Miracle-dz/UniFAR-FTUs huggingface dataset:
Properties of Immersions for Systems with Multiple Limit Sets with Implications to Learning Koopman Embeddings

Linear immersions (or Koopman eigenmappings) of a nonlinear system have wide applications in prediction and control. In this work, we study the properties of linear immersions for nonlinear systems with multiple omega-limit sets. While previous research has indicated the possibility of discontinuous one-to-one linear immersions for such systems, it has been unclear whether continuous one-to-one linear immersions are attainable. Under mild conditions, we prove that any continuous immersion to a class of systems including linear systems collapses all the omega-limit sets, and thus cannot be one-to-one. Furthermore, we show that this property is also shared by approximate linear immersions learned from data as sample size increases and sampling interval decreases. Multiple examples are studied to illustrate our results.
The Energy Response of LaBr3(Ce), LaBr3(Ce,Sr) and NaI(Tl) Crystals for GECAM

The GECAM series of satellites utilize LaBr3(Ce), LaBr3(Ce,Sr), and NaI(Tl) crystals as sensitive materials for gamma-ray detectors (GRDs). To investigate the non-linearity in the detection of low-energy gamma rays and address errors in the E-C relationship calibration, comprehensive tests and comparative studies of the non-linearity of these three crystals were conducted using Compton electrons, radioactive sources, and mono-energetic X-rays. The non-linearity test results for Compton electrons and X-rays displayed substantial differences, with all three crystals showing higher non-linearity for X-rays and gamma-rays than for Compton electrons. Despite LaBr3(Ce) and LaBr3(Ce,Sr) crystals having higher absolute light yields, they exhibited a noticeable non-linear decrease in light yield, especially at energies below 400 keV. The NaI(Tl) crystal demonstrated excess light output in the 6~200 keV range, reaching a maximum excess of 9.2% at 30 keV in X-ray testing and up to 15.5% at 14 keV during Compton electron testing, indicating a significant advantage in the detection of low-energy gamma rays. Furthermore, this paper explores the underlying causes of the observed non-linearity in these crystals. This study not only elucidates the detector responses of GECAM, but also marks the inaugural comprehensive investigation into the non-linearity of domestically produced lanthanum bromide and sodium iodide crystals.
Second-Order Subdifferential Optimality Conditions in Nonsmooth Optimization

The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces. The established conditions are expressed in terms of second-order subdifferentials of lower semicontinuous functions and mainly concern prox-regular objectives that cover a large territory in nonsmooth optimization and its applications. Our tools are based on the machinery of variational analysis and second-order generalized differentiation. The obtained general results are applied to problems of nonlinear programming, where the derived second-order optimality conditions are new even for problems with twice continuously differential data, being expressed there in terms of the classical Hessian matrices.
Evolution of the Angular Momentum of Molecular Cloud Cores in Magnetized Molecular Filaments

The angular momentum of molecular cloud cores plays a key role in the star formation process. However, the evolution of the angular momentum of molecular cloud cores formed in magnetized molecular filaments is still unclear. In this paper, we perform 3D magnetohydrodynamics simulations to reveal the effect of the magnetic field on the evolution of the angular momentum of molecular cloud cores formed through filament fragmentation. As a result, we find that the angular momentum decreases by 30% and 50% at the mass scale of 1 M ⊙ in the case of weak and strong magnetic field, respectively. By analyzing the torques exerted on fluid elements, we identify the magnetic tension as the dominant process for angular momentum transfer for mass scales ≲3 M ⊙ for the strong magnetic field case. This critical mass scale can be understood semianalytically as the timescale of magnetic braking. We show that the anisotropy of the angular momentum transfer due to the presence of a strong magnetic field changes the resultant angular momentum of the core only by a factor of 2. We also find that the distribution of the angle between the rotation axis and the magnetic field does not show strong alignment even just before the first core formation. Our results also indicate that the variety of the angular momentum of the cores is inherited from the difference in the phase of the initial turbulent velocity field. The variety could contribute to the diversity in size and other properties of protoplanetary disks recently reported by observations.
Sum of squares decomposition of positive polynomials with rational coefficients

