Time series analysis from gravitational-wave detectors often relies on the assumption that time chunks, or frequency bins, are uncorrelated. We discuss the validity of this approximation in the context of searches for stochastic gravitational-wave backgrounds. We examine the impact of averaging over time and frequency, a reduction technique commonly employed to minimize the computational expense of likelihood evaluations. We introduce an analytical tool based on Fisher information to quantify the error in parameter inference arising from ignoring these effects. Finally, we address the issue of locally stationary processes and optimal time chunking.

Large Language Models (LLMs) have become indispensable for evaluating writing. However, text feedback they provide is often unintelligible, generic, and not specific to user criteria. Inspired by structured rubrics in education and intelligible AI explanations, we propose iRULER following identified design guidelines to \textit{scaffold} the review process by \textit{specific} criteria, providing \textit{justification} for score selection, and offering \textit{actionable} revisions to target different quality levels. To \textit{qualify} user-defined criteria, we recursively used iRULER with a rubric-of-rubrics to iteratively \textit{refine} rubrics. In controlled experiments on writing revision and rubric creation, iRULER most improved validated LLM-judged review scores and was perceived as most helpful and aligned compared to read-only rubric and text-based LLM feedback. Qualitative findings further support how iRULER satisfies the design guidelines for user-defined feedback. This work contributes interactive rubric tools for intelligible LLM-based review and revision of writing, and user-defined rubric creation.

Asymptotic Giant Branch (AGB) stars significantly contribute to the chemical composition of the universe. In their outflows, complex chemistry takes place, which critically depends on the local temperature. Therefore, if we want to accurately model the AGB environment, we need accurate cooling rates. The CO molecule is abundant in AGB outflows, and has a dipole moment, which enables it to cool through emission from its rotational transitions. We therefore expect it to significantly contribute to cooling in this environment, even at low temperatures ($10$ K $\leqslant T\leqslant 3000$ K). Currently, CO cooling rates are available for ISM-like conditions, which encompasses a different parameter regime, with generally lower densities and velocity gradients, compared to AGB winds. Therefore, these ISM cooling rates might not be applicable to the AGB regime. In this paper, we compute CO cooling rates for hydrodynamics simulations of AGB outflows. To evaluate the net cooling rate, we calculate the energy level distribution of CO self-consistently, using the non Local Thermodynamical Equilibrium (NLTE) line radiative transfer code Magritte. We verify whether already existing CO cooling rate prescriptions for the interstellar medium (ISM) are applicable for this regime. We noticed minor differences between these prescriptions and our calculated cooling rates in general. However, when used far outside their originally intended parameter regimes, significant differences occur. Therefore, we propose a new CO cooling rate prescription for the AGB environment and we study how the computed cooling rate varies depending on input parameters.

Large-scale energy storage has become an inevitable solution for integrating stochastically available renewable energy sources into the electric grid. Vanadium redox flow batteries offer a viable option among other technologies, due to their long lifetime and independently scalable output power and capacity. The electrolyte temperature should be maintained within the range of 5-40 Celsius for safe operation; therefore, a thermal management system is necessary, which affects battery efficiency. The study presents a detailed, containerized battery model with a hybrid thermal management system that considers thermal radiation and real ambient temperatures. A total of 180 configurations were investigated in 10 cases, ranging from 4 to 400 kW, with 18 different discharging current-cell number ratios in each case, including multistack arrangements. Current-dependent ohmic losses influence the electric efficiency, which increases from a minimum of 68% to 89% in low-current configurations. However, the net system efficiency ranges between 43% and 66% due to the self-consumption of pumps, the inverter, and the thermal management system. In addition to the detailed efficiency analysis, a comprehensive investigation of thermal processes is provided in terms of the current-cell number ratio and output power, which is crucial for designing thermal management systems and sizing batteries.

