Miracle-dz/UniFAR-FTUs huggingface dataset:
Self-Supervised Point Cloud Understanding via Mask Transformer and Contrastive Learning

Self-supervised point cloud understanding can pre-train the point cloud learning network on a large dataset, which helps boost the performance of fine-tuning on other smaller datasets in downstream tasks. Motivated to design an efficient self-supervised pre-training strategy and capture useful and discriminative representations of the 3D point cloud, we propose ContrastMPCT, a self-reconstruction scheme with the contrastive learning principle. Specifically, two contrastive loss functions are designed for 3D point clouds to maximize the dependence between the input tokens and output tokens of the encoder and fasten the convergence of the model. Extensive experiments show that our pre-training strategy of ContrastMPCT can effectively improve the fine-tuning performance on the downstream tasks, including object classification and part segmentation. Moreover, compared with both CNN-based and Transformer-based existing works, the superior results indicate the efficacy of the proposed method.
Turbulent flows over smooth erodible sand beds in flumes

The characteristic flow parameters of an open channel flow with an erodible hydraulically smooth sand bed were investigated for sand grains at rest, and for the flow regime in which an intermittent transport occurs. The experimental results show the following: (1) The grains are only transported by sweeps. (2) The sediment transport is responsible for up to 30% of the wall shear velocity. (3) No noticeable drag reducing effect occurs. (4) At high intermittent sediment transport the sweep frequency was found to be constant over the water depth. (5) With increasing wall shear stress the intensity distribution of the sweeps becomes more homogeneous and the maxima smaller. All these results are discussed based on a quadrant analysis of the main features of the so-called coherent structures of turbulent flows.
Sharp local smoothing for manifolds with smooth inflection transmission

We consider a family of spherically symmetric, asymptotically Euclidean manifolds with two trapped sets, one which is unstable and one which is semi-stable. The phase space structure is that of an inflection transmission set. We prove a sharp local smoothing estimate for the linear Schr\"odinger equation with a loss which depends on how flat the manifold is near each of the trapped sets. The result interpolates between the family of similar estimates in \cite{ChWu-lsm}. As a consequence of the techniques of proof, we also show a sharp high energy resolvent estimate with a polynomial loss depending on how flat the manifold is near each of the trapped sets.
Hedetniemi's conjecture from the topological viewpoint

This paper is devoted to studying some topological questions related to well known Hedetniemi's conjecture on the chromatic number of the categorical product of graphs. It is surprisingly shown that Hedetniemi's conjecture implies a statement in Topology by M. Wrochna and T. Matsushita (independently). Precisely, they showed if Hedetniemi's conjecture is true, then the $\mathbb{Z}_2$-index of the Cartesian product of two $\mathbb{Z}_2$-spaces is equal to the minimum of their $\mathbb{Z}_2$-indexes. In addition, Wrochna conjectured the correctness of the latter statement. We show Wrochna's conjecture is true for the case that one of the $\mathbb{Z}_2$-spaces is an $n$-sphere $\mathbb{S}^n$, and fully confirm the version of this conjecture for the homological index. There is also a generalization of Hedetniemi's conjecture for hypergraphs. To approach this conjecture, we establish a topological lower bound for the chromatic number of the categorical product of hypergraphs. Consequently, we enrich the family of known hypergraphs satisfying this conjecture. Especially, we reprove the known fact that the conjecture is valid for the usual Kneser $r$-hypergraphs. We also give some other applications of this bound, such as a new proof of a well-known conjecture of Erd\H{o}s, and a new way for constructing $r$-hypergraphs with arbitrary high chromatic numbers and small clique numbers.
Fast nonlinearity of the refractive index of solid-state dielectric active media

Research on the nonlinear refractive indices of solid dielectric active media is reviewed. The review is restricted to media for which the nonlinear refractive index is fast, i.e., has a relaxation time τ < 10−9 s. The nature of the nonlinear refractive index, its relaxation time, and its dispersion are discussed. Measurements of the parameters of the nonlinear refractive index of more than 160 laser and optical glasses and crystals are collected.
$L_{\infty}$-actions of Lie algebroids

