Miracle-dz/UniFAR-FTUs huggingface dataset:
Derivation of a Bilayer Model for Shallow Water Equations with Viscosity. Numerical Validation

In this work we present a new two-dimensional bilayer Shallow-Water model including viscosity and friction effects on the bottom and interface level. It is obtained following [[6]] from an asymptotic analysis of non-dimensional and incompressible Navier-Stokes equations with hydrostatic approximation. In order to obtain the viscosity effects into the model we must have into account a second order approximation. To evaluate this model we perform two numerical tests consisting of an internal dam-break problem for both, one and two dimensional cases. In the first one we make a comparison between the model obtained and the NavierStokes simulation. Shallow Water equations, bilayer models, viscosity, friction, capillarity, Finite Volume methods.
Provable Advantage of Curriculum Learning on Parity Targets with Mixed Inputs

Experimental results have shown that curriculum learning, i.e., presenting simpler examples before more complex ones, can improve the efficiency of learning. Some recent theoretical results also showed that changing the sampling distribution can help neural networks learn parities, with formal results only for large learning rates and one-step arguments. Here we show a separation result in the number of training steps with standard (bounded) learning rates on a common sample distribution: if the data distribution is a mixture of sparse and dense inputs, there exists a regime in which a 2-layer ReLU neural network trained by a curriculum noisy-GD (or SGD) algorithm that uses sparse examples first, can learn parities of sufficiently large degree, while any fully connected neural network of possibly larger width or depth trained by noisy-GD on the unordered samples cannot learn without additional steps. We also provide experimental results supporting the qualitative separation beyond the specific regime of the theoretical results.
A MODIFIED STEP-LENGTH ALGORITHM IN NONLINEAR PROGRAMMING

In this paper we consider a modification of the Armijo step-length algorithm based on so- called "forcing functions". It is proved that this modified algorithm is well-defined. Proof is given of the convergence of the obtained sequence of points to a first-order point of the problem of unconstrained optimization, as well as an estimate of the rate of convergence. Finally, numerical results obtained using of TURBO PASCAL programmes are given.
Fermionic quantum gas at finite temperature within a Lorentz violating background

In this work we consider a fermionic quantum gas within a Lorentz-Violating background at finite temperature. We derive the effective action within Path Integral formalism considering the interaction of external electromagnetic field and Lorentz violating background fields with quantum fermions. To introduce the temperature effects, we employ the Matsubara formalism. Comments about the corresponding phenomenology are also made.
RAPGen: An Approach for Fixing Code Inefficiencies in Zero-Shot

Performance bugs are non-functional bugs that can even manifest in well-tested commercial products. Fixing these performance bugs is an important yet challenging problem. In this work, we address this challenge and present a new approach called Retrieval-Augmented Prompt Generation (RAPGen). Given a code snippet with a performance issue, RAPGen first retrieves a prompt instruction from a pre-constructed knowledge-base of previous performance bug fixes and then generates a prompt using the retrieved instruction. It then uses this prompt on a Large Language Model (such as Codex) in zero-shot to generate a fix. We compare our approach with the various prompt variations and state of the art methods in the task of performance bug fixing. Our evaluation shows that RAPGen can generate performance improvement suggestions equivalent or better than a developer in ~60% of the cases, getting ~42% of them verbatim, in an expert-verified dataset of past performance changes made by C# developers.
Influence Maximization based on Simplicial Contagion Model in Hypergraph

In recent years, the issue of node centrality has been actively and extensively explored due to its applications in product recommendations, opinion propagation, disease spread, and other areas involving maximizing node influence. This paper focuses on the problem of influence maximization on the Simplicial Contagion Model, using the susceptible-infected-recovered (SIR) model as an example. To find practical solutions to this optimization problem, we have developed a theoretical framework based on message passing processes and conducted stability analysis of equilibrium solutions for the self-consistent equations. Furthermore, we introduce a metric called collective influence and propose an adaptive algorithm, known as the Collective Influence Adaptive (CIA), to identify influential propagators in the spreading process. This method has been validated on both synthetic hypergraphs and real hypergraphs, outperforming other competing heuristic methods.
SaGess: Sampling Graph Denoising Diffusion Model for Scalable Graph Generation