The sense of presence is central to immersive experiences in Virtual Reality (VR), and particularly salient in socially rich platforms like social VR. While prior studies have explored various aspects related to presence, less is known about how ongoing usage behaviors shape presence in everyday engagement. To address this gap, we examine whether usage intensity, captured through frequency of use, session duration, and years of VR experience, predicts presence in social VR. A survey of 295 users assessed overall, social, spatial, and self-presence using validated scales. Results show that both frequency and duration consistently predict higher presence across all dimensions, with interaction effects indicating that frequent and extended sessions synergistically amplify the experience of "being there." These effects were stable across age and gender. Our findings extend presence research beyond the laboratory by identifying behavioral predictors in social VR and offer insights for building inclusive environments that reliably foster presence.

Packages capable of supporting large arrays of high-coherence superconducting qubits are vital for the realisation of fault-tolerant quantum computers and the necessary high-throughput metrology required to optimise fabrication and manufacturing processes. We present a wafer-scale packaging architecture supporting over 500 qubits on a single 3-inch die. The package is engineered to suppress parasitic RF modes, and to mitigate material loss through simulation-informed design while managing differential thermal contraction to ensure robust operation at millikelvin temperatures. System-level heat-load calculations from a large wiring payload show this package may be operated in commercial dilution refrigerators. Measurements of the qubits loaded into the package show median $T_1$, $T_{2e} \sim 100~μ$s ($\sim$100 qubits) alongside readout with median fidelity of 97.5% (54 qubits) and a median qubit temperature of 36 mK (54 qubits). These results validate the performance of these packages and demonstrate that large-scale integration can be achieved without compromising device performance. Finally, we highlight the utility of these packages as a tool for high throughput feedback on qubit figures of merit over large sample sizes, allowing identification of performance outliers in the tails of the coherence distribution, a critical capability for informing fabrication and manufacture of high-quality quantum qubits and quantum processors.

Humans live and act in 3D space, but often work and communicate on 2D surfaces. The prevalence of online communication on 2D screens raises the issue of whether human spatial configuration affects our capabilities, social perception, and behaviors when interacting with others in 2D video chat. How do factors like location, setting, and context subtly shape our online communication, particularly in scenarios such as social support and topic-based discussions? Using Ohyay.co as a platform, we compared a normal gallery interface with a scene-based Room-type interface where participants are located in circular arrangement on screen in a social support task, and found that participants allocated attention to the group as a whole, and had pronounced self-awareness in the Room format. We then chose a two-sided topic for discussion in the Gallery interface and the Room interface where participants on each team face-off against each other, and found that they utilized spatial references to orient their allegiances, expressing greater engagement with those farther away in digital space and greater empathy with those closer, in the Room over the Gallery format. We found spatial effects in the way participants hide from the spotlight, in perspective-taking, and in their use of expressive gestures in time on the screen. This work highlights the need for considering spatial configuration in 2D in the design of collaborative communication systems to optimize for psychological needs for particular tasks.

Valuing corporate bonds in systemic economies is challenging due to intricate webs of inter-institutional exposures. When a bank defaults, cascading losses propagate through the network, with payments determined by a system of fixed-point equations lacking closed-form solutions. Standard Monte Carlo methods cannot capture rare yet critical default events, while existing rare-event simulation techniques fail to account for higher-order network effects and scale poorly with network size. To overcome these challenges, we propose a novel approach -- Bi-Level Importance Sampling with Splitting -- and characterize individual bank defaults by decoupling them from the network's complex fixed-point dynamics. This separation enables a two-stage estimation process that directly generates samples from the banks' default events. We demonstrate theoretically that the method is both scalable and asymptotically optimal, and validate its effectiveness through numerical studies on empirically observed networks.

