Miracle-dz/UniFAR-FTUs huggingface dataset:
Bridging Graph Position Encodings for Transformers with Weighted Graph-Walking Automata

A current goal in the graph neural network literature is to enable transformers to operate on graph-structured data, given their success on language and vision tasks. Since the transformer's original sinusoidal positional encodings (PEs) are not applicable to graphs, recent work has focused on developing graph PEs, rooted in spectral graph theory or various spatial features of a graph. In this work, we introduce a new graph PE, Graph Automaton PE (GAPE), based on weighted graph-walking automata (a novel extension of graph-walking automata). We compare the performance of GAPE with other PE schemes on both machine translation and graph-structured tasks, and we show that it generalizes several other PEs. An additional contribution of this study is a theoretical and controlled experimental comparison of many recent PEs in graph transformers, independent of the use of edge features.
Local Probabilistic Decoding of a Quantum Code

flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser) which are uncorrectable for this decoder, so previous studies have considered modified versions of flip, sometimes in conjunction with other decoders. We argue that this may not always be necessary, and present numerical evidence for the existence of a threshold for flip when applied to the looplike syndromes of a three-dimensional toric code on a cubic lattice. This result can be attributed to the fact that the lowest-weight uncorrectable errors for this decoder are closer (in terms of Hamming distance) to correctable errors than to other uncorrectable errors, and so they are likely to become correctable in future code cycles after transformation by additional noise. Introducing randomness into the decoder can allow it to correct these "uncorrectable" errors with finite probability, and for a decoding strategy that uses a combination of belief propagation and probabilistic flip we observe a threshold of ∼5.5% under phenomenological noise. This is comparable to the best known threshold for this code (∼7.1%) which was achieved using belief propagation and ordered statistics decoding [Higgott and Breuckmann, 2022], a strategy with a runtime of O(n3) as opposed to the O(n) (O(1) when parallelised) runtime of our local decoder. We expect that this strategy could be generalised to work well in other low-density parity check codes, and hope that these results will prompt investigation of other previously overlooked decoders.
NoPe-NeRF: Optimising Neural Radiance Field with No Pose Prior

Training a Neural Radiance Field (NeRF) without precomputed camera poses is challenging. Recent advances in this direction demonstrate the possibility of jointly optimising a NeRF and camera poses in forward-facing scenes. However, these methods still face difficulties during dramatic camera movement. We tackle this challenging problem by incorporating undistorted monocular depth priors. These priors are generated by correcting scale and shift parameters during training, with which we are then able to constrain the relative poses between consecutive frames. This constraint is achieved using our proposed novel loss functions. Experiments on real-world indoor and outdoor scenes show that our method can handle challenging camera trajectories and outperforms existing methods in terms of novel view rendering quality and pose estimation accuracy. Our project page is https://nope-nerf.active. vision.
Exploring the origin of stronger survival of polarized vortex beams through scattering media

Laguerre-Gaussian (LG) beams carrying orbital angular momentum (OAM) have shown promise in deep tissue imaging, medical diagnostics, and optical communication due to their robust propagation properties through scattering media. However, an exact model that provides a mechanism for the en-hanced scattering properties of LG beams over Gaussian beams has not been established till date. Here, we examine this issue by studying the propagation of polarized vortex beams transmitted through tissue-like turbid scattering media. We demonstrate that the intensity proﬁle has a much more profound eﬀect on depolarization than the phase proﬁle for LG beams. Our results indicate that the observed stronger propagation for the higher order LG beams is due to a higher anisotropy factor g as seen by the incident beam. This insight is expected to contribute towards building a complete picture of light transport in the presence of scattering, as well as guide optimization of the intensity and polarization structure of light for use in biomedical applications.
Chemical composition of open clusters. I. Fe/H from high-resolution spectroscopy. II. C/H and C/Fe in F dwarfs from high-resolution spectroscopy