Over recent years, denoising diffusion generative models have come to be considered as state-of-the-art methods for synthetic data generation, especially in the case of generating images. These approaches have also proved successful in other applications such as tabular and graph data generation. However, due to computational complexity, to this date, the application of these techniques to graph data has been restricted to small graphs, such as those used in molecular modeling. In this paper, we propose SaGess, a discrete denoising diffusion approach, which is able to generate large real-world networks by augmenting a diffusion model (DiGress) with a generalized divide-and-conquer framework. The algorithm is capable of generating larger graphs by sampling a covering of subgraphs of the initial graph in order to train DiGress. SaGess then constructs a synthetic graph using the subgraphs that have been generated by DiGress. We evaluate the quality of the synthetic data sets against several competitor methods by comparing graph statistics between the original and synthetic samples, as well as evaluating the utility of the synthetic data set produced by using it to train a task-driven model, namely link prediction. In our experiments, SaGess, outperforms most of the one-shot state-of-the-art graph generating methods by a significant factor, both on the graph metrics and on the link prediction task.
Two-tiered Online Optimization of Region-wide Datacenter Resource Allocation via Deep Reinforcement Learning

This paper addresses the important need for advanced techniques in continuously allocating workloads on shared infrastructures in data centers, a problem arising due to the growing popularity and scale of cloud computing. It particularly emphasizes the scarcity of research ensuring guaranteed capacity in capacity reservations during large-scale failures. To tackle these issues, the paper presents scalable solutions for resource management. It builds on the prior establishment of capacity reservation in cluster management systems and the two-level resource allocation problem addressed by the Resource Allowance System (RAS). Recognizing the limitations of Mixed Integer Linear Programming (MILP) for server assignment in a dynamic environment, this paper proposes the use of Deep Reinforcement Learning (DRL), which has been successful in achieving long-term optimal results for time-varying systems. A novel two-level design that utilizes a DRL-based algorithm is introduced to solve optimal server-to-reservation assignment, taking into account of fault tolerance, server movement minimization, and network affinity requirements due to the impracticality of directly applying DRL algorithms to large-scale instances with millions of decision variables. The paper explores the interconnection of these levels and the benefits of such an approach for achieving long-term optimal results in the context of large-scale cloud systems. We further show in the experiment section that our two-level DRL approach outperforms the MIP solver and heuristic approaches and exhibits significantly reduced computation time compared to the MIP solver. Specifically, our two-level DRL approach performs 15% better than the MIP solver on minimizing the overall cost. Also, it uses only 26 seconds to execute 30 rounds of decision making, while the MIP solver needs nearly an hour.
Numerical and experimental study on the addition of surface roughness to micro-propellers

Micro aerial vehicles are making a large impact in applications such as search-and-rescue, package delivery, and recreation. Unfortunately, these diminutive drones are currently constrained to carrying small payloads, in large part because they use propellers optimized for larger aircraft and inviscid flow regimes. Fully realizing the potential of emerging microflyers requires next-generation propellers that are specifically designed for low Reynolds number conditions and that include new features advantageous in highly viscous flows. One aspect that has received limited attention in the literature is the addition of roughness to propeller blades as a method of reducing drag and increasing thrust. To investigate this possibility, we used direct numerical simulation to conduct a numerical investigation of smooth and rough propellers. Our results indicate that roughness produces a 2% increase in thrust and a 5% decrease in power relative to a baseline smooth propeller operating at the same Reynolds number of Rec = 6500, held constant by rotational speed. We complement our numerical findings using thrust-stand-based experiments of 3D-printed propellers identical to those of the numerical simulations. Our study indicates that surface roughness is an additional parameter within the design space for micro-propellers, which may offer improved drone efficiencies and payloads.
Free fermionic webs of heterotic T-folds