Viscous hydrodynamic flow in a small, slowly evaporating, sessile hemispherical droplet with a pinned contact line is considered. Analytical solutions are obtained for the Deegan outward flow, which is responsible for the coffee ring effect, as well as the Marangoni flow excited by a surface tension gradient. It is assumed that the surface tension gradient may be caused by anisotropic cooling of droplet surface or other factors, such as nonuniform illumination of an optically active surfactant. Two main types of boundary conditions, no-slip and full-slip, are considered in describing the flow-substrate interaction. It is shown that under the no-slip condition, there is a rigid relationship between the evaporation rate and the surface tension gradient, which imposes strict requirements on the temperature regime inside the droplet. This result offers a new vision of the critical Marangoni number, which describes the threshold for the transition of an evaporating droplet from capillary flow to developed Marangoni convection. The results of this work may attract the attention of experimenters to the study of the sensitivity of viscous flow in an evaporating droplet to the liquid-substrate boundary conditions, especially if the system under consideration passes into the Marangoni regime, when the no-slip condition changes to a partial or full slip condition due to the increase in viscous shear stress near the substrate.

Most well-known constructions of $(N \times n, q^{Nk}, d)$ maximum rank distance (MRD) codes rely on the arithmetic of $\mathbb{F}_{q^N}$, whose increasing complexity with larger $N$ hinders parameter selection and practical implementation. In this work, based on circular-shift operations, we present a construction of $(J \times n, q^{Jk}, d)$ MRD codes with efficient encoding, where $J$ equals to the Euler's totient function of a defined $L$ subject to $\gcd(q, L) = 1$. The proposed construction is performed entirely over $\mathbb{F}_q$ and avoids the arithmetic of $\mathbb{F}_{q^J}$. We further characterize the constructed MRD codes, Gabidulin codes and twisted Gabidulin codes using a set of $q$-linearized polynomials over the row vector space $\mathbb{F}_{q}^N$, and clarify their inherent difference and connection. For the case $J \neq m_L$, where $m_L$ denotes the multiplicative order of $q$ modulo $L$, we show that the proposed MRD codes, in a family of settings, are different from any Gabidulin code and any twisted Gabidulin code. For the case $J = m_L$, we prove that every constructed $(J \times n, q^{Jk}, d)$ MRD code coincides with a $(J \times n, q^{Jk}, d)$ Gabidulin code, yielding an equivalent circular-shift-based construction that operates directly over $\mathbb{F}_q$. In addition, we prove that under some parameter settings, the constructed MRD codes are equivalent to a generalization of Gabidulin codes obtained by summing and concatenating several $(m_L \times n, q^{m_Lk}, d)$ Gabidulin codes. When $q=2$, $L$ is prime and $n\leq m_L$, it is analyzed that generating a codeword of the proposed $((L-1) \times n, 2^{(L-1)k}, d)$ MRD codes requires $O(nkL)$ exclusive OR (XOR) operations, while generating a codeword of $((L-1) \times n, 2^{(L-1)k}, d)$ Gabidulin codes, based on customary construction, requires $O(nkL^2)$ XOR operations.

We present a compact, cost-effective method for measuring the emittance of kHz-repetition-rate laser-wakefield accelerated electron beams using a permanent solenoid. The measured normalized emittance, $ε_n = 124\,\mathrm{nm \cdot rad}$ ($\simeq 0.04 π\,\mathrm{mm \cdot mrad}$) at $2.7\,$MeV, is comparable to that of ultra-low emittance radiofrequency guns used for electron diffraction. Leveraging this low emittance, we successfully applied the electron beam to electron diffraction. We demonstrate diffraction images obtained from a single crystal Silicon nano-membrane sample, clearly resolving diffraction peaks across multiple orders.

Extensive research has examined presence and basic psychological needs (drawing on Self-Determination Theory) in digital media. While prior work offers hints of potential connections, we lack a systematic account of whether and how distinct presence dimensions map onto the basic needs of autonomy, competence, and relatedness. We surveyed 301 social VR users and analyzed using Structural Equation Modeling. Results show that social presence predicts all three needs, while self-presence predicts competence and relatedness, and spatial presence shows no direct or moderating effects. Gender and age moderated these relationships: women benefited more from social presence for autonomy and relatedness, men from self- and spatial presence for competence and autonomy, and younger users showed stronger associations between social presence and relatedness, and between self-presence and autonomy. These findings position presence as a motivational mechanism shaped by demographic factors. The results offer theoretical insights and practical implications for designing inclusive, need-supportive multiuser VR environments.

