Miracle-dz/UniFAR-FTUs huggingface dataset:
On Abelian extensions in mixed characteristic and ramification in codimension one

A theorem of Paul Roberts states that the integral closure of a regular local ring in a generically abelian extension is Cohen-Macaulay, provided the characteristic of the residue field does not divide the order of the Galois group. An example of Koh shows the conclusion is false in the modular case. After a modification to the statement concerning ramification over $p$ in codimension one, we give an extension of Roberts's theorem to the modular case for unramified regular local rings in mixed characteristic when the $p$-torsion of the Galois group is annihilated by $p$.
The Moving Discontinuous Galerkin Method with Interface Condition Enforcement for the Simulation of Hypersonic, Viscous Flows

The moving discontinuous Galerkin method with interface condition enforcement (MDG-ICE) is a high-order, r-adaptive method that treats the grid as a variable and weakly enforces the conservation law, constitutive law, and corresponding interface conditions in order to implicitly fit high-gradient flow features. In this paper, we develop an optimization solver based on the Levenberg-Marquardt algorithm that features an anisotropic, locally adaptive penalty method to enhance robustness and prevent cell degeneration in the computation of hypersonic, viscous flows. Specifically, we incorporate an anisotropic grid regularization based on the mesh-implied metric that inhibits grid motion in directions with small element length scales, an element shape regularization that inhibits nonlinear deformations of the high-order elements, and a penalty regularization that penalizes degenerate elements. Additionally, we introduce a procedure for locally scaling the regularization operators in an adaptive, elementwise manner in order to maintain grid validity. We apply the proposed MDG-ICE formulation to two- and three-dimensional test cases involving viscous shocks and/or boundary layers, including Mach 17.6 hypersonic viscous flow over a circular cylinder and Mach 5 hypersonic viscous flow over a sphere, which are very challenging test cases for conventional numerical schemes on simplicial grids. Even without artificial dissipation, the computed solutions are free from spurious oscillations and yield highly symmetric surface heat-flux profiles.
Provably Time-Optimal Cooling of Markovian Quantum Systems

We address the problem of cooling a Markovian quantum system to a pure state in the shortest amount of time possible. Here the system drift takes the form of a Lindblad master equation and we assume fast unitary control. This setting allows for a natural reduction of the control system to the eigenvalues of the state density matrix. We give a simple necessary and sufficient characterization of systems which are (asymptotically) coolable and present a powerful result which allows to considerably simplify the search for optimal cooling solutions. With these tools at our disposal we derive explicit provably time-optimal cooling protocols for rank one qubit systems, inverted $\Lambda$-systems on a qutrit, and a certain system consisting of two coupled qubits.
Examination of WSR-88D VWP Data in Proximity to Strong Tornadoes

Among other factors, it is well-established that influences of at least sufficiently strong shear and storm relative helicity (SRH) within the lowest few km AGL are key ingredients with respect to supercells that tend to produce tornadoes. Observationally monitoring and evaluating temporal trends and relatively fine-scale changes of low-level shear and SRH are critically important to operational forecasters at the Storm Prediction Center (SPC) and other National Weather Service (NWS) offices. One method for monitoring such low-level wind changes can be done through means such as the Weather Surveillance Radar-1988 Doppler (WSR88D) network derived velocity azimuth display (VAD) wind profile (VWP). VWP data from WSR-88Ds offer much greater temporal and spatial observational density as compared to observed rawinsondes (typically only twice a day) and wind profilers (mainly central United States and recently decreasing in number). Wind information is processed by the WSR88D VAD algorithm and if sufficient data reliability exists (symmetry and lack of statistical error), the VWP displays areal-averaged horizontal winds on a time versus height basis for each radar volume scan when sufficient scatterers are available (Klazura and Imy 1993). Stensrud et al. (1990) found VAD wind data to be comparable to a digital sounding system except when winds were weak. A number of other studies have discussed possible VWP biases and contamination issues from migratory birds and fronts (e.g. Niziol 1998; Gauthreaux et al. 1998) along with other potential errors and discrepancies (Nelson et al. 1995). While VWP data may be subject to reliability uncertainty and associated caveats (as any dataset), available VWP data (for which sufficient scatterers existed) were used in this study on an as-is basis, especially given its operational availability and, oftentimes, lack of pseudo real-time alternatives. A number of past studies have used proximity rawinsonde data (Davies and Johns 1993; Craven and Brooks 2004) and model-based (e.g., RUC; Thompson et al. 2003) information to estimate supercell tornado environments, but relatively fewer aggregate tornado studies have utilized WSR-88D VWP information to evaluate vertical wind shear associated with tornadoes. Medlin and Bunkers
Group Privacy Amplification and Unified Amplification by Subsampling for R\'enyi Differential Privacy