Moduli stabilisation is key to obtaining phenomenologically viable string models. Non-geometric compactifications, like T-duality orbifolds (T-folds), are capable of freezing many moduli. However, in this Letter we emphasise that T-folds, admitting free fermionic descriptions, can be associated with a large number of different T-folds with varying number of moduli, since the fermion pairings for bosonisation are far from unique. Consequently, in one description a fermionic construction might appear to be asymmetric, and hence non-geometric, while in another it admits a symmetric orbifold description. We introduce the notion of intrinsically asymmetric T-folds for fermionic constructions that do not admit any symmetric orbifold description after bosonisation. Finally, we argue that fermion symmetries induce mappings in the bosonised description that extend the T-duality group.
Finite-Sample Symmetric Mean Estimation with Fisher Information Rate

The mean of an unknown variance-$\sigma^2$ distribution $f$ can be estimated from $n$ samples with variance $\frac{\sigma^2}{n}$ and nearly corresponding subgaussian rate. When $f$ is known up to translation, this can be improved asymptotically to $\frac{1}{n\mathcal I}$, where $\mathcal I$ is the Fisher information of the distribution. Such an improvement is not possible for general unknown $f$, but [Stone, 1975] showed that this asymptotic convergence $\textit{is}$ possible if $f$ is $\textit{symmetric}$ about its mean. Stone's bound is asymptotic, however: the $n$ required for convergence depends in an unspecified way on the distribution $f$ and failure probability $\delta$. In this paper we give finite-sample guarantees for symmetric mean estimation in terms of Fisher information. For every $f, n, \delta$ with $n>\log \frac{1}{\delta}$, we get convergence close to a subgaussian with variance $\frac{1}{n \mathcal I_r}$, where $\mathcal I_r$ is the $r$-$\textit{smoothed}$ Fisher information with smoothing radius $r$ that decays polynomially in $n$. Such a bound essentially matches the finite-sample guarantees in the known-$f$ setting.
Decomposing spiking neural networks with Graphical Neural Activity Threads

A satisfactory understanding of information processing in spiking neural networks requires appropriate computational abstractions of neural activity. Traditionally, the neural population state vector has been the most common abstraction applied to spiking neural networks, but this requires artificially partitioning time into bins that are not obviously relevant to the network itself. We introduce a distinct set of techniques for analyzing spiking neural networks that decomposes neural activity into multiple, disjoint, parallel threads of activity. We construct these threads by estimating the degree of causal relatedness between pairs of spikes, then use these estimates to construct a directed acyclic graph that traces how the network activity evolves through individual spikes. We find that this graph of spiking activity naturally decomposes into disjoint connected components that overlap in space and time, which we call Graphical Neural Activity Threads (GNATs). We provide an efficient algorithm for finding analogous threads that reoccur in large spiking datasets, revealing that seemingly distinct spike trains are composed of similar underlying threads of activity, a hallmark of compositionality. The picture of spiking neural networks provided by our GNAT analysis points to new abstractions for spiking neural computation that are naturally adapted to the spatiotemporally distributed dynamics of spiking neural networks.
Filtering of SPDEs -- The Ensemble Kalman Filter and related methods

This paper is concerned with the derivation and mathematical analysis of continuous time Ensemble Kalman Filters (EnKBFs) and related data assimilation methods for Stochastic Partial Differential Equations (SPDEs) with finite dimensional observations. The signal SPDE is allowed to be nonlinear and is posed in the standard abstract variational setting. Its coefficients are assumed to satisfy global one-sided Lipschitz conditions. We first review classical filtering algorithms in this setting, namely the Kushner--Stratonovich and the Kalman--Bucy filter, proving a law of total variance. Then we consider mean-field filtering equations, deriving both a Feedback Particle Filter and a mean-field EnKBF for nonlinear signal SPDEs. The second part of the paper is devoted to the elementary mathematical analysis of the EnKBF in this infinite dimensional setting, showing the well posedness of both the mean-field EnKBF and its interacting particle approximation. Finally we prove the convergence of the particle approximation. Under the additional assumption that the observation function is bounded, we even recover explicit and (nearly) optimal rates.
Improving Fairness in Deepfake Detection