We present a family of flattening methods of tensors which we call Kronecker-Koszul flattenings, generalizing the famous Koszul flattenings and further equations of secant varieties studied among others by Landsberg, Manivel, Ottaviani and Strassen. We establish new border rank criteria given by vanishing of minors of Kronecker-Koszul flattenings. We obtain the first explicit polynomial equations -- tangency flattenings -- vanishing on secant varieties of Segre variety, but not vanishing on cactus varieties. Additionally, our polynomials have simple determinantal expressions. As another application, we provide a new, computer-free proof that the border rank of the $2\times2$ matrix multiplication tensor is $7$.

We consider quantum walks defined on arbitrary infinite graphs, parameterized by a family of scattering matrices attached to the vertices. Multiplying each scattering matrix by an i.i.d. random phase, we obtain a random scattering quantum walk. We prove dynamical localization for random scattering walks in a large-disorder regime. The result is based on a relation between fractional moment estimates and eigenfunction correlators of independent interest, which we establish for general random unitary operators.

Reconfigurable intelligent surfaces (RISs) are envisioned as a key enabler for next-generation wireless networks, offering programmable control over propagation environments. While extensive research focuses on planar RIS architectures, practical deployments often involve non-planar surfaces, such as structural columns or curved facades, where standard planar beamforming models fail. Moreover, existing analytical solutions for curved RISs are often restricted to specific, pre-defined array manifold geometries. To address this limitation, this paper proposes a novel deep learning (DL) framework for optimizing the phase shifts of non-planar RISs. We first introduce a low-dimensional parametric model to capture arbitrary surface curvature effectively. Based on this, we design a neural network (NN) that utilizes a sparse set of received power measurements to estimate the surface geometry and derive the optimal phase configuration. Simulation results demonstrate that the proposed algorithm converges fast and significantly outperforms conventional planar beamforming designs, validating its robustness against arbitrary surface curvature. We also analyze the impact of the measurement location error on the algorithm's performance.

This report summarizes recent results of differential top quark cross section measurements performed by the ATLAS and CMS experiments. The $t\bar{t}$ process is studied as well as the production of single (anti-)top quarks and the interference with other Standard Model processes of the same final state. State-of-the-art theory predictions are compared to the data. No theory model is able to describe the data across all bins, but an improved description of the data when moving to predictions in higher orders in perturbative QCD can be observed.

Superconducting high field magnets have the capability to generate over 40 T, with multiple existing practical applications globally. However, at such high magnetic fields, these magnets are prone to rapid electrothermal quench which can affect the continuous operation of such magnets. A nested stack configuration, with multiple HTS inserts inside a LTS outsert, can be used for better thermal stability and compact design. We have performed detailed multiphysics quench analysis of such a nested stack high field magnet design under SuperEMFL project using our in-house software, which considers screening currents. Through various case studies, we have identified various weak spots in such a magnet, where thermal quench can be the most detrimental for magnet operation, and various ways are suggested to overcome this important issue.