We present an example of a strictly positive polynomial with rational coefficients that can be decomposed as a sum of squares of polynomials over $\R$ but not over $\Q$. This answers an open question by C. Scheiderer posed as the second question in Section 5.1 of the paper Sums of squares of polynomials with rational coefficients (2012). We verify that the example we construct defines a nonsingular projective hypersurface, giving also a positive answer to the third question posed in that section.
Timing and Spectral Analysis of HMXB 4U 1700-37 Observed with Insight-HXMT

We report timing and spectral studies of the high-mass X-ray binary 4U 1700-37 using Insight-HXMT observations carried out in 2020 during its out-of-eclipse state. We found significant variations in flux on a timescale of kilo-seconds, while the hardness (count rate ratio between 10–30 keV and 2–10 keV) remains relatively stable. No evident pulsations were found over a frequency range of 10−3–2000 Hz. During the spectral analysis, for the first time, we took the configuration of different Insight-HXMT detectors’ orientations into account, which allows us to obtain reliable results even if stable contamination exists in the field of view. We found that the spectrum could be well described by some phenomenological models that are commonly used in accreting pulsars (e.g., a power law with a high energy cutoff) in the energy range of 2–100 keV. We found hints of cyclotron absorption features around ∼16 keV or/and ∼50 keV.
Green Deen What Islam Teaches About Protecting The Planet

green deen what islam teaches about protecting the planet is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library hosts in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the green deen what islam teaches about protecting the planet is universally compatible with any devices to read.
SoK: Taming the Triangle - On the Interplays between Fairness, Interpretability and Privacy in Machine Learning

Machine learning techniques are increasingly used for high-stakes decision-making, such as college admissions, loan attribution or recidivism prediction. Thus, it is crucial to ensure that the models learnt can be audited or understood by human users, do not create or reproduce discrimination or bias, and do not leak sensitive information regarding their training data. Indeed, interpretability, fairness and privacy are key requirements for the development of responsible machine learning, and all three have been studied extensively during the last decade. However, they were mainly considered in isolation, while in practice they interplay with each other, either positively or negatively. In this Systematization of Knowledge (SoK) paper, we survey the literature on the interactions between these three desiderata. More precisely, for each pairwise interaction, we summarize the identified synergies and tensions. These findings highlight several fundamental theoretical and empirical conflicts, while also demonstrating that jointly considering these different requirements is challenging when one aims at preserving a high level of utility. To solve this issue, we also discuss possible conciliation mechanisms, showing that a careful design can enable to successfully handle these different concerns in practice.
Branching Brownian motion with generation-dependent diffusivity and nonlocal partial differential equations

We study a voting model on a branching Brownian motion process on $\mathbb{R}$ in which the diffusivity of each child particle is increased from that of the parent by a factor of $\gamma>1$. The probability distribution of the overall vote is given in terms of the solution to a nonlocal nonlinear PDE. We exhibit conditions on the nonlinearity such that the long-time behavior of the distribution undergoes a phase transition in $\gamma$. If $\gamma$ is sufficiently large, then the long-time distribution converges to uniform. If $\gamma$ is close enough to $1$, then the long-time distribution depends in a nontrivial way on the location of the initial particle. The limiting dependence is given by a steady-state solution to the nonlocal PDE. Our study gives a probabilistic interpretation of a class of semilinear nonlocal PDEs. Interestingly, while the PDE are nonlocal, the underlying random process does not require any non-local interactions.
Non-split sharply 2-transitive groups of odd positive characteristic

It is well-known that every sharply 2-transitive group of characteristic 3 splits. Here we construct the first examples of non-split sharply 2-transitive groups in odd positive characteristic $p$, for sufficiently large primes $p$. Furthermore, we show that any group without 2-torsion can be embedded into a non-split sharply 2-transitive group of characteristic $p$ for all sufficiently large primes $p$, yielding $2^{\aleph_0}$ many pairwise non-isomorphic countable non-split sharply 2-transitive groups in any sufficiently large characteristic.
Effects of principal stress direction and intermediate principal stress on undrained shear behavior of sand.