Despite the development of effective deepfake detection models in recent years, several recent studies have demonstrated that biases in the training data utilized to develop deepfake detection models can lead to unfair performance for demographic groups of different races and/or genders. Such can result in these groups being unfairly targeted or excluded from detection, allowing misclassified deepfakes to manipulate public opinion and erode trust in the model. While these studies have focused on identifying and evaluating the unfairness in deepfake detection, no methods have been developed to address the fairness issue of deepfake detection at the algorithm level. In this work, we make the first attempt to improve deepfake detection fairness by proposing novel loss functions to train fair deepfake detection models in ways that are agnostic or aware of demographic factors. Extensive experiments on four deepfake datasets and five deepfake detectors demonstrate the effectiveness and flexibility of our approach in improving the deepfake detection fairness.
SRL: Scaling Distributed Reinforcement Learning to Over Ten Thousand Cores

The ever-growing complexity of reinforcement learning (RL) tasks demands a distributed RL system to efficiently generate and process a massive amount of data to train intelligent agents. However, existing open-source libraries suffer from various limitations, which impede their practical use in challenging scenarios where large-scale training is necessary. While industrial systems from OpenAI and DeepMind have achieved successful large-scale RL training, their system architecture and implementation details remain undisclosed to the community. In this paper, we present a novel abstraction on the dataflows of RL training, which unifies practical RL training across diverse applications into a general framework and enables fine-grained optimizations. Following this abstraction, we develop a scalable, efficient, and extensible distributed RL system called ReaLly Scalable RL (SRL). The system architecture of SRL separates major RL computation components and allows massively parallelized training. Moreover, SRL offers user-friendly and extensible interfaces for customized algorithms. Our evaluation shows that SRL outperforms existing academic libraries in both a single machine and a medium-sized cluster. In a large-scale cluster, the novel architecture of SRL leads to up to 3.7x speedup compared to the design choices adopted by the existing libraries. We also conduct a direct benchmark comparison to OpenAI's industrial system, Rapid, in the challenging hide-and-seek environment. SRL reproduces the same solution as reported by OpenAI with up to 5x speedup in wall-clock time. Furthermore, we also examine the performance of SRL in a much harder variant of the hide-and-seek environment and achieve substantial learning speedup by scaling SRL to over 15k CPU cores and 32 A100 GPUs. Notably, SRL is the first in the academic community to perform RL experiments at such a large scale.
Killing Symmetries of Deformed Relativity in Five Dimensions

This is the first of two papers devoted to investigating the main mathematical aspects of the Kaluza-Klein-like scheme known as Deformed Relativity in five dimensions (DR5). It is based on a five-dimensional Riemannian space in which the four-dimensional space-time metric is deformed (i.e. it depends on the energy) and energy plays the role of the fifth dimension. After a brief survey of the physical and mathematical foundations of DR5, we discuss in detail the Killing symmetries of the theory. In particular, we consider the case of physical relevance in which the metric coefficients are power functions of the energy (Power Ansatz). In order to solve the related Killing equations, we introduce a simplifying hypothesis of functional independence (Y hypothesis). The explicit expressions of the Killing vectors for the energy- dependent metrics corresponding to the four fundamental interactions (electromagnetic, weak, strong and gravitational) are derived. A preliminary discussion of the infinitesimal-algebraic structure of the Killing symmetries of DR5 is also given. c
Oriented Spanners