Extended Reality (XR) combines dense sensing, real-time rendering, and close-range interaction, making its use in early childhood education both promising and high risk. To investigate this, we conduct a Systematization of Knowledge (SoK) of 111 peer-reviewed studies with children aged 3-8, quantifying how technical, pedagogical, health, privacy, and equity challenges arise in practice. We found that AR dominates the landscape (73%), focusing primarily on tablets or phones, while VR remains uncommon and typically relies on head mounted displays (HMDs). We integrate these quantitative patterns into a joint risk and attention matrix and an Augmented Human Development (AHD) model that link XR pipeline properties to cognitive load, sensory conflict, and access inequity. Finally, implementing a seven dimension coding scheme on a 0 - 2 scale, we obtain mean scholarly attention scores of 1.56 for pedagogy, 1.04 for privacy (primarily procedural consent), 0.96 for technical reliability, 0.92 for accessibility in low resource contexts, 0.81 for medical and health issues, 0.52 for accessibility for disabilities, and 0.14 for data security practices. This indicates that pedagogy receives the most systematic scrutiny, while data access practices is largely overlooked. We conclude by offering a roadmap for Child-Centered XR that helps HCI researchers and educators move beyond novelty to design systems that are developmentally aligned, secure by default, and accessible to diverse learners.

We study the impact of light GeV-scale heavy neutral leptons (HNLs) on Big Bang nucleosynthesis (BBN) in the neutrino-extended Standard Model Effective Field Theory ($ν$SMEFT). We show that, based on very general considerations, BBN constraints complement laboratory searches at colliders, beam dumps, and neutrinoless double beta decay, by providing an upper bound on the cut-off scale of the effective field theory for HNL masses above $\sim$100 MeV. We identify target regions for future laboratory probes of the $ν$SMEFT parameter space that is bounded from above and below.

Advanced computational tools that describe the interaction of electrons with structured nanophotonic materials are crucial for theoretical predictions, specific design tasks, and the interpretation of experimental results. These tools open the door to systematic exploration of free-electron-driven nanophotonic light sources, among others. Here, we report on the implementation of electron-beam spectroscopy in a T-matrix-based scattering formulation. Such a framework is quite versatile in predicting the electromagnetic response of complex photonic materials composed of periodically or aperiodically arranged individual scatterers. By extending this formalism to describe interactions with fast electrons, we provide a fast and accurate numerical tool for simulating cathodoluminescence (CL) and electron energy-loss spectroscopy (EELS) measurements. The desired functionalities are implemented into the existing software suite treams for electromagnetic scattering computations, and the extended code treams_ebeam is available online at https://github.com/tfp-photonics/treams_ebeam. We demonstrate the implementation details on a carefully selected set of problems, including single scatterers of various shapes and materials, a periodic chain of elliptical nanodisks, and a finite cluster of nanospheres arranged in a two-dimensional (2D) lattice. By uniting fast-electron physics with advanced scattering theory, our framework unlocks new possibilities for designing, understanding, and engineering next-generation nanoscale light-matter interactions.

Data on marriage flows are not available in most developing countries, making marriage market imbalance difficult to measure. Existing measures use crude fertility rates and do not account for early-life mortality, overstating the number of births surviving to marriageable ages. This paper develops the Surplus Groom Index to quantify marriage market imbalance under monogamy using census age structure, vital registration of births and deaths, and marriage timing data. The index incorporates effective fertility-total births adjusted for under-five mortality - to reflect actual cohort progression from birth to marriageable ages. This adjustment matters in settings where child mortality shapes the supply of marriage partners. Using India's 2011 Census data, we find that eleven percent of men aged 15-54 cannot marry due to bride shortage, approximately 39 million men. Marriage imbalance is widespread rather than regionally concentrated. Punjab records the highest deficit at 33 percent, but states considered demographically progressive show substantial imbalance: Kerala 18 percent, West Bengal 14 percent, Karnataka and Tamil Nadu 11 percent each. Declining fertility has produced smaller female cohorts unable to absorb male-heavy cohorts from earlier birth years. Balanced sex ratios at birth do not ensure marriage market equilibrium once fertility declines and marriage is delayed.

Let $Λ$ be the category of based finite sets $\mathbf{n}$ and based injections. We study properties of monoids and modules in $Λ$-sequences under the Kelly monoidal structure. In particular, we show that the forgetful functor from right modules in $Λ$-sequences to right modules in symmetric sequences is an isomorphism. We show that any compatible lower data extends to a normal oplax monoidal structure and use this to establish a universal normal oplax monoidal structure on $Λ$-sequences extending the Kelly product, identifying unital operads to monoids in unital $Λ$-sequences for a general symmetric monoidal category $\mathscr{V}$. We also establish a closed monoidal localization theorem.