ABSTRACT Undrained monotonic loading triaxial compression and extension tests were conducted on Toyoura sand. It was found that the shear behavior was more contractive and softer in triaxial extension than in triaxial compression. This difference suggests that the stress conditions, such as the direction of the principal stress and the magnitude of the intermediate principal stress have some effects on the undrained behavior of sand. To clarify these effects, a series of tests was performed by means of an automated hollow cylindrical torsional shear apparatus. Dry-deposited Toyoura sand was used in these tests. The angle of the maximum principal stress from the vertical to the bedding plane, α, and the intermediate principal stress coefficient, b, were fixed in each test. The intermediate principal stress was fixed to horizontal. For any density, tests with a larger α-value, namely, a larger inclination of σ1 from the vertical, and a larger intermediate principal stress coefficient b were shown to generate greater excess pore water pressure. In addition, the undrained simple shear behavior of sand under initial isotropic and anisotropic stress conditions was studied. It was made clear that triaxial compression (α = 0°, b = 0) gives the highest resistance with lowest contrac- tancy, while triaxial extension (α = 90°, b = 1) gives the opposite extreme in the assessment of flow failure. Simple shear mode of deformation was shown to exhibit an intermediate stress-strain behavior between triaxial compression and extension, which is closer to most of the field conditions.
SCTNet: Single-Branch CNN with Transformer Semantic Information for Real-Time Segmentation

Recent real-time semantic segmentation methods usually adopt an additional semantic branch to pursue rich long-range context. However, the additional branch incurs undesirable computational overhead and slows inference speed. To eliminate this dilemma, we propose SCTNet, a single branch CNN with transformer semantic information for real-time segmentation. SCTNet enjoys the rich semantic representations of an inference-free semantic branch while retaining the high efficiency of lightweight single branch CNN. SCTNet utilizes a transformer as the training-only semantic branch considering its superb ability to extract long-range context. With the help of the proposed transformer-like CNN block CFBlock and the semantic information alignment module, SCTNet could capture the rich semantic information from the transformer branch in training. During the inference, only the single branch CNN needs to be deployed. We conduct extensive experiments on Cityscapes, ADE20K, and COCO-Stuff-10K, and the results show that our method achieves the new state-of-the-art performance. The code and model is available at https://github.com/xzz777/SCTNet.
On Inapproximability of Reconfiguration Problems: PSPACE-Hardness and some Tight NP-Hardness Results

The field of combinatorial reconfiguration studies search problems with a focus on transforming one feasible solution into another. Recently, Ohsaka [STACS'23] put forth the Reconfiguration Inapproximability Hypothesis (RIH), which roughly asserts that for some $\epsilon>0$, given as input a $k$-CSP instance (for some constant $k$) over some constant sized alphabet, and two satisfying assignments $\psi_s$ and $\psi_t$, it is PSPACE-hard to find a sequence of assignments starting from $\psi_s$ and ending at $\psi_t$ such that every assignment in the sequence satisfies at least $(1-\epsilon)$ fraction of the constraints and also that every assignment in the sequence is obtained by changing its immediately preceding assignment (in the sequence) on exactly one variable. Assuming RIH, many important reconfiguration problems have been shown to be PSPACE-hard to approximate by Ohsaka [STACS'23; SODA'24]. In this paper, we prove RIH and establish the first (constant factor) PSPACE-hardness of approximation results for many reconfiguration problems, resolving an open question posed by Ito et al. [TCS'11]. Our proof uses known constructions of Probabilistically Checkable Proofs of Proximity (in a black-box manner) to create the gap. Independently, Hirahara and Ohsaka [STOC'24] have also proved RIH. We also prove that the aforementioned $k$-CSP Reconfiguration problem is NP-hard to approximate to within a factor of $1/2 + \epsilon$ (for any $\epsilon>0$) when $k=2$. We complement this with a $(1/2 - \epsilon)$-approximation polynomial time algorithm, which improves upon a $(1/4 - \epsilon)$-approximation algorithm of Ohsaka [2023] (again for any $\epsilon>0$). Finally, we show that Set Cover Reconfiguration is NP-hard to approximate to within a factor of $2 - \epsilon$ for any constant $\epsilon>0$, which matches the simple linear-time 2-approximation algorithm by Ito et al. [TCS'11].
FCDNet: Frequency-Guided Complementary Dependency Modeling for Multivariate Time-Series Forecasting