We consider homotopy actions of a Lie algebroid on a graded manifold, defined as suitable $L_{\infty}$-algebra morphisms. On the "semi-direct product" we construct a homological vector field that projects to the Lie algebroid. Our main theorem states that this construction is a bijection. Since several classical geometric structures can be described by homological vector fields as above, we can display many explicit examples, involving Lie algebroids (including extensions, representations up to homotopy and their cocycles) as well as transitive Courant algebroids.
Ferroelectriclike dielectric response and metal-insulator transition in organic Mott insulator-gate insulator interface

A ferroelectriclike dielectric response was observed in a field-effect transistor using oriented bis(ethylenedithio)tetrathiafulvalene-tetracyanoquinodimethane crystals. Phase transitions at 285 and 320 K were clearly observed in the temperature dependence of field-effect electron mobility. The phase transition at 320 K corresponds to the metal-insulator transition previously reported in a bulk crystal. On the other hand, the field-effect electron and hole mobilities exhibited an abrupt increase at 285 K, which had not been discovered by other physical measurements in the bulk crystal and is nonetheless sufficiently stable and reproducible. In addition, the abrupt increase in carrier mobilities was clearly correlated with the decrease in the dielectric response. The temperature variation in difference hysteresis curves demonstrated the feature of ferroelectric transition.
Regularity of the solution to a nonstandard system of phase field equations

A nonstandard system of differential equations describing two-species phase segregation is considered. This system naturally arises in the asymptotic analysis recently done by Colli, Gilardi, Krejci, and Sprekels as the diffusion coefficient in the equation governing the evolution of the order parameter tends to zero. In particular, a wellposedness result is proved for the limit system. This paper deals with the above limit problem in a less general but still very significant framework and provides a very simple proof of further regularity for the solution. As a byproduct, a simple uniqueness proof is given as well.
The KdV equation on the half-line: the Dirichlet to Neumann map

We consider initial-boundary value problems for the KdV equation ut + ux + 6uux + uxxx = 0 on the half-line x ⩾ 0. For a well-posed problem, the initial data u(x, 0) as well as one of the three boundary values {u(0, t), ux(0, t), uxx(0, t)} can be prescribed; the other two boundary values remain unknown. We provide a characterization of the unknown boundary values for the Dirichlet as well as the two Neumann problems in terms of a system of nonlinear integral equations. The characterizations are effective in the sense that the integral equations can be solved perturbatively to all orders in a well-defined recursive scheme.
Simulating Flow Over Circular Spillways by Using Different Turbulence Models

Abstract Fluent software has been used to simulate flow over a circular spillway and results were compared with experimental data. As the flow over a circular spillway is turbulent and has a free surface, its characteristics are complex and often difficult to be predicted. This study assesses the performance of some turbulence models to predict the hydraulic condition of flow over circular spillways. The Volume of Fluid (VOF) method is applied to obtain the free surface in each case. Such cases include highly swirling flows, stress-driven secondary flows and flows over circular spillways. Finally it is concluded that the results of RSM, RNG k-ε, Realizable k-ε, SST k-ω turbulence models agree well with experimental data.
Anisotropy and Asymptotic Degeneracy of the Physical-Hilbert-Space Inner-Product Metrics in an Exactly Solvable Unitary Quantum Model

A unitary-evolution process leading to an ultimate collapse and to a complete loss of observability alias quantum phase transition is studied. A specific solvable N−state model is considered, characterized by a non-stationary non-Hermitian Hamiltonian. Our analysis uses quantum mechanics formulated in Schrödinger picture in which, in principle, only the knowledge of a complete set of observables (i.e., operators Λj) enables one to guarantee the uniqueness of the related physical Hilbert space (i.e., of its inner-product metric Θ). Nevertheless, for the sake of simplicity, we only assume the knowledge of just a single input observable (viz., of the energy-representing Hamiltonian H≡Λ1). Then, out of all of the eligible and Hamiltonian-dependent “Hermitizing” inner-product metrics Θ=Θ(H), we pick up just the simplest possible candidate. Naturally, this slightly restricts the scope of the theory, but in our present model, such a restriction is more than compensated for by the possibility of an alternative, phenomenologically better motivated constraint by which the time-dependence of the metric is required to be smooth. This opens a new model-building freedom which, in fact, enables us to force the system to reach the collapse, i.e., a genuine quantum catastrophe as a result of the mere conventional, strictly unitary evolution.
Approach for optimal power flow with transient stability constraints