Differential privacy (DP) has various desirable properties, such as robustness to post-processing, group privacy, and amplification by subsampling, which can be derived independently of each other. Our goal is to determine whether stronger privacy guarantees can be obtained by considering multiple of these properties jointly. To this end, we focus on the combination of group privacy and amplification by subsampling. To provide guarantees that are amenable to machine learning algorithms, we conduct our analysis in the framework of R\'enyi-DP, which has more favorable composition properties than $(\epsilon,\delta)$-DP. As part of this analysis, we develop a unified framework for deriving amplification by subsampling guarantees for R\'enyi-DP, which represents the first such framework for a privacy accounting method and is of independent interest. We find that it not only lets us improve upon and generalize existing amplification results for R\'enyi-DP, but also derive provably tight group privacy amplification guarantees stronger than existing principles. These results establish the joint study of different DP properties as a promising research direction.
BNSR-Invariants of Surface Houghton Groups

The surface Houghton groups $\mathcal{H}_{n}$ are a family of groups generalizing Houghton groups $H_n$, which are constructed as asymptotically rigid mapping class groups. We give a complete computation of the BNSR-invariants $\Sigma^{m}(P\mathcal{H}_{n})$ of their intersection with the pure mapping class group. To do so, we prove that the associated Stein--Farley cube complex is CAT(0), and we adapt Zaremsky's method for computing the BNSR-invariants of the Houghton groups. As a consequence, we give a criterion for when subgroups of $H_n$ and $P\mathcal{H}_{n}$ having the same finiteness length as their parent group are finite index. We also discuss the failure of some of these groups to be co-Hopfian.
Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size $\gamma$ and momentum parameter $\beta$ that allows us to identify an intrinsic quantity $\lambda = \frac{ \gamma }{ (1 - \beta)^2 }$ which uniquely defines the optimisation path and provides a simple acceleration rule. When training a $2$-layer diagonal linear network in an overparametrised regression setting, we characterise the recovered solution through an implicit regularisation problem. We then prove that small values of $\lambda$ help to recover sparse solutions. Finally, we give similar but weaker results for stochastic momentum gradient descent. We provide numerical experiments which support our claims.
Corrective or Backfire: Characterizing and Predicting User Response to Social Correction

Online misinformation poses a global risk with harmful implications for society. Ordinary social media users are known to actively reply to misinformation posts with counter-misinformation messages, which is shown to be effective in containing the spread of misinformation. Such a practice is defined as"social correction". Nevertheless, it remains unknown how users respond to social correction in real-world scenarios, especially, will it have a corrective or backfire effect on users. Investigating this research question is pivotal for developing and refining strategies that maximize the efficacy of social correction initiatives. To fill this gap, we conduct an in-depth study to characterize and predict the user response to social correction in a data-driven manner through the lens of X (Formerly Twitter), where the user response is instantiated as the reply that is written toward a counter-misinformation message. Particularly, we first create a novel dataset with 55, 549 triples of misinformation tweets, counter-misinformation replies, and responses to counter-misinformation replies, and then curate a taxonomy to illustrate different kinds of user responses. Next, fine-grained statistical analysis of reply linguistic and engagement features as well as repliers' user attributes is conducted to illustrate the characteristics that are significant in determining whether a reply will have a corrective or backfire effect. Finally, we build a user response prediction model to identify whether a social correction will be corrective, neutral, or have a backfire effect, which achieves a promising F1 score of 0.816. Our work enables stakeholders to monitor and predict user responses effectively, thus guiding the use of social correction to maximize their corrective impact and minimize backfire effects. The code and data is accessible on https://github.com/claws-lab/response-to-social-correction.
High-resolution evolution : calibration and application of fossil foraminifera in evolutionary time series