The recent discovery of robust quantum anomalous Hall (QAH) effect in rhombohedral multilayer graphene (RMG) aligned with hexagonal boron nitride (hBN) has established a highly versatile platform for correlated topological matter. This review synthesizes the experimental and theoretical progress in understanding these interaction-driven topological phases. Experimentally, the landscape has rapidly expanded from initial Chern insulators in trilayer systems to fully quantized QAH states in thicker systems. Theoretically, it is believed that moiré potential and electron-electron interaction cooperate and produce the QAH effect in such systems. Theoretical calculations also bring interesting questions, such as the formation of an interaction-driven topological phase known as an anomalous Hall crystal (AHC). This review comprehensively covers the experimental hallmarks, the theoretical frameworks, including continuum models and many-body approaches, and the ensuing physical picture that reconciles the roles of interactions, displacement fields, and the moiré potentials. We conclude by outlining outstanding open questions and future directions, positioning RMG/hBN systems at the forefront of topological quantum matter.

The kinematics of particles and rigid bodies in the plane are investigated up to higher-order accelerations. Discussion of point trajectories leads from higher-order poles to higher-order Bresse circles of the moving plane. Symplectic geometry in vector space R^2 is used here as a new approach and leads to some new recursive vector formulas. This article is dedicated to the memory of Professor Pennestri.

QUIC, as the transport layer of the next-generation Web stack (HTTP/3), natively provides security and performance improvements over TCP-based stacks. However, since QUIC provides end-to-end encryption for both data and packet headers, in-network assistance like Performance-Enhancing Proxy (PEP) is unavailable for QUIC. To achieve the similar optimization as TCP, some works seek to collaborate endpoints and middleboxes to provide in-network assistance for QUIC. But involving both host and in-network devices increases the difficulty of deployment in the Internet. In this paper, by analyzing the QUIC standard, implementations, and the locality of application traffic, we identify opportunities for transparent middleboxes to measure RTT and infer packet loss for QUIC connections, despite the absence of plaintext ACK information. We then propose PEMI as a concrete system that continuously measures RTT and infers lost packets, enabling fast retransmissions for QUIC. PEMI enables performance enhancement for QUIC in a completely transparent manner, without requiring any explicit cooperation from the endpoints. To keep fairness, PEMI employs a delay-based congestion control and utilizes feedback-based methods to enforce CWND. Extensive evaluation results, including Mininet and trace-driven dynamic experiments, show that PEMI can significantly improve the performance of QUIC. For example, in the Mininet experiments, PEMI increases the goodput of file transfers by up to 2.5$\times$, and reduces the 90th percentile jitter of RTC frames by 20-75%.

A consequence of the recent work of Ren and Zhu on Gorenstein projective dimensions of modules over Hopf algebras is that if $A$ and $B$ are Hopf algebras with bijective antipodes having equivalent linear tensor categories of comodules and both having finite global dimensions, then their global dimensions coincide. In this note we provide a direct proof of this result, without using Gorenstein projective dimensions, and we notice that the assumption on the bijectivity of the antipodes can be removed.

Life over the past four billion years has been shaped by proteins and their capacity to assemble into three dimensional conformations. Protein sequence alignments have been the enabling technology for exploring the evolution and functional adaptation of proteins across the tree of life. Recent advancements in scaling the prediction of three dimensional protein structures from primary sequence alone, revealed that different modes of conservation and function operate on the sequence and structure level. This difference in protein conservation patterns and their underlying functional change that could emerge in suboptimal alignment configurations is often ignored in optimal protein alignment approaches. We introduce EMERALD-UI, an open-source interactive web application which is designed to reveal unexplored biology by visualising stable structural conformations or protein regions hidden in the suboptimal alignment space. Availability: EMERALD-UI is available at https://algbio.github.io/emerald-ui/. Contact: hdrost001@dundee.ac.uk or alexandru.tomescu@helsinki.fi.