Optimal power flow with transient stability (OTS) is a nonlinear optimisation problem in functional space that can be transformed to a static optimisation problem via constraint transcription techniques. However, the solution of the transformed OTS by ordinary numerical methods involves a massive calculation due to the stability constraints. Hence, the authors propose a penalty-based approach for OTS, in which the adjoint equation method is applied to evaluate the gradient of the penalty term associated with the stability constraints. It is demonstrated that the implementation of the adjoint equation method significantly reduces the computational burden in solving the OTS. A numerical test on a power system using prototype code is presented.
Sturm-Liouville hypergroups without the compactness axiom

We establish a positive product formula for the solutions of the Sturm-Liouville equation $\ell(u) = \lambda u$, where $\ell$ belongs to a general class which includes singular and degenerate Sturm-Liouville operators. Our technique relies on a positivity theorem for possibly degenerate hyperbolic Cauchy problems and on a regularization method which makes use of the properties of the diffusion semigroup generated by the Sturm-Liouville operator. We show that the product formula gives rise to a convolution algebra structure on the space of finite measures, and we discuss whether this structure satisfies the basic axioms of the theory of hypergroups. We introduce the notion of a degenerate hypergroup of full support and improve the known existence theorems for Sturm-Liouville hypergroups. Convolution-type integral equations on weighted Lebesgue spaces are also introduced, and a solvability condition is established.
Model Space Localization Is Not Always Better Than Observation Space Localization for Assimilation of Satellite Radiances

AbstractCovariance localization is an essential component of ensemble-based data assimilation systems for large geophysical applications with limited ensemble sizes. For integral observations like the satellite radiances, where the concepts of location or vertical distance are not well defined, vertical localization in observation space is not as straightforward as in model space. The detailed differences between model space and observation space localizations are examined using a real radiance observation. Counterintuitive analysis increments can be obtained with model space localization; the magnitude of the increment can increase and the increment can change sign when the localization scale decreases. This occurs when there are negative background-error covariances and a predominately positive forward operator. Too narrow model space localization can neglect the negative background-error covariances and result in the counterintuitive analysis increments. An idealized 1D model with integral observations.
STRUCTURE OF A SHOCK WAVE IN FULLY IONIZED HYDROGEN

The Fokker-Planck equations are used to examine the structure of a shock wave in fully ionized hydrogen. This is done by assuming a bimodal Maxwellian distribution for the protons in the interior of the shock and noting that the electrons are in thermal equilibrium with themselves but not necessarily with the protons. The method is essentially an extension of that used by Mott-Smith tn his analysis of the Boltzmann equation for a shock wave in a gas of neutral atoms. (auth)
Generalized method for electromagnetic scattering by two-dimensional periodic discrete composites using lattice sums

A very efficient and accurate method to characterize the electromagnetic scattering from multilayered periodic arrays of two-dimensional composite cylindrical objects is presented, using the lattice sums formula and the aggregate T-matrix for cylindrical structures. The method is quite general and applies to various configurations of two-dimensional periodic arrays. The unit cell of the array call contain two or more cylinders, which may be dielectric, conductor, gyrotropic medium, or their mixture with different sizes.
Average structures associated with a Finsler space

Given a Finsler space (M,F) on a manifold M, the averaging method associates to Finslerian geometric objects affine geometric objects} living on $M$. In particular, a Riemannian metric is associated to the fundamental tensor $g$ and an affine, torsion free connection is associated to the Chern-Rund connection. As an illustration of the technique, a generalization of the Gauss-Bonnet theorem to Berwald surfaces using the average metric is presented. The parallel transport and curvature endomorphisms of the average connection are obtained. The holonomy group for a Berwald space is discussed. New affine, local isometric invariants of the original Finsler metric. The heredity of the property of symmetric space from the Finsler space to the average Riemannian metric is proved.
Complexity of Strong Approximation on the Sphere