Multivariate time-series (MTS) forecasting is a challenging task in many real-world non-stationary dynamic scenarios. In addition to intra-series temporal signals, the inter-series dependency also plays a crucial role in shaping future trends. How to enable the model's awareness of dependency information has raised substantial research attention. Previous approaches have either presupposed dependency constraints based on domain knowledge or imposed them using real-time feature similarity. However, MTS data often exhibit both enduring long-term static relationships and transient short-term interactions, which mutually influence their evolving states. It is necessary to recognize and incorporate the complementary dependencies for more accurate MTS prediction. The frequency information in time series reflects the evolutionary rules behind complex temporal dynamics, and different frequency components can be used to well construct long-term and short-term interactive dependency structures between variables. To this end, we propose FCDNet, a concise yet effective framework for multivariate time-series forecasting. Specifically, FCDNet overcomes the above limitations by applying two light-weight dependency constructors to help extract long- and short-term dependency information adaptively from multi-level frequency patterns. With the growth of input variables, the number of trainable parameters in FCDNet only increases linearly, which is conducive to the model's scalability and avoids over-fitting. Additionally, adopting a frequency-based perspective can effectively mitigate the influence of noise within MTS data, which helps capture more genuine dependencies. The experimental results on six real-world datasets from multiple fields show that FCDNet significantly exceeds strong baselines, with an average improvement of 6.82% on MAE, 4.98% on RMSE, and 4.91% on MAPE.
FedSDD: Scalable and Diversity-enhanced Distillation for Model Aggregation in Federated Learning

Recently, innovative model aggregation methods based on knowledge distillation (KD) have been proposed for federated learning (FL). These methods not only improved the robustness of model aggregation over heterogeneous learning environment, but also allowed training heterogeneous models on client devices. However, the scalability of existing methods is not satisfactory, because the training cost on the server increases with the number of clients, which limits their application in large scale systems. Furthermore, the ensemble of existing methods is built from a set of client models initialized from the same checkpoint, causing low diversity. In this paper, we propose a scalable and diversity-enhanced federated distillation scheme, FedSDD, which decouples the training complexity from the number of clients to enhance the scalability, and builds the ensemble from a set of aggregated models with enhanced diversity. In particular, the teacher model in FedSDD is an ensemble built by a small group of aggregated (global) models, instead of all client models, such that the computation cost will not scale with the number of clients. Furthermore, to enhance diversity, FedSDD only performs KD to enhance one of the global models, i.e., the \textit{main global model}, which improves the performance of both the ensemble and the main global model. While partitioning client model into more groups allow building an ensemble with more aggregated models, the convergence of individual aggregated models will be slow down. We introduce the temporal ensembling which leverage the issues, and provide significant improvement with the heterogeneous settings. Experiment results show that FedSDD outperforms other FL methods, including FedAvg and FedDF, on the benchmark datasets.
Dynamic In-Context Learning from Nearest Neighbors for Bundle Generation