We introduce a real-parameter refinement of the classical integer hierarchies underlying Schmidt number, block-positivity, and $k$-positivity for maps between matrix algebras. Starting from a compact family of $α$-admissible unit vectors ($α\in[1,d]$), we define closed cones $\mathsf K_α$ of bipartite positive operators that interpolate strictly between successive Schmidt-number cones, together with their dual witness cones. Via the Choi--Jamiołkowski correspondence this yields a matching filtration of map cones $\mathsf P_α$, recovering the usual $k$-positive/$k$-superpositive classes at integer parameters and complete positivity at the top endpoint. Two results show that the fractional levels capture genuinely new structure. First, we prove a \emph{fractional Kraus theorem}: $α$-superpositive maps are precisely the completely positive maps admitting a Kraus decomposition whose Kraus operators satisfy an explicit singular-value (Ky--Fan) constraint, extending the classical rank-$k$ characterization. Second, for non-integer $α$ the cones $\mathsf P_α$ fail stability under CP post-composition, highlighting a sharp structural transition away from the integer theory. Finally, we derive sharp thresholds on canonical symmetric families (including the depolarizing ray and the isotropic slice), turning familiar stepwise criteria into continuous, computable profiles.

This study systematically investigates the cosmological dynamics of two well-motivated functional forms in $f(T,B)$ gravity within a flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. Here $T$ denotes the torsion scalar and $B$ the boundary term, with the special choice $f(T,B) = - T + B$ recovering General Relativity. We focus on a multiplicative power-law model $f(T,B) = c_1 T^αB^β$ and an additive mixed power-law model $f(T,B) = c_2 T^α+ c_3 B^β$. Using dynamical system techniques, we construct autonomous systems and identify de Sitter attractors that naturally explain late-time cosmic acceleration. Analytical stability conditions for these fixed points are derived, and numerical simulations reveal characteristic evolutionary patterns, such as spiral trajectories and damped oscillations in the additive mixed power-law model. Furthermore, statefinder diagnostics are applied to quantitatively distinguish these models from the standard $Λ$CDM paradigm and other dark energy scenarios. The results indicate that $f(T,B)$ gravity offers a theoretically consistent and observationally distinguishable geometric framework for explaining cosmic acceleration, presenting a compelling alternative to conventional dark energy models.

Modern knowledge-intensive systems, such as retrieval-augmented generation (RAG), rely on effective retrievers to establish the performance ceiling for downstream modules. However, retriever training has been bottlenecked by sparse, single-positive annotations, which lead to false-negative noise and suboptimal supervision. While the advent of large language models (LLMs) makes it feasible to collect comprehensive multi-positive relevance labels at scale, the optimal strategy for incorporating these dense signals into training remains poorly understood. In this paper, we present a systematic study of multi-positive optimization objectives for retriever training. We unify representative objectives, including Joint Likelihood (JointLH), Summed Marginal Likelihood (SumMargLH), and Log-Sum-Exp Pairwise (LSEPair) loss, under a shared contrastive learning framework. Our theoretical analysis characterizes their distinct gradient behaviors, revealing how each allocates probability mass across positive document sets. Empirically, we conduct extensive evaluations on Natural Questions, MS MARCO, and the BEIR benchmark across two realistic regimes: homogeneous LLM-annotated data and heterogeneous mixtures of human and LLM labels. Our results show that LSEPair consistently achieves superior robustness and performance across settings, while JointLH and SumMargLH exhibit high sensitivity to the quality of positives. Furthermore, we find that the simple strategy of random sampling (Rand1LH) serves as a reliable baseline. By aligning theoretical insights with empirical findings, we provide practical design principles for leveraging dense, LLM-augmented supervision to enhance retriever effectiveness.