By assuming some widely believed arithmetic conjectures, we show that the task of accepting a number that is representable as a sum of $d\geq 2$ squares subjected to given congruence conditions is NP-complete. On the other hand, we develop and implement a deterministic polynomial-time algorithm that represents a number as a sum of four squares with some restricted congruence conditions, by assuming a polynomial-time algorithm for factoring integers and Conjecture 1.1. As an application, we develop and implement a deterministic polynomial-time algorithm for navigating Lubotzky, Phillips, Sarnak (LPS) Ramanujan graphs, under the same assumptions.
HALE-IoT: Hardening Legacy Internet of Things Devices by Retrofitting Defensive Firmware Modifications and Implants

Internet of Things (IoT) devices and their firmware are notorious for their lifelong vulnerabilities. As device infection increases, vendors also fail to release patches at a competitive pace. Despite security in acrshort IoT being an active area of research, prior work has mainly focused on vulnerability detection and exploitation, threat modeling, and protocol security. However, these methods are ineffective in preventing attacks against legacy and End-Of-Life devices that are already vulnerable. Current research mainly focuses on implementing and demonstrating the potential of malicious modifications. Hardening emerges as an effective solution to provide acrshort IoT devices with an additional layer of defense. In this article, we bridge these gaps through the design of $\textit {HALE-IoT}$ , a generically applicable systematic approach to HArdening LEgacy acrshort IoT non-low-end devices by retrofitting defensive firmware modifications without access to the original source code. $\textit {HALE-IoT}$ approaches this nontrivial task via binary firmware reversing and modification while being underpinned by a semiautomated toolset that aims to keep cybersecurity of such devices in a hale state. Our focus is on both modern and, especially, legacy or obsolete acrshort IoT devices as they become increasingly prevalent. To evaluate the effectiveness and efficiency of HALE-IoT, we apply it to a wide range of acrshort IoT devices by retrofitting 395 firmware images with defensive implants containing an intrusion prevention system in the form of a Web Application Firewall (for prevention of Web-attack vectors), and an HTTPS-proxy (for latest and full end-to-end HTTPS support) using emulation. We also test our approach on four physical devices, where we show that HALE-IoT successfully runs on protected and quite constrained devices with as low as 32 MB of RAM and 8 MB of storage. Overall, in our evaluation, we achieve good performance and reliability with a remarkably accurate detection and prevention rate for attacks coming from both real CVEs and synthetic exploits.
Poles of the Standard ${\mathcal{L}}$ -function of $G_{2}$ and the Rallis–Schiffmann Lift

Abstract We characterize the cuspidal representations of $G_{2}$ whose standard ${\mathcal{L}}$ -function admits a pole at $s=2$ as the image of the Rallis–Schiffmann lift for the commuting pair ( $\widetilde{\text{SL}}_{2}$ , $G_{2}$ ) in $\widetilde{\text{Sp}}_{14}$ . The image consists of non-tempered representations. The main tool is the recent construction, by the second author, of a family of Rankin–Selberg integrals representing the standard ${\mathcal{L}}$ -function.
Optimal State-Feedback Design for MIMO systems subject to multiple SNR constraints

Abstract This paper studies optimal control problems associated to networked systems. In particular, we focus on a case where a multiple-input multiple-output (MIMO) plant is controlled over a channel subject to multiple signal-to-noise ratio (SNR) constraints. For this setup, we establish necessary and sufficient conditions for the existence of static state-feedback controllers that stabilize the plant in a mean square sense. Such conditions are given in terms of a convex optimization problem involving linear matrix inequalities (LMIs). An optimal design procedure is also presented. As an application of our results, we study a class of networked systems closed over erasure channels.
Wieferich Primes and a mod $p$ Leopoldt Conjecture