Using high-resolution spectroscopy, the abundance ratios Fe/H, C/H, and C/Fe were determined for F dwarfs in the Alpha Per, the Pleiades, and the Hyades clusters; the UMa, Hyades, and Wolf 630 moving groups; and a selection of bright F field dwarfs. The age span of these objects ranges from 5 x 10 to the 7th to 2 x 10 to the 9th yr. No evidence was found of a trend in Fe/H with age for these clusters and groups, but there were clear differences in Fe/H among these groups, indicating intrinsic differences in the metal content of the local gas out of which these groups were formed. No evidence was found for a trend of C/H with age of these stellar groups, but there were cluster-to-cluster variations, implying differences in the content of carbon in the precluster gas. The C/H cluster differences followed the same pattern as the Fe/H cluster differences and yield C/Fe values which are constant, and equal to the solar value, in all the groups. 53 refs.
The quasi-periods of the Weierstrass zeta-function

We study the ratio $p=\eta_1/\eta_2$ of the pseudo-periods of the Weierstrass $\zeta$-function in dependence of the ratio $\tau=\omega_1/\omega_2$ of the generators of the underlying rank-2 lattice. We will give an explicit geometric description of the map $\tau\mapsto p(\tau)$. As a consequence, we obtain an explanation of a theorem by Heins who showed that $p$ attains every value in the Riemann sphere infinitely often. Our main result is implicit in the classical literature, but it seems not to be very well known. Essentially, this is an expository paper. We hope that it is easily accessible and may serve as an introduction to these classical themes.
Spectral properties of a class of cographs

We explore several properties of the adjacency matrix of a class of connected cographs. Those cographs can be deﬁned by a ﬁnite sequence of natural numbers. Using that sequence we obtain multiplicity of the eigenvalues 0 , − 1, inertia for the adjacency matrix of the cograph under consideration. We ﬁnd an eigenvalue-free interval for such graphs which is better than previously obtained interval ( − 1 , 0). Finally, we establish a suitable formula for the characteristic polynomial of the adjacency matrix for such graphs.
Shock impingement on a transitional hypersonic high-enthalpy boundary layer

The dynamics of a shock wave impinging on a transitional high-enthalpy boundary layer out of thermochemical equilibrium is investigated for the first time by means of a direct numerical simulation. The freestream Mach number is equal to 9 and the oblique shock impinges with a cooled flat-plate boundary layer with an angle of 10{\deg}, generating a reversal flow region. In conjunction with freestream disturbances, the shock impingement triggers a transition to a fully turbulent regime shortly downstream of the interaction region. Accordingly, wall properties emphasize the presence of a laminar region, a recirculation bubble, a transitional zone and fully turbulent region. The breakdown to turbulence is characterized by an anomalous increase of skin friction and wall heat flux, due to the particular shock pattern. At the considered thermodynamic conditions the flow is found to be in a state of thermal non-equilibrium throughout, with non-equilibrium effects enhanced and sustained by the shock-induced laminar/turbulent transition, while chemical activity is almost negligible due to wall cooling. In the interaction region, relaxation towards thermal equilibrium is delayed and the fluctuating values of the rototranslational and the vibrational temperatures strongly differ, despite the strong wall-cooling. The fully turbulent portion exhibits evolutions of streamwise velocity, Reynolds stresses and turbulent Mach number in good accordance with previous results for highly-compressible cooled-wall boundary layers in thermal nonequilibrium, with turbulent motions sustaining thermal nonequilibrium. Nevertheless, the vibrational energy is found to contribute little to the total wall heat flux.
Improving group robustness under noisy labels using predictive uncertainty