Many evolutionary processes are well-studied on generational and macroevolutionary time scales, but much less is known about the processes bridging short- and long-term biotic change. This is commonly due to a lack of sufficiently-high-resolution fossil records over long microevolutionary time scales. The work presented in this thesis describes new calibrations and applications of planktonic foraminifera in evolutionary biology. The high-resolution fossil archives of planktonic foraminifera enable construction of continuous, long-term microevolutionary time series of large numbers (>10,000) of individuals.In Chapter 2 I study the repeatability of traits commonly used in studies describing foraminifera evolution. The results show that some traits are reliable, whereas others are very susceptible to small mounting-induced errors and should be used with caution.Chapter 3 deals with various representations of foraminifera body size, and whether these proxies remain accurate in a lineage undergoing morphological change. This was shown to be the case for foraminifera shell area as measured from a two-dimensional image, but less so for shell diameter.In Chapter 4 I study within- and among-population allometries during an interval of global climatic upheaval. When climate remains constant the within-population allometries predict evolutionary change from one time-step to the next. However, the evolutionary allometry measured across step-wise environmental change deviates significantly from the static evolutionary allometries.Changes in biodiversity are often linked to climate change, usually represented by global temperature. However, climate consists of many interacting variables, and species likely respond to the entire climate system as opposed to individual variables. In Chapter 5 I show that evolutionary response in two species of planktonic foraminifera is indeed best explained by combinations of environmental parameters.Chapter 6 presents evolutionary time series of two species of planktonic foraminifera from six sites along an Atlantic transect over 600,000 years. The results show that temporal dynamics do not match spatial variation, implying that care should be taken when extrapolating one population’s predicted response to another location.
Towards Multimodal Sentiment Analysis Debiasing via Bias Purification

Multimodal Sentiment Analysis (MSA) aims to understand human intentions by integrating emotion-related clues from diverse modalities, such as visual, language, and audio. Unfortunately, the current MSA task invariably suffers from unplanned dataset biases, particularly multimodal utterance-level label bias and word-level context bias. These harmful biases potentially mislead models to focus on statistical shortcuts and spurious correlations, causing severe performance bottlenecks. To alleviate these issues, we present a Multimodal Counterfactual Inference Sentiment (MCIS) analysis framework based on causality rather than conventional likelihood. Concretely, we first formulate a causal graph to discover harmful biases from already-trained vanilla models. In the inference phase, given a factual multimodal input, MCIS imagines two counterfactual scenarios to purify and mitigate these biases. Then, MCIS can make unbiased decisions from biased observations by comparing factual and counterfactual outcomes. We conduct extensive experiments on several standard MSA benchmarks. Qualitative and quantitative results show the effectiveness of the proposed framework.
Quantum duality principal and quantum symmetric pairs

The quantum duality principal (QDP) by Drinfeld predicts a connection between the quantized universial enveloping algebras and the quantized coordinate algebras, where the underlying classical objects are related by the duality in Poisson geometry. The current paper gives an explicit formulization of the QDP for quantum symmetric pairs. Let $\mathfrak{g}$ be a complex semi-simple Lie algebra, equipped with the standard Lie bialgebra structure. Let $\theta$ be a Lie algebra involution on $\mathfrak{g}$ and denote by $\mathfrak{k}=\mathfrak{g}^\theta$ the fixed point subalgebra. The quantum symmetric pair $(\mathrm{U},\mathrm{U}^\imath)$ is originally defined to be a quantization of the symmetric pair of the universial enveloping algebras $(U(\mathfrak{g}),U(\mathfrak{k}))$. In this paper, we show that an explicit specialisation of $(\mathrm{U},\mathrm{U}^\imath)$ gives rise to the pair of the coordinate algebras $(\mathcal{O}(G^*),\mathcal{O}(K^\perp\backslash G^*))$, where $G^*$ is the dual Poisson-Lie group with the Lie algebra $\mathfrak{g}^*$, and $K^\perp\backslash G^*$ is a $G^*$-Poisson homogeneous space. Here $K^\perp$ is the closed subgroup of $G^*$associated to the complementary dual of $\mathfrak{k}$. Therefore $(\mathrm{U},\mathrm{U}^\imath)$ can be viewed as a pair of quantized coordinate algebras. This generalises the well-known fact that the quantum group $\mathrm{U}$ provides a quantization of the coordinate algebra $\mathcal{O}(G^*)$.
A conditional lower bound for the Tur\'an number of spheres