We consider questions in Galois cohomology which arise by considering mod $p$ Galois representations arising from automorphic forms. We find a Galois cohomological analog for the standard heuristics about the distribution of Wieferich primes, i.e. prime $p$ such that $2^{p-1}$ is 1 mod $p^2$. This analog leads to formulating a strengthening for almost all primes $p$ of the classical Leopoldt conjecture which says that for a number field $F$ and a prime $p$ the $p$-adic regulator $R_{F,p}$ is non-zero. Our mod $p$ analog is that for a fixed number field $F$, for almost all primes $p$, the $p$-adic regulator $R_{F,p}$ is a unit at $p$.
Experiments on the stability of streamwise streaks in plane Poiseuille flow

The development and stability of streamwise streaks are studied in an air-flow channel experiment at subcritical Reynolds numbers. The streaks were generated by continuous suction through small slots at the wall. The streak amplitude first grows algebraically, and if the amplitude exceeds a certain threshold secondary instability in the form of travelling waves is observed. These waves give rise to high urms values in the region of large spanwise mean flow gradient. Measurements with two hot-wire probes indicate that velocity fluctuations are 180° out of phase at two neighboring peaks at each side of a low velocity region and implies the existence of a sinuous type instability. Measurements were also made with controlled disturbances where earphones were used to force the secondary instability. Phase averaged data clearly show the oscillation of the low velocity region and also provides the growth rate, phase speed as well as amplitude and phase distributions of the secondary instability. Several of these.
Infrared Observations of Comets by COBE

Comets C/Okazaki-Levy-Rudenko 1989 XX (C/OLR), C/Austin 1990 V, (C/Austin) P/Schwassmann-Wachmann 3 1990 VIII (P/SW3), and C/Levy 1990 XX (C/Levy) were detected by the COBE/Diffuse Infrared Background Experiment (DIRBE) with broadband photometry at 1-240 μm between 1989 November and 1990 September. Extended dust tails were found at 12 and 25 μm, with detailed structure due to variations in particle properties and mass-loss rate. Spectrophotometry of the central 42' × 42' was found to agree with that of a graybody of temperature 1.1 times the local blackbody temperature for C/OLR and C/Austin, while a nongraybody distribution with a spectral index of emissivity 0.26 ± 0.15 and temperature 1.25 times the local temperature was found for C/Levy. A model using modified Mie dust particles composed of fractal mixtures of vacuum, silicates, and carbonaceous material was found to fit the observations. Comparison with IUE and ground-based observations indicates that large dark particles of radius greater than 20 μm predominate by surface area for C/OLR and C/Austin, but 1-10 μm particles predominate for C/Levy. The detection of P/SW3, an optically faint comet, was surprising, especially since four optically brighter comets were not detected by DIRBE. This may be related to the nuclear breakup observed during its next apparition. The total estimated mass loss from these comets in a perihelion passage is ~10 times larger than that expected from optical observations, and the loss rate is similar to that needed to supply the interplanetary dust cloud. No comet trails were detected to a limiting surface brightness of 1 MJy sr-1, although large, β < 5 × 104 particles, which could evolve into a dust trail, were detected in C/Austin.
A Closed-Form Spatial Green’s Function for Finite Dielectric Structures

A novel technique to derive the closed-form spatial Green’s function for finite dielectric structures is presented by employing a combination of the characteristic Green’s function (CGF) and complex images (CI) techniques. To show the versatility of this technique, a two-dimensional finite dielectric substrate is studied in detail. Since the structure is nonseparable, the derived Green’s function is an approximate solution especially in the corners. It is shown that by applying certain corrections on the reflection coefficient of the fields at edges, more accurate results are obtained. The derived Green’s function exhibits excellent agreement with the available rigorous method of moments solution of the problem.
Stochastic adaptive control with small observation noise

Controlled diffusions depending on an unknown parameter and with small system perturbation are considered in this paper. Two parameter identification methods are proposed and error probabilities are estimated in terms of the small perturbation parameter. These methods are then used to choose among competing filters on successive time intervals. Asymptotically optimal controls based on partial observations are found on successive time intervals by using the best filter identified on the previous time intervals.