The standard empirical risk minimization (ERM) can underperform on certain minority groups (i.e., waterbirds in lands or landbirds in water) due to the spurious correlation between the input and its label. Several studies have improved the worst-group accuracy by focusing on the high-loss samples. The hypothesis behind this is that such high-loss samples are \textit{spurious-cue-free} (SCF) samples. However, these approaches can be problematic since the high-loss samples may also be samples with noisy labels in the real-world scenarios. To resolve this issue, we utilize the predictive uncertainty of a model to improve the worst-group accuracy under noisy labels. To motivate this, we theoretically show that the high-uncertainty samples are the SCF samples in the binary classification problem. This theoretical result implies that the predictive uncertainty is an adequate indicator to identify SCF samples in a noisy label setting. Motivated from this, we propose a novel ENtropy based Debiasing (END) framework that prevents models from learning the spurious cues while being robust to the noisy labels. In the END framework, we first train the \textit{identification model} to obtain the SCF samples from a training set using its predictive uncertainty. Then, another model is trained on the dataset augmented with an oversampled SCF set. The experimental results show that our END framework outperforms other strong baselines on several real-world benchmarks that consider both the noisy labels and the spurious-cues.
Verifiable Coded Computation of Multiple Functions

We consider the problem of evaluating distinct multivariate polynomials over several massive datasets in a distributed computing system with a single master node and multiple worker nodes. We focus on the general case when each multivariate polynomial is evaluated over its corresponding dataset and propose a generalization of the Lagrange Coded Computing framework (Yu et al. 2019) to perform all computations simultaneously while providing robustness against stragglers who do not respond in time, adversarial workers who respond with wrong computation and information-theoretic security of dataset against colluding workers. Our scheme introduces a small computation overhead which results in a reduction in download cost and also offers comparable resistance to stragglers over existing solutions. On top of it, we also propose two verification schemes to detect the presence of adversaries, which leads to incorrect results, without involving additional nodes.
DeepIPC: Deeply Integrated Perception and Control for an Autonomous Vehicle in Real Environments

In this work, we introduce DeepIPC, a novel end-to-end model tailored for autonomous driving, which seamlessly integrates perception and control tasks. Unlike traditional models that handle these tasks separately, DeepIPC innovatively combines a perception module, which processes RGBD images for semantic segmentation and generates bird's eye view (BEV) mappings, with a controller module that utilizes these insights along with GNSS and angular speed measurements to accurately predict navigational waypoints. This integration allows DeepIPC to efficiently translate complex environmental data into actionable driving commands. Our comprehensive evaluation demonstrates DeepIPC's superior performance in terms of drivability and multi-task efficiency across diverse real-world scenarios, setting a new benchmark for end-to-end autonomous driving systems with a leaner model architecture. The experimental results underscore DeepIPC's potential to significantly enhance autonomous vehicular navigation, promising a step forward in the development of autonomous driving technologies. For further insights and replication, we will make our code and datasets available at https://github.com/oskarnatan/DeepIPC.
Special left invariant conic Finsler metrics and homogeneous conic Landsberg Problem in two dimension

In this paper, we study left invariant conic Finsler metrics on the 2-dimensional non-Abelian Lie group $G$ with nowhere vanishing spray vector fields, and classify those satisfying the constant curvature condition, the Landsberg condition or the Berwald condition respectively. We prove that any left invariant conic Landsberg metric on $G$ must be Berwald. This discovery enable us to propose a homogeneous conic Landsberg Conjecture, which guesses that every homogeneous conic Landsberg metric is Berwald, and prove the 2-dimensional case for it.
Electron–Phonon Interaction Contribution to the Total Energy of Group IV Semiconductor Polymorphs: Evaluation and Implications

