and $ZZ$) is a smoking-gun signature of the Georgi-Machacek (GM) Model. Notably, ATLAS has observed a $3.3σ$ excess in $W^\pm W^\pm$ at $\approx 450\,$GeV and a $2.8σ$ excess in the $WZ$ channel at $\approx 375\,$GeV, while CMS reported weaker-than-expected limits at these masses. However, the canonical custodial-symmetric GM Model cannot accommodate these signals, as it predicts mass degeneracy among the new gauge-philic Higgs bosons. To overcome this obstacle, we consider a generalized version of the GM Model without the custodial $SU(2)_C$ symmetry in the scalar potential. In the limit of small mixing among the Higgs bosons, the $W^\pm W^\pm$ and $WZ$ excesses can be explained by the doubly and singly-charged Higgs bosons originating primarily from the $Y=1$ triplet, while respecting the bounds from $ZZ$ searches. Furthermore, the neutral Higgs boson mostly contained in the $Y=0$ triplet can account for the excess at $\approx 152\,$GeV in associated di-photon production, while being consistent with constraints from vacuum stability and the Standard Model Higgs signal strength measurements.

Local Differential Privacy (LDP) offers strong privacy protection, especially in settings in which the server collecting the data is untrusted. However, designing LDP mechanisms that achieve an optimal trade-off between privacy, utility and robustness to adversarial inference and integrity attacks remains challenging. In this work, we introduce a general multi-objective optimization framework for refining LDP protocols, enabling the joint optimization of privacy and utility under various adversarial settings. While our framework is flexible to accommodate multiple privacy and security attacks as well as utility metrics, in this paper, we specifically optimize for Attacker Success Rate (ASR) under \emph{data reconstruction attack} as a concrete measure of privacy leakage and Mean Squared Error (MSE) as a measure of utility. Complementarily, we evaluate integrity-oriented threats through data poisoning attacks, providing an additional adversarial perspective. More precisely, we systematically revisit these trade-offs by analyzing eight state-of-the-art LDP frequency estimation protocols and proposing refined counterparts that leverage tailored optimization techniques. Experimental results demonstrate that our proposed adaptive mechanisms consistently outperform their non-adaptive counterparts, achieving substantial reductions in ASR while preserving utility, and pushing closer to the ASR-MSE Pareto frontier. By bridging the gap between theoretical guarantees and real-world vulnerabilities, our framework enables modular and context-aware deployment of LDP mechanisms with tunable privacy-utility-attackability trade-offs.

We analyze the domain of validity of a quantum optical model that describes the effects of gravitational redshift on the quantum state of photons that propagate in curved spacetime. This model assumes that the modes defining the initial state of the photon are mixed with an auxiliary environment mode via an effective multimode mixer. We find that the model, as proposed, is consistent only to first order for small redshift, where the range of validity is conditional not only to the gravitational parameters, but also to those that define the photonic modes. We identify the problem and provide a partial solution in terms of a necessary condition on the transformation matrix representing the process, which requires the use of a number of auxiliary modes that is at least equal to the number of modes that define the photonic state. We conclude by discussing implications for theoretical quantum optics and photonics in curved spacetime, as well as for the development of quantum technologies.

The holographic heavy quark potential is investigated via holographic Wilson loops in the AdS soliton with gauge potential. We analyze two types of holographic Wilson loops. {In the first type, holographic heavy quark potential shows the area law behavior. In the second type, the potential becomes zero at a critical length and physics analogous to the dissociation occurs. The mass of heavy quarkonia and the binding energy are examined.} Lastly, the mass of $0^{++}$ glueball-like operators dual to massless dilaton is calculated. The mass of $0^{++}$ glueball-like operator decreases with increase of the gauge potential as expected in arXiv:2309.03491 [hep-th]. The results are comparable with lattice QCD.