Product bundling has evolved into a crucial marketing strategy in e-commerce. However, current studies are limited to generating (1) fixed-size or single bundles, and most importantly, (2) bundles that do not reflect consistent user intents, thus being less intelligible or useful to users. This paper explores two interrelated tasks, i.e., personalized bundle generation and the underlying intent inference based on users' interactions in a session, leveraging the logical reasoning capability of large language models. We introduce a dynamic in-context learning paradigm, which enables ChatGPT to seek tailored and dynamic lessons from closely related sessions as demonstrations while performing tasks in the target session. Specifically, it first harnesses retrieval augmented generation to identify nearest neighbor sessions for each target session. Then, proper prompts are designed to guide ChatGPT to perform the two tasks on neighbor sessions. To enhance reliability and mitigate the hallucination issue, we develop (1) a self-correction strategy to foster mutual improvement in both tasks without supervision signals; and (2) an auto-feedback mechanism to recurrently offer dynamic supervision based on the distinct mistakes made by ChatGPT on various neighbor sessions. Thus, the target session can receive customized and dynamic lessons for improved performance by observing the demonstrations of its neighbor sessions. Finally, experimental results on three real-world datasets verify the effectiveness of our methods on both tasks. Additionally, the inferred intents can prove beneficial for other intriguing downstream tasks, such as crafting appealing bundle names.
A canonical generator for congruence ideals of Hida families

We construct canonical adjoint $p$-adic $L$-functions generating the congruence ideal attached to Hida families using Ohta's pairing. We show that these $p$-adic $L$-functions, suitably modified by certain Euler factors, are interpolated by a regular element of Hida's universal ordinary Hecke algebra. We also relate them to characteristic series of primitive adjoint Selmer groups.
FlexSSL : A Generic and Efficient Framework for Semi-Supervised Learning

Semi-supervised learning holds great promise for many real-world applications, due to its ability to leverage both unlabeled and expensive labeled data. However, most semi-supervised learning algorithms still heavily rely on the limited labeled data to infer and utilize the hidden information from unlabeled data. We note that any semi-supervised learning task under the self-training paradigm also hides an auxiliary task of discriminating label observability. Jointly solving these two tasks allows full utilization of information from both labeled and unlabeled data, thus alleviating the problem of over-reliance on labeled data. This naturally leads to a new generic and efficient learning framework without the reliance on any domain-specific information, which we call FlexSSL. The key idea of FlexSSL is to construct a semi-cooperative"game", which forges cooperation between a main self-interested semi-supervised learning task and a companion task that infers label observability to facilitate main task training. We show with theoretical derivation of its connection to loss re-weighting on noisy labels. Through evaluations on a diverse range of tasks, we demonstrate that FlexSSL can consistently enhance the performance of semi-supervised learning algorithms.
An asymptotic relationship between Lane-Emden systems and the 1-bilaplacian equation

Consider the following Lane-Emden system with Dirichlet boundary conditions: \[ -\Delta U = |V|^{\beta-1}V,\ -\Delta V = |U|^{\alpha-1}U \text{ in }\Omega,\qquad U=V= 0 \text{ on }\partial \Omega, \] in a bounded domain $\Omega$, for $(\alpha,\beta)$ subcritical. We study the asymptotic behavior of least-energy solutions when $\beta\to \infty$, for any fixed $\alpha$ which, in the case $N\geq 3$, is smaller than $2/(N-2)$. We show that these solutions converge to least-energy solutions of a semilinear equation involving the 1-bilaplacian operator, establishing a new relationship between these objects. As a corollary, we deduce the asymptotic behavior of solutions to $p$-bilaplacian Lane-Emden equations as the power in the nonlinearity goes to infinity. For the proof, we rely on the reduction by inversion method and on tools from nonsmooth analysis, considering an auxiliary nonlinear eigenvalue problem. We characterize its value in terms of the Green function, and prove a Faber-Krahn type result. In the case of a ball, we can characterize explicitly the eigenvalue, as well as the limit profile of least-energy solutions to the system as $\beta\to\infty$.