In density functional theory (DFT)-based total energy studies, the van der Waals (vdW) and zero-point vibrational energy (ZPVE) correction terms are included to obtain energy differences between polymorphs. We propose and compute a new correction term to the total energy, due to electron–phonon interactions (EPI). We rely on Allen’s general formalism, which goes beyond the quasi-harmonic approximation (QHA), to include the free energy contributions due to quasiparticle interactions. We show that, for semiconductors and insulators, the EPI contributions to the free energies of electrons and phonons are the corresponding zero-point energy contributions. Using an approximate version of Allen’s formalism in combination with the Allen–Heine theory for EPI corrections, we calculate the zero-point EPI corrections to the total energy for cubic and hexagonal polytypes of carbon, silicon and silicon carbide. The EPI corrections alter the energy differences between polytypes. In SiC polytypes, the EPI correction term is more sensitive to crystal structure than the vdW and ZPVE terms and is thus essential in determining their energy differences. It clearly establishes that the cubic SiC-3C is metastable and hexagonal SiC-4H is the stable polytype. Our results are consistent with the experimental results of Kleykamp. Our study enables the inclusion of EPI corrections as a separate term in the free energy expression. This opens the way to go beyond the QHA by including the contribution of EPI on all thermodynamic properties.
Non-perturbative analysis for a massless minimal quantum scalar with V(ϕ) = λϕ 4/4! + βϕ 3/3! in the inflationary de Sitter spacetime

We consider a massless, minimally coupled quantum scalar field theory with an asymmetric self interaction, V(ϕ) = λϕ 4/4! + βϕ 3/3! (λ > 0) in the inflationary de Sitter spacetime. The potential is bounded from below. While the β=0 case has been much well studied, the motivation behind taking such a hybrid potential corresponds to the fact that it might generate finite negative vacuum expectation values of V(ϕ) as well of ϕ, leading to some dynamical screening of the inflationary cosmological constant Λ, at late times, with the initial conditions, 〈ϕ〉 = 0 = 〈V(ϕ)〉. In this work we first compute the vacuum expectation values of ϕ, ϕ 2 and V(ϕ), using the late time, non-perturbative and infrared effective stochastic formalism. The backreactions to the inflationary Λ are estimated. We also compute the dynamically generated mass of the scalar field using 〈ϕ 2〉. We next compute 〈ϕ 2〉 using quantum field theory with respect to the initial Bunch-Davies vacuum at one and two loops, using the Schwinger-Keldysh formalism. These results show non-perturbative secular logarithms, growing with the cosmological time. Using next a recently proposed renormalisation group inspired formalism, we attempt to find out a resummed 〈ϕ 2〉. We have been able to resum some part of the same which contains contributions only from the local self energy. The corresponding dynamically generated mass is computed. Comparison of the stochastic and the quantum field theory results shows that they differ numerically, although they have similar qualitative behaviour. Possible reasons for such quantitative mismatch is discussed. The manifestation of strong non-classical effects in the results found via both the formalisms has been emphasised.
On the poisson equation with intersecting interfaces

The interface problem is considered for the Poisson equation in two independent variables, The interface curves, along which jump conditions are prescribed, are allowed to intersect, The second derivatives of solutions of the interface problem are shown to lie in a certain "twisted" Soboiev space. The solution operator is shown to be a closed, densely defined, operator in L2 whose domain can be determined exactly
Simulations of Compact Groups of Galaxies: The Effect of the Dark Matter Distribution

The dynamical evolution of compact groups, beginning from virial equilibrium, is explored by using self-consistent N-body simulations employing Hernquist's implementation of the Barnes-Hut tree algorithm. A total N=5000 particles is used to represent both galaxies and a smoothly distributed intracluster background (ICB). The ICB mass fraction, β, is varied from 0 to 0.9, with all the models beginning in a virialized state. The first merger occurs near the center of the cluster; the product of this merger is quickly involved in further merging. This process is found to take longer as less of the cluster mass is put into the galaxy halos
On a Backward-Forward Parabolic Equation and Its Regularization

Abstract The steady-state diffusion of heat in a fluid which flows rapidly but not unidirectionally in a semi-infinite channel leads to a singular perturbation of a backwards-forwards heat equation with Neumann conditions on the channel walls. The temperature is prescribed on the whole channel entrance for the perturbed problems, but only at the points where the fluid flow is inward for the limiting problem. Conditions are obtained for uniqueness, and the additional arbitrary constants needed to obtain a well-posed problem when uniqueness does not hold are characterized. Conditions for the convergence of the solution of the perturbed problem to that of the limiting problem are also found.
The New French Operational Radar Rainfall Product. Part II: Validation

