Miracle-dz/UniFAR-FTUs huggingface dataset:
Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property

In the present paper we initiate the challenging task of building a mathematically sound theory for Adaptive Virtual Element Methods (AVEMs). Among the realm of polygonal meshes, we restrict our analysis to triangular meshes with hanging nodes in 2d -- the simplest meshes with a systematic refinement procedure that preserves shape regularity and optimal complexity. A major challenge in the a posteriori error analysis of AVEMs is the presence of the stabilization term, which is of the same order as the residual-type error estimator but prevents the equivalence of the latter with the energy error. Under the assumption that any chain of recursively created hanging nodes has uniformly bounded length, we show that the stabilization term can be made arbitrarily small relative to the error estimator provided the stabilization parameter of the scheme is sufficiently large. This quantitative estimate leads to stabilization-free upper and lower a posteriori bounds for the energy error. This novel and crucial property of VEMs hinges on the largest subspace of continuous piecewise linear functions and the delicate interplay between its coarser scales and the finer ones of the VEM space. An important consequence for piecewise constant data is a contraction property between consecutive loops of AVEMs, which we also prove. Our results apply to $H^1$-conforming (lowest order) VEMs of any kind, including the classical and enhanced VEMs.
Electron recoil effect in electrically tunable 
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 monolayers

Radiative recombination of excitons dressed by the interactions with free charge carriers often occurs under simultaneous excitation of either electrons or holes to unbound states. This phenomenon, known as the electron recoil effect, manifests itself in pronounced, asymmetric spectral lineshapes of the resulting emission. We study the electron recoil effect experimentally in electrically-tunable monolayer semiconductors and derive it theoretically using both trion and Fermi-polaron pictures. Time-resolved analysis of the recoil lineshapes is employed to access transient, non-equilibrium states of the exciton-carrier complexes. We demonstrate cooling of the initially overheated populations on the picosecond timescales and reveal the impact of lattice temperature and free carrier density. Both thermally activated phonons and the presence of free charges are shown to accelerate equilibration. Finally, we find strong correlations between relaxation times from recoil analysis and luminescence rise times, providing a consistent interpretation for the initial dynamics of trion/Fermi-polaron states.
RAINBOW HAMILTON CYCLE IN HYPERGRAPH SYSTEMS

Rödl, Ruciński and Szemerédi proved that every n-vertex k-graph H, k ≥ 3, γ > 0 and n is sufficiently large, with δk−1(H) ≥ (1/2 + γ)n contains a tight Hamilton cycle, which can be seen as a generalization of Dirac’s theorem in hypergraphs. In this paper, we extend this result to the rainbow setting as follows. A k-graph system H = {Hi}i∈[m] is a family of not necessarily distinct k-graphs on the same n-vertex set V , a k-graph G on V is rainbow if E(G) ⊆ ⋃ i∈[m] E(Hi) and |E(G)∩E(Hi)| ≤ 1 for i ∈ [m]. Then we show that given k ≥ 3, γ > 0, sufficiently large n and an n-vertex k-graph system H = {Hi}i∈[n], if δk−1(Hi) ≥ (1/2 + γ)n for i ∈ [n], then there exists a rainbow tight Hamilton cycle.
Generalized phase-shifting interferometry

This paper describes a generalized phase shifting interferometiy where the reference phase instead of being set to predetermined values is directly evaluated at each time the interference fringe data are read. The evaluation of the phase shifted is achieved by introducing the FF1'' method for analyzing additional straight fringes on the interfering plane. The repeatability in the measurements of an optical surface is V500 when the generalized algorithm with 8 data acquisitions is used. 1.
Monaural Source Separation: From Anechoic To Reverberant Environments

Impressive progress in neural network-based single-channel speech source separation has been made in recent years. But those improvements have been mostly reported on anechoic data, a situation that is hardly met in practice. Taking the SepFormer as a starting point, which achieves state-of-the-art performance on anechoic mixtures, we gradually modify it to optimize its performance on reverberant mixtures. Although this leads to a word error rate improvement by 7 percentage points compared to the standard SepFormer implementation, the system ends up with only marginally better performance than a PIT-BLSTM separation system, that is optimized with rather straightforward means. This is surprising and at the same time sobering, challenging the practical usefulness of many improvements reported in recent years for monaural source separation on nonrever-berant data.
Unsupervised Lightweight Single Object Tracking with UHP-SOT++

—An unsupervised, lightweight and high- performance single object tracker, called UHP-SOT, was proposed by Zhou et al. recently. As an extension, we present an enhanced version and name it UHP-SOT++ in this work. Built upon the foundation of the discriminative-correlation- ﬁlters-based (DCF-based) tracker, two new ingredients are introduced in UHP-SOT and UHP-SOT++: 1) background motion modeling and 2) object box trajectory modeling. The main difference between UHP-SOT and UHP-SOT++ is the fusion strategy of proposals from three models (i.e., DCF, background motion and object box trajectory models). An improved fusion strategy is adopted by UHP-SOT++ for more robust tracking performance against large-scale tracking datasets. Our second contribution lies in an extensive evaluation of the performance of state-of-the-art supervised and unsupervised methods by testing them on four SOT benchmark datasets – OTB2015, TC128, UAV123 and LaSOT. Experiments show that UHP-SOT++ outperforms all previous unsupervised methods and several deep-learning (DL) methods in tracking accuracy. Since UHP-SOT++ has extremely small model size, high tracking performance, and low computational complexity (operating at a rate of 20 FPS on an i5 CPU even without code optimization), it is an ideal solution in real-time object tracking on resource-limited platforms. Based on the experimental results, we compare pros and cons of supervised and unsupervised trackers and provide a new perspective to understand the performance gap between supervised and unsupervised methods, which is the third contribution of this work.
Fully Linear Graph Convolutional Networks for Semi-Supervised Learning and Clustering