In this work, we consider the initial value problem (IVP) for a system of modified Korteweg-de Vries (mKdV) equations \begin{equation} \begin{cases} \partial_t v + \partial_x^3 v+ \partial_x (v w^2) = 0, \hspace{0.98 cm} v(x,0)=ψ(x),\\ \partial_t w + α\partial_x^3 w+\partial_x (v^2 w) = 0,\hspace{0.5 cm} w(x,0)=ϕ(x). \end{cases} \end{equation} The main interest is in addressing the well-posedness issues of the IVP when the initial data are considered in the modulation space $M_s^{2,p}(\mathbb{R})$, $p\geq 2$. In the case when $0<α\ne 1$, we derive new trilinear estimates in these spaces and prove that the IVP is locally well-posed for data in $M_s^{2,p}(\mathbb{R})$ whenever $s> \frac14-\frac{1}{p}$ and $p\geq 2$. In deriving the trilinear estimate, the fact that the Fourier supports of the solution components $v$ and $w$ lie on distinct cubic curves, namely $τ= ξ^3$ and $τ= αξ^3$, introduces additional difficulties in handling the resonant case. This makes the analysis substantially different from what one encounters in the single-equation setting. To overcome the difficulties arising in the resonant case, it was necessary to impose the more restrictive condition $s> \frac14-\frac{1}{p}$ on the trilinear estimate, rather than the natural threshold $s> \frac14-\frac{3}{2p}$ , which would otherwise yield sharp local well-posedness for $s>-\frac12$ when $p=2$.

We investigate objects in symmetric tensor categories that have simultaneously finite symmetric and finite exterior algebra. This forces the characteristic of the base field to be $p>0$, and the maximal degree of non-vanishing symmetric and exterior powers to add up to a multiple of $p$. We give a complete classification of objects in tensor categories for which this sum equals $p$. All resulting tensor categories are Verlinde categories of reductive groups and we fill in some gaps in the literature on these categories.

The control of the thermocapillary assembly of colloidal particle clusters is important for a variety of applications, including the creation of photonic crystals for microelectronics and optoelectronics, membrane formation for biotechnology, and surface cleaning for laboratory-on-chip devices. It is important to understand the main mechanisms that influence the formation of such clusters. This article considers a two-dimensional mathematical model describing the transfer of particles by a thermocapillary flow in an unevenly heated cell during the evaporation of a liquid. This gave us the opportunity to study one of the main processes that triggers the formation of a particle cluster. Whether the particle will move with the flow or stop at the heater, becoming the basis for the cluster, is determined by the ratio between gravity and the drag force. The results of numerical calculations show that, for small particle concentrations, their fraction entering the cluster decreases as the volumetric heat flux density $Q$ increases. The reason for this is an increase in the thermocapillary flow with an increase in the volumetric heat flux $Q$. It reduces the probability of particles entering the cluster.

Let $M$ be a closed hyperbolic $3$-manifold. A homotopy class $[S]$ of surfaces in $M$ is filling if any representative cuts $M$ into components contractible in $M$. We prove that there exist $ε_0, g_0>0$ such that every homotopy class of $(1+ε)$-quasi-Fuchsian surfaces with $0<ε\leq ε_0$ or totally geodesic surfaces of genus $\geq g_0$ in $M$ is filling. As a corollary, except for at most finitely many totally geodesic surfaces, embedded incompressible quasi-Fuchsian surfaces in $M$ have constants bounded below by $1+ε_0$. This also gives a gap theorem for embedded minimal surfaces. Each of these surfaces separates any pair of distinct points at the sphere of infinity. Crucial tools include the rigidity results of Mozes-Shah, Ratner, and Shah. This work is inspired by a question of Wu and Xue whether random geodesics on random hyperbolic surfaces are filling.

We assess the replicability of Orr (2022)'s method for estimating within-plant productivity across product lines, which combines demand estimation with cost minimization. The original study uses input price shocks in other output markets as instrumental variables, with exclusion restrictions based on downstream purchase shares. Reconstructing the original dataset of Indian machinery producers from 2000-2007, we reproduce the main productivity patterns and demonstrate their robustness to variations in the exclusion threshold. The main results remain robust in extended samples (2010-2019, 2000-2019) when calibrating demand parameters to Orr (2022)'s 2000-2007 estimates, as estimation on these extended periods yields inadmissible demand systems.