We consider the hypergraph Tur\'an problem of determining $\mathrm{ex}(n, S^d)$, the maximum number of facets in a $d$-dimensional simplicial complex on $n$ vertices that does not contain a simplicial $d$-sphere (a homeomorph of $S^d$) as a subcomplex. We show that if there is an affirmative answer to a question of Gromov about sphere enumeration in high dimensions, then $\mathrm{ex}(n, S^d) \geq \Omega(n^{d + 1 - (d + 1)/(2^{d + 1} - 2)})$. Furthermore, this lower bound holds unconditionally for 2-LC spheres, which includes all shellable spheres and therefore all polytopes. We also prove an upper bound on $\mathrm{ex}(n, S^d)$ of $O(n^{d + 1 - 1/2^{d - 1}})$ using a simple induction argument. We conjecture that the upper bound can be improved to match the conditional lower bound.
Explaining Pre-Trained Language Models with Attribution Scores: An Analysis in Low-Resource Settings

Attribution scores indicate the importance of different input parts and can, thus, explain model behaviour. Currently, prompt-based models are gaining popularity, i.a. , due to their easier adaptability in low-resource settings. However, the quality of attribution scores extracted from prompt-based models has not been investigated yet. In this work, we address this topic by analyzing attribution scores extracted from prompt-based models w.r. t. plausibility and faithfulness and comparing them with attribution scores extracted from fine-tuned models and large language models. In contrast to previous work, we introduce training size as another dimension into the analysis. We find that using the prompting paradigm (with either encoder-based or decoder-based models) yields more plausible explanations than fine-tuning the models in low-resource settings and Shapley Value Sampling consistently outperforms attention and Integrated Gradients in terms of leading to more plausible and faithful explanations.
of the

: Usher syndrome (US) is a clinically and genetically heterogeneous disorder that involves three main features: sensorineural hearing loss, retinitis pigmentosa (RP), and vestibular impairment. With a prevalence of 4–17/100,000, it is the most common cause of deaf-blindness worldwide. Genetic research has provided crucial insights into the complexity of US. Among nine conﬁrmed causative genes, MYO7A and USH2A are major players in US types 1 and 2, respectively, whereas CRLN1 is the sole conﬁrmed gene associated with type 3. Variants in these genes also contribute to isolated forms of hearing loss and RP, indicating intersecting molecular pathways. While hearing loss can be adequately managed with hearing aids or cochlear implants (CIs), approved RP treatment modalities are lacking. Gene replacement and editing, antisense oligonucleotides, and small-molecule drugs hold promise for halting RP progression and restoring vision, enhancing patients’ quality of life. Massively parallel sequencing has identiﬁed gene variants (e.g., in PCDH15 ) that inﬂuence CI results. Accordingly, preoperative genetic examination appears valuable for predicting CI success. To explore genetic mutations in CI recipients and establish correlations between implant outcomes and involved genes, we comprehensively reviewed the literature to gather data covering a broad spectrum of CI outcomes across all known US-causative genes. Implant outcomes were categorized as excellent or very good, good, poor or fair, and very poor. Our review of 95 cochlear-implant patients with US, along with their CI outcomes, revealed the importance of presurgical genetic testing to elucidate potential challenges and provide tailored counseling to improve auditory outcomes. The multifaceted nature of US demands a comprehensive understanding and innovative interventions. Genetic insights drive therapeutic advancements, offering potential remedies for the retinal component of US. The synergy between genetics and therapeutics holds promise for individuals with US and may enhance their sensory experiences through customized interventions.
Strong increases in flood frequency and discharge of the River Meuse over the late Holocene : impacts of long-term anthropogenic land use change and climate variability