Given a point set $P$ in the Euclidean plane and a parameter $t$, we define an \emph{oriented $t$-spanner} as an oriented subgraph of the complete bi-directed graph such that for every pair of points, the shortest cycle in $G$ through those points is at most a factor $t$ longer than the shortest oriented cycle in the complete bi-directed graph. We investigate the problem of computing sparse graphs with small oriented dilation. As we can show that minimising oriented dilation for a given number of edges is NP-hard in the plane, we first consider one-dimensional point sets. While obtaining a $1$-spanner in this setting is straightforward, already for five points such a spanner has no plane embedding with the leftmost and rightmost point on the outer face. This leads to restricting to oriented graphs with a one-page book embedding on the one-dimensional point set. For this case we present a dynamic program to compute the graph of minimum oriented dilation that runs in $O(n^8)$ time for $n$ points, and a greedy algorithm that computes a $5$-spanner in $O(n\log n)$ time. Expanding these results finally gives us a result for two-dimensional point sets: we prove that for convex point sets the greedy triangulation results in an oriented $O(1)$-spanner.
On Wave Interference in Planet Migration: Dead Zone Torques Modified by Active Zone Forcing

We investigate planetary migration in the dead zone of a protoplanetary disk where there is a set of spiral waves propagating inward due to the turbulence in the active zone and the Rossby wave instability, which occurs at the transition between the dead and active zones. We perform global 3D unstratified magnetohydrodynamical simulations of a gaseous disk with the FARGO3D code, using weak gradients in the static resistivity profiles that trigger the formation of a vortex at the outer edge of the dead zone. We find that once the Rossby vortex develops, spiral waves in the dead zone emerge and interact with embedded, migrating planets by wave interference, which notably changes their migration. The inward migration becomes faster depending on the mass of the planet, due mostly to the constructive (destructive) interference between the outer (inner) spiral arm of the planet and the destruction of the dynamics of the horseshoe region by means of the set of background spiral waves propagating inward. The constructive wave interference produces a more negative Lindblad differential torque, which inevitably leads to an inward migration. Lastly, for massive planets embedded in the dead zone, we find that the spiral waves can create an asymmetric, wider, and deeper gap than in the case of α-disks and can prevent the formation of vortices at the outer edge of the gap. The latter could generate a faster or slower migration compared to the standard type-II migration.
PASSIVE LOCATION ALGORITHM USING KUSHNER EQUATION

Kalman filtering algorithm is an effective linear filter, but in the nonlinear state its covariance is uncontrolled. Kushner equation is effective for the nonlinear filtering. According to the Kushner equation and the nonlinear of passive location, a new passive location algorithm based on the Kushner equation is presented. And it is used in passive location tracking. Experiments are made in MATLAB and its validity is proved.
DNA-TEQ: An Adaptive Exponential Quantization of Tensors for DNN Inference

Quantization is commonly used in Deep Neural Networks (DNNs) to reduce the storage and computational complexity by decreasing the arithmetical precision of activations and weights, a.k. a. tensors. Efficient hardware architectures employ linear quantization to enable the deployment of recent DNNs onto embedded systems and mobile devices. However, linear uniform quantization cannot usually reduce the numerical precision to less than 8 bits without sacrificing high performance in terms of model accuracy. The performance loss is due to the fact that tensors do not follow uniform distributions. In this paper, we show that a significant amount of tensors fit into an exponential distribution. Then, we propose DNA-TEQ to exponentially quantize DNN tensors with an adaptive scheme that achieves the best trade-off between numerical precision and accuracy loss. The experimental results show that DNA-TEQ provides a much lower quantization bit-width compared to previous proposals, resulting in an average compression ratio of 40% over the linear INT8 baseline, with negligible accuracy loss and without retraining the DNNs. Besides, DNA-TEQ leads the way in performing dot-product operations in the exponential domain, which saves 66% of energy consumption on average for a set of widely used DNNs.
A CONTRIBUTION TO DIFFERENTIAL GEOMETRY IN THE LARGE

The contribution can be simply formulated in the following theorem. I first formulate HYPOTHESIS A: Let Mn n > 2, be a manifold of class C'(3 ? a? w) with a Riemannian metric given by a positive-definite tensor gij(i, j = 1, ***, n) of class Ca such that M' is complete with respect to the metric. THEOREM 1. Assume A. If the Riemannian curvature K(P, -y) (P e yf, y a 2-dimensional plane through P) formed from gij satisfies