Subnational monitoring of public health and development indicators often relies on household surveys where data are sparse at the desired spatial resolution. Small area estimation (SAE) methods address this challenge by borrowing strength across areas and incorporating auxiliary information. However, comparing these estimators remains difficult in the absence of ground truth. We propose a design-based cross-validation framework for evaluating small area estimators that accommodates complex survey designs. Our approach enables model-agnostic comparisons between area-level and unit-level SAE models. We derive a decomposition of the conditional mean squared error that yields a consistent cross-validation score, show that finite-sample comparisons carry an unidentifiable bias that can be bounded, and use this bound as a principled threshold for ranking models. We further show that leave-one-area-out cross-validation, a popular alternative, targets extrapolation rather than smoothing error and can reverse the correct ranking. We evaluate the framework through extensive design-based simulations. We apply the framework to compare subnational female literacy estimators in Zambia using the
The emergence of breakthrough artificial intelligence (AI) techniques has led to a renewed focus on how small data settings, i.e., settings with limited information, can benefit from such developments. This includes societal issues such as how best to include under-represented groups in data-driven policy and decision making, or the health benefits of assistive technologies such as wearables. We provide a conceptual overview, in particular contrasting small data with big data, and identify common themes from exemplary case studies and application areas. Potential solutions are described in a more detailed technical overview of current data analysis and modelling techniques, highlighting contributions from different disciplines, such as knowledge-driven modelling from statistics and data-driven modelling from computer science. By linking application settings, conceptual contributions and specific techniques, we highlight what is already feasible and suggest what an agenda for fully leveraging small data might look like.
Large Language Models (LLMs) have made significant progress in advancing artificial general intelligence (AGI), leading to the development of increasingly large models such as GPT-4 and LLaMA-405B. However, scaling up model sizes results in exponentially higher computational costs and energy consumption, making these models impractical for academic researchers and businesses with limited resources. At the same time, Small Models (SMs) are frequently used in practical settings, although their significance is currently underestimated. This raises important questions about the role of small models in the era of LLMs, a topic that has received limited attention in prior research. In this work, we systematically examine the relationship between LLMs and SMs from two key perspectives: Collaboration and Competition. We hope this survey provides valuable insights for practitioners, fostering a deeper understanding of the contribution of small models and promoting more efficient use of computational resources. The code is available at https://github.com/tigerchen52/role_of_small_models
GPT has become nearly synonymous with large language models (LLMs), an increasingly popular term in AIED proceedings. A simple keyword-based search reveals that 61% of the 76 long and short papers presented at AIED 2024 describe novel solutions using LLMs to address some of the long-standing challenges in education, and 43% specifically mention GPT. Although LLMs pioneered by GPT create exciting opportunities to strengthen the impact of AI on education, we argue that the field's predominant focus on GPT and other resource-intensive LLMs (with more than 10B parameters) risks neglecting the potential impact that small language models (SLMs) can make in providing resource-constrained institutions with equitable and affordable access to high-quality AI tools. Supported by positive results on knowledge component (KC) discovery, a critical challenge in AIED, we demonstrate that SLMs such as Phi-2 can produce an effective solution without elaborate prompting strategies. Hence, we call for more attention to developing SLM-based AIED approaches.
Supersymmetric elementary string states in the compactified heterotic string theory are described by small black holes that have zero area event horizon. In this paper we compute the supersymmetric index of such elementary string states using gravitational path integral. The dominant contribution to the path integral comes from an Euclidean rotating black hole solution of the supergravity theory with a finite area event horizon, but the logarithm of the index, computed from the saddle point, vanishes. Nevertheless we show that the solution is singular on certain subspaces of the horizon where higher derivative corrections can be important, and once the higher derivative corrections are taken into account the solution could yield a finite result for the logarithm of the index whose form agrees with the microscopic results up to an overall numerical constant. While the numerical constant is not determined in our analysis, we show that it is independent of the details of the compactification and even the number of non-compact dimensions, in agreement with the microscopic results.
In this paper we propose a novel solution called dynamic spectrum refarming (DSR) for deploying LTE small cells using the same spectrum as existing GSM networks. The basic idea of DSR is that LTE small cells are deployed in the GSM spectrum but suppress transmission of all signals including the reference signals in some specific physical resource blocks corresponding to a portion of the GSM carriers to ensure full GSM coverage. Our study shows that the proposed solution can provide LTE mobile terminals with high speed data services when they are in the coverage of the LTE small cells while minimally affecting the service provided to GSM terminals located within the LTE small cell coverage area. Thus, the proposal allows the normal operation of the existing GSM networks even with LTE small cells deployed in that spectrum. Though the focus of this paper is about GSM spectrum refarming, an analogous approach can be applied to reuse code division multiple access (CDMA) spectrum for LTE small cells.