Papers published in Hydrology and Earth System Sciences Discussions are under open-access review for the journal Hydrology and Earth System Sciences Strong increases in flood frequency and discharge of the River Meuse over the late Holocene: impacts of long-term anthropogenic land use change and climate variability Abstract Introduction Conclusions References Tables Figures ◭ ◮ ◭ ◮ Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion EGU Abstract In recent years the frequency of high-flow events on the Meuse (northwest Europe) has been relatively great, and flooding has become a major research theme. To date, research has focused on observed discharge records of the last century and simulations of the coming century. However, it is difficult to delineate changes caused by 5 human activities (land use change and greenhouse gas emissions) and natural fluctuations on these timescales. To address this problem we coupled a climate model (ECBilt-CLIO-VECODE) and a hydrological model (STREAM) to simulate daily Meuse discharge in two time-slices: 4000–3000 BP (natural situation), and 1000–2000 AD (includes anthropogenic influence). For 4000–3000 BP the basin is assumed to be 10 almost fully forested; for 1000–2000 AD we reconstructed land use based on historical sources. For 1000–2000 AD the simulated mean annual discharge (260.9 m 3 s −1) is significantly higher than for 4000–3000 BP (244.8 m 3 s −1), and the frequency of large high-flow events (discharge >3000 m 3 s −1) is higher (recurrence time decreases from 77 to 65 years). On a millennial timescale almost all of this increase can be ascribed to 15 land use changes (especially deforestation); the effects of climatic change are insignificant. For the 20th Century, the simulated mean discharge (270.0 m 3 s −1) is higher than in any other century studied, and is ca. 2.5% higher than in the 19th Century (despite an increase in evapotranspiration). Furthermore, the recurrence time of large high-flow events is almost twice as short as under natural conditions (recurrence time 20 decreases from 77 to 40 years). On this timescale climate change (strong increase in annual and winter precipitation) overwhelmed land use change as the dominant forcing mechanism.
Hyporheic Passive Flux Meters Reveal Inverse Vertical Zonation and High Seasonality of Nitrogen Processing in an Anthropogenically Modified Stream (Holtemme, Germany)

Transformation and retention of nitrogen and other biologically reactive solutes in the hyporheic zones of running water contribute to an essential ecosystem service. However, the synoptic impact of intense agricultural or urban land‐uses, elevated nutrient loading, flow alterations, riparian clear‐cutting, and channelization on the source‐sink behavior of solutes in hyporheic zones remains largely uncharacterized and unquantified. Therefore, we studied nutrient dynamics in a hydromorphologically and chemically modified stream reach using a new monitoring approach allowing the simultaneous measurement of nutrient and water flux through a screened area in the subsurface of rivers (hyporheic passive flux meter, HPFM). With HPFMs we directly assessed time‐integrated lateral hyporheic nitrate fluxes during early spring and midsummer covering different temperature and discharge regimes. Contrary to our expectations, higher stream discharge coincided with substantially lower hyporheic exchange rates. While in streams featuring a natural morphology, bed form induced exchange commonly increases with surface flow, the influence of groundwater level was dominant in this reach. Furthermore, in contrast to less impacted environments, where progressive substrate depletion with depths reduces metabolic rates in the subsurface, we identified not the upper, but the intermediate layer of the hyporheic zone as hot spot of nutrient turnover. Overall, the hyporheic zone at the study site functioned partly as nitrate source, partly as a sink. Neither of the commonly used determinants redox state and residence time could explain this source or sink function. Our results give clear evidence to carefully transfer the knowledge of hyporheic zone processes from “natural” systems to anthropologically modified streams.