Abstract A new operational radar-based rainfall product has been developed at Meteo-France and is currently being deployed within the French operational network. The new quantitative precipitation estimation (QPE) product is based entirely on radar data and includes a series of modules aimed at correcting for ground clutter, partial beam blocking, and vertical profile of reflectivity (VPR) effects, as well as the nonsimultaneity of radar measurements. The surface rainfall estimation is computed as a weighted mean of the corrected tilts. In addition to the final QPE, a map of quality indexes is systematically generated. This paper is devoted to the validation of the new radar QPE. The VPR identification module has been specifically validated by analyzing 489 precipitation events observed over 1 yr by a representative eight-radar subset of the network. The conceptual model of VPR used in the QPE processing chain is shown to be relevant. A climatology of the three shape parameters of the conceptual VPR (brig.
A two-station decentralized LQG problem with noisy communication

We consider a two-station decentralized linear quadratic Gaussian problem, where the stations are allowed to communicate some pieces of information. We investigate a possible sub-optimal approach where the controls are obtained based on two separate centralized problems. Various cases are considered in which the two stations communicate their measurements, their controls or estimates, and their estimation residual through noisy channels. We mainly focus on the closed-loop stability properties. We show that even if the stations communicate all their measurements through low noise or even noiseless channels, the controls obtained from the two centralized LQG problems may fail to stabilize the closed-loop decentralized system.
Patterns of Heterochromatin Transitions Linked to Changes in the Expression of Plasmodium falciparum Clonally Variant Genes

The survival of malaria parasites in the changing human blood environment largely depends on their ability to alter gene expression by epigenetic mechanisms. The active state of Plasmodium falciparum clonally variant genes (CVGs) is associated with euchromatin characterized by the histone mark H3K9ac, whereas the silenced state is characterized by H3K9me3-based heterochromatin. ABSTRACT The survival of malaria parasites in the changing human blood environment largely depends on their ability to alter gene expression by epigenetic mechanisms. The active state of Plasmodium falciparum clonally variant genes (CVGs) is associated with euchromatin characterized by the histone mark H3K9ac, whereas the silenced state is characterized by H3K9me3-based heterochromatin. Expression switches are linked to euchromatin-heterochromatin transitions, but these transitions have not been characterized for the majority of CVGs. To define the heterochromatin distribution patterns associated with the alternative transcriptional states of CVGs, we compared H3K9me3 occupancy at a genome-wide level among several parasite subclones of the same genetic background that differed in the transcriptional state of many CVGs. We found that de novo heterochromatin formation or the complete disruption of a heterochromatin domain is a relatively rare event, and for the majority of CVGs, expression switches can be explained by the expansion or retraction of heterochromatin domains. We identified different modalities of heterochromatin changes linked to transcriptional differences, but despite this complexity, heterochromatin distribution patterns generally enable the prediction of the transcriptional state of specific CVGs. We also found that in some subclones, several var genes were simultaneously in an active state. Furthermore, the heterochromatin levels in the putative regulatory region of the gdv1 antisense noncoding RNA, a regulator of sexual commitment, varied between parasite lines with different sexual conversion rates. IMPORTANCE The malaria parasite P. falciparum is responsible for more than half a million deaths every year. P. falciparum clonally variant genes (CVGs) mediate fundamental host-parasite interactions and play a key role in parasite adaptation to fluctuations in the conditions of the human host. The expression of CVGs is regulated at the epigenetic level by changes in the distribution of a type of chromatin called heterochromatin. Here, we describe at a genome-wide level the changes in the heterochromatin distribution associated with the different transcriptional states of CVGs. Our results also reveal a likely role for heterochromatin at a particular locus in determining the parasite investment in transmission to mosquitoes. Additionally, this data set will enable the prediction of the transcriptional state of CVGs from epigenomic data, which is important for the study of parasite adaptation to the conditions of the host in natural malaria infections.