Standard error correction techniques only provide a quantum memory and need extra gadgets to perform computation. Central to quantum algorithms are small angle rotations, which can be fault-tolerantly implemented given a supply of an unconventional species of magic state. We present a low-cost distillation routine for preparing these small angle magic states. Our protocol builds on the work of Duclos-Cianci and Poulin [Phys. Rev. A, 91, 042315 (2015)] by compressing their circuit. Additionally, we present a method of diluting magic states that reduces costs associated with very small angle rotations. We quantify performance by the expected number of noisy magic states consumed per rotation, and compare with other protocols. For modest size angles, our protocols offer a factor 24 improvement over the best known gate synthesis protocols and a factor 2 over the Duclos-Cianci and Poulin protocol. For very small angle rotations, the dilution protocol dramatically reduces costs, giving several orders magnitude improvement over competitors. There also exists an intermediary regime of small, but not very small, angles where our approach gives a marginal improvement over gate synthesis. We
We extend the small cap decoupling program established by Demeter, Guth, and Want to paraboloids in $\mathbb{R}^n$ for some range of $p$.
It is most natural to assume that mysterious Small Ionized and Neutral Structures (SINS) indiffuse ISM arise from turbulence. There are two obvious problem with such an explanation, however. First of all, it is generally believed that at the small scales turbulence should be damped. Second, turbulence with Kolmogorov spectrum cannot be the responsible for the SINS. We consider, however, effects, that provide spectral index flatter than the Kolmogorov one and allow action at very small scales. These are the shocks that arise in high Mach number turbulence and transfer of energy to small scales by instabilities in cosmic rays. Our examples indicate that the origin of SINS may be discovered through systematic studies of astrophysical turbulence.
A constellation of remote sensing small satellite system has been developed for infrastructure monitoring in India by using SAR Payload. The LEO constellation of the small satellites is designed in a way, which can cover the entire footprint of India. Since India lies a little above the equatorial region, the orbital parameters are adjusted in a way that inclination of 36 degrees and RAAN varies from 70-130 degrees at a height of 600 km has been considered. A total number of 4 orbital planes are designed in which each orbital plane consisting 3 small satellites with 120-degrees true anomaly separation. Each satellite is capable of taking multiple look images with the minimum resolution of 1 meter per pixel and swath width of 10 km approx. The multiple look images captured by the SAR payload help in continuous infrastructure monitoring of our interested footprint area in India. Each small satellite is equipped with a communication payload that uses X-band and VHF antenna, whereas the TT&C will use a high data-rate S-band transmitter. The paper presents only a coverage metrics analysis method of our designed constellation for our India footprint by considering the important metri
The generation of large-scale magnetic fields is generically accompanied by the more rapid growth of small-scale fields. The growing Lorentz force due to these fields back reacts on the turbulence to saturate the mean-field and small-scale dynamos. For the mean-field dynamo, in a quasi-linear treatment of this saturation, it is generally thought that, while the alpha-effect gets renormalised and suppressed by non-linear effects, the turbulent diffusion is left unchanged. We show here that this is not true and the effect of the Lorentz forces, is also to generate additional non-linear hyperdiffusion of the mean field. A combination of such non-linear hyperdiffusion with diffusion at small scales, also arises in a similar treatment of small-scale dynamos, and is crucial to understand its saturation.
Attitude estimation or determination is a fundamental task for satellites to remain effectively operational. This task is furthermore complicated on small satellites by the limited space and computational power available on-board. This, coupled with a usually low budget, restricts small satellites from using high precision sensors for its especially important task of attitude estimation. On top of this, small satellites, on account of their size and weight, are comparatively more sensitive to environmental or orbital disturbances as compared to their larger counterparts. Magnetic disturbance forms the major contributor to orbital disturbances on small satellites in Lower Earth Orbits (LEO). This magnetic disturbance depends on the Residual Magnetic Moment (RMM) of the satellite itself, which for higher accuracy should be determined in real-time. This paper presents a method for in-orbit estimation of the satellite magnetic dipole using a Random Walk Model in order to circumnavigate the inaccuracy arising due to unknown orbital magnetic disturbances. It is also ensured that the dipole as well as attitude estimation of the satellite is done using only a magnetometer as the sensor.
We consider the quotient group $T(G)$ of the multiple holomorph by the holomorph of a finite $p$-group $G$ of class two for an odd prime $p$. By work of the first-named author, we know that $T(G)$ contains a cyclic subgroup of order $p^{r-1}(p-1)$, where $p^r$ is the exponent of the quotient of $G$ by its center. In this paper, we shall exhibit examples of $G$ (with $r = 1$) such that $T(G)$ has order exactly $p-1$, which is as small as possible.