Although social bots can be engineered for constructive applications, their potential for misuse in manipulative schemes and malware distribution cannot be overlooked. This dichotomy underscores the critical need to detect social bots on social media platforms. Advances in artificial intelligence have improved the abilities of social bots, allowing them to generate content that is almost indistinguishable from human-created content. These advancements require the development of more advanced detection techniques to accurately identify these automated entities. Given the heterogeneous information landscape on social media, spanning images, texts, and user statistical features, we propose MSM-BD, a Multimodal Social Media Bot Detection approach using heterogeneous information. MSM-BD incorporates specialized encoders for heterogeneous information and introduces a cross-modal fusion technology, Cross-Modal Residual Cross-Attention (CMRCA), to enhance detection accuracy. We validate the effectiveness of our model through extensive experiments using the TwiBot-22 dataset.

As large language models scale, training them requires thousands of GPUs over extended durations--making frequent failures an inevitable reality. While checkpointing remains the primary fault-tolerance mechanism, existing methods fall short when applied to Mixture-of-Experts (MoE) models. Due to their substantially larger training state, MoE models exacerbate checkpointing overheads, often causing costly stalls or prolonged recovery that severely degrade training efficiency. We present MoEvement, a distributed, in-memory checkpointing system tailored for MoE models. MoEvement is built on three key ideas: (1) sparse checkpointing, which incrementally snapshots subsets of experts across iterations to reduce overhead; (2) a sparse-to-dense checkpoint conversion mechanism that incrementally reconstructs consistent dense checkpoints from sparse snapshots; and (3) upstream logging of activations and gradients at pipeline-stage boundaries, enabling localized recovery without re-executing unaffected workers. Evaluations across diverse MoE models with up to 64 experts show that MoEvement reduces checkpointing overhead by up to $4\times$ and recovery overhead by up to $31\times$ compared to state-of-the-art approaches, sustaining ETTR $\ge 0.94$ even under frequent failures (MTBF as low as 10 minutes) and delivering up to $8\times$ overall training speedup, all without compromising synchronous training semantics. Overall, MoEvement offers a robust and scalable fault-tolerance solution for the next generation of sparsely activated models.

First idea is to compute a quantity like the angular momentum with respect to (0, 0), of an unitary mass of coordinates (<[Xi(s)], =[Xi(s)]) while =[s] is the time, and, <[s] = constant. If we impose that the derivative along <[s], at points <[s] = 1/2 is grater than zero, then, we find exactly a known RH equivalence statement about relative maxima and minima of Xi(1/2 + i=[s]) along critical line. After representing this fictitious angular momentum by Euler Product, and, using PNT as a tool, it can be proved that this positivity condition is granted everywhere at least for Xi(1/2 + i=[s]) 6 = 0. So, if the above equivalence is true, it is found that off-critical line zeros must be excluded for Z(s) function along all critical strip . Further analysis on Euler Product(Lemma 2) has evidenced others shorter ways to same objective. Besides the converging spectrum of prime numbers is highlighted as a by-product.

The Maximum Weight Independent Set (MWIS) problem, as well as its related problems such as Minimum Weight Vertex Cover, are fundamental NP-hard problems with numerous practical applications. Due to their computational complexity, a variety of data reduction rules have been proposed in recent years to simplify instances of these problems, enabling exact solvers and heuristics to handle them more effectively. Data reduction rules are polynomial time procedures that can reduce an instance while ensuring that an optimal solution on the reduced instance can be easily extended to an optimal solution for the original instance. Data reduction rules have proven to be especially useful in branch-and-reduce methods, where successful reductions often lead to problem instances that can be solved exactly. This survey provides a comprehensive overview of data reduction rules for the MWIS problem. We also provide a reference implementation for these reductions. This survey will be updated as new reduction techniques are developed, serving as a centralized resource for researchers and practitioners.