We study the cosmological origin of small-scale DM clumps in the hierarchical scenario with the most conservative assumption of adiabatic Gaussian fluctuations. The mass spectrum of small-scale clumps with M<10^3Msun is calculated with tidal destruction of the clumps taken into account within the hierarchical model of clump structure. Only 0.1-0.5% of small clumps survive the stage of tidal destruction in each logarithmic mass interval. The mass distribution of clumps has a cutoff at Mmin due to diffusion of DM particles out of a fluctuation and free streaming at later stage. Mmin is a model dependent quantity. In the case the neutralino DM, considered as a pure bino, Mmin~10^-8 Msun. The evolution of density profile in a DM clump does not result in the singularity because of formation of the core under influence of tidal interaction. The radius of the core is ~0.1R, where R is radius of the clump. The applications for annihilation of DM particles in the Galactic halo are studied. The number density of clumps as a function of their mass, radius and distance to the Galactic center is presented. The enhancement of annihilation signal due to clumpiness, valid for arbitrary DM parti
The generation of dark matter in late decays of quasi-stable massive particles has been proposed as a viable framework to address the excess of power found in numerical N-body simulations for cold dark matter cosmologies. We identify a convenient set of variables to illustrate which requirements need to be satisfied in any generic particle physics model to address the small scale problems and to fulfill other astrophysical constraints. As a result of this model-independent analysis, we point out that meeting these requirements in a completely natural way is inherently difficult. In particular, we re-examine the role of gravitinos and Kaluza-Klein gravitons in this context and find them disfavoured as a solution to the small-scale problems in case they are DM candidates generated in the decay of thermally produced WIMPs. We propose right-handed sneutrinos and right-handed Kaluza-Klein neutrinos as alternatives. We find that they are viable dark matter candidates, but that they can contribute to a solution of the small scale problems only in case the associated Dirac neutrino mass term appears as a subdominant contribution in the neutrino mass matrix.
A profinite group is called small if it has only finitely many open subgroups of index n for each positive integer n. We show that every Frattini cover of a small profinite group is small. A profinite group is called strongly complete if every subgroup of finite index is open. We show that two profinite groups that are elementarily equivalent, in the first-order language of groups, are isomorphic if one of them is strongly complete, extending a result of Moshe Jarden and Alexander Lubotzky which treats the case of finitely generated profinite groups.
Interactions between galaxies have spectacular effects on gas dynamics, and small galaxy groups are a privileged place to investigate them. In particular, they could test the existence of cold H2 gas as dark matter in the outer parts of galaxies. HI observations have revealed that galaxies in small groups are deficient in atomic gas, like in richer galaxy clusters such as Virgo, although in a lesser extent. Galaxy interactions could be the cause of this deficiency, stripping the gas out of galaxies and enriching the inter-cluster medium (ICM) in hot gas, which in turn strips gas through ram pressure. Alternatively, the gas present at the formation of the group could have been heated to its virial temperature, and be observed now as X-rays. The dynamical processes related to this extended gas in small galaxy groups are reviewed.
A third workshop on small-x physics, within the Small-x Collaboration, was held in Hamburg in May 2004 with the aim of overviewing recent theoretical progress in this area and summarizing the experimental status.
We investigate the role of compressibility in the modified quasi-linear viscoelastic (MQLV) constitutive framework for soft solids at finite strain, where shear and bulk responses are governed by distinct relaxation functions. Analytical and semi-analytical results are derived for simple shear and torsion, under incompressible and slightly compressible assumptions. We show that compressibility affects the response only when volume changes occur: under isochoric deformations, the bulk contribution vanishes, while even small deviations from isochoricity significantly alter the normal response. Shear stress and torque are largely insensitive to compressibility, whereas normal stress and axial force exhibit pronounced sensitivity due to the coupling between shear and bulk relaxation. We further demonstrate that volumetric effects interact with the Poynting effect: in simple shear they oppose each other, reducing relaxation, while in torsion they reinforce each other, enhancing it. These trends agree with brain tissue experiments but reveal limitations of the slightly compressible model for highly compressible materials, such as agarose gels. Overall, the results emphasise the importanc
This paper examines changes in occupational crowding of immigrant women in frontline industries in the United States during the onset of COVID-19, and we contextualize their experiences against the backdrop of broader race-based and gender-based occupational crowding. Building on the occupational crowding hypothesis, which suggests that marginalized workers are crowded in a small number of occupations to prop up wages of socially-privileged workers, we hypothesize that immigrant, Black, and Hispanic workers were shunted into frontline work to prop up the health of others during the pandemic. Our analysis of American Community Survey microdata indicates that immigrant workers, particularly immigrant women, were increasingly crowded in frontline work during the onset of the pandemic. We also find that US-born Black and Hispanic workers disproportionately faced COVID-19 exposure in their work, but were not increasingly crowded into frontline occupations following the onset of the pandemic. The paper also provides a rationale for considering the occupational crowding hypothesis along the dimensions of both wages and occupational health.