This paper presents FLGC, a simple yet effective fully linear graph convolutional network for semi-supervised and unsupervised learning. Instead of using gradient descent, we train FLGC based on computing a global optimal closed-form solution with a decoupled procedure, resulting in a generalized linear framework and making it easier to implement, train, and apply. We show that (1) FLGC is powerful to deal with both graph-structured data and regular data, (2) training graph convolutional models with closed-form solutions improve computational efficiency without degrading performance, and (3) FLGC acts as a natural generalization of classic linear models in the non-Euclidean domain, e.g., ridge regression and subspace clustering. Furthermore, we implement a semi-supervised FLGC and an unsupervised FLGC by introducing an initial residual strategy, enabling FLGC to aggregate long-range neighborhoods and alleviate over-smoothing. We compare our semi-supervised and unsupervised FLGCs against many state-of-the-art methods on a variety of classification and clustering benchmarks, demonstrating that the proposed FLGC models consistently outperform previous methods in terms of accuracy, robustness, and learning efficiency. The core code of our FLGC is released at https://github.com/AngryCai/FLGC.
Local Multi-Head Channel Self-Attention for Facial Expression Recognition

Since the Transformer architecture was introduced in 2017, there has been many attempts to bring the self-attention paradigm in the field of computer vision. In this paper, we propose LHC: Local multi-Head Channel self-attention, a novel self-attention module that can be easily integrated into virtually every convolutional neural network, and that is specifically designed for computer vision, with a specific focus on facial expression recognition. LHC is based on two main ideas: first, we think that in computer vision, the best way to leverage the self-attention paradigm is the channel-wise application instead of the more well explored spatial attention. Secondly, a local approach has the potential to better overcome the limitations of convolution than global attention, at least in those scenarios where images have a constant general structure, as in facial expression recognition. LHC-Net achieves a new state-of-the-art in the FER2013 dataset, with a significantly lower complexity and impact on the “host” architecture in terms of computational cost when compared with the previous state-of-the-art.
Category-orthogonal object features guide information processing in recurrent neural networks trained for object categorization

Recurrent neural networks (RNNs) have been shown to perform better than feedforward architectures in visual object categorization tasks, especially in challenging conditions such as cluttered images. However, little is known about the exact computational role of recurrent information flow in these conditions. Here we test RNNs trained for object categorization on the hypothesis that recurrence iteratively aids object categorization via the communication of category-orthogonal auxiliary variables (the location, orientation, and scale of the object). Using diagnostic linear readouts, we find that: (a) information about auxiliary variables increases across time in all network layers, (b) this information is indeed present in the recurrent information flow, and (c) its manipulation significantly affects task performance. These observations confirm the hypothesis that category-orthogonal auxiliary variable information is conveyed through recurrent connectivity and is used to optimize category inference in cluttered environments.
Observation of different scenarios in different temperatures in small and large collision systems

We used the modified Hagedron function and analyzed the experimental data measured by the BRAHMS, STAR, PHENIX and ALICE Collaborations in Copper-Copper, Gold-Gold, deuteron-Gold, Lead-Lead, proton-Lead and proton-proton collisions, and extracted the related parameters (kinetic freeze-out temperature, transverse flow velocity, kinetic freeze-out volume, mean transverse momentum and initial temperature) from the transverse momentum spectra of the particles (non-strange and strange particles). We observed that all the above parameters decrease from central to peripheral collisions, except transverse flow velocity which remains unchanged from central to peripheral collisions. The kinetic freeze-out temperature depends on the cross-section interaction of the particle such that larger cross-section of the particle corresponds to smaller T0, and reveals the two kinetic freeze-out scenario, while the initial temperature depends on the mass of the particle and it increase with the particle mass. The transverse flow velocity and mean transverse momentum depends on the mass of the particle and the former decrease while the later increase with the particle mass. In addition, the kinetic kinetic freeze-out volume also decrease with particle mass which reveals the volume differential freeze-out scenario and indicates different freeze-out surfaces for different particles. We also extracted the entropy index-parameter n and the parameter N0, and the former remains almost unchanged while the later decrease from central to peripheral collisions. Furthermore, the kinetic freeze-out temperature, transverse flow velocity, kinetic freeze-out volume, initial temperature, mean transverse momentum and the parameter N0 at LHC are larger than that of RHIC, and they show their dependence on the collision cross-section as well as on collision energy at RHIC and LHC.
Committing to interdependence: Implications from game theory for human–robot trust

Abstract Human–robot interaction (HRI) and game theory have developed distinct theories of trust for over three decades in relative isolation from one another. HRI has focused on the underlying dimensions, layers, correlates, and antecedents of trust models, while game theory has concentrated on the psychology and strategies behind singular trust decisions. Both fields have grappled to understand over-trust and trust calibration, as well as how to measure trust expectations, risk, and vulnerability. This article presents initial steps in closing the gap between these fields. By using insights and experimental findings from interdependence theory and social psychology, this work starts by analyzing a large game theory competition data set to demonstrate that the strongest predictors for a wide variety of human–human trust interactions are the interdependence-derived variables for commitment and trust that we have developed. It then presents a second study with human subject results for more realistic trust scenarios, involving both human–human and human–machine trust. In both the competition data and our experimental data, we demonstrate that the interdependence metrics better capture social “overtrust” than either rational or normative psychological reasoning, as proposed by game theory. This work further explores how interdependence theory – with its focus on commitment, coercion, and cooperation – addresses many of the proposed underlying constructs and antecedents within human–robot trust, shedding new light on key similarities and differences that arise when robots replace humans in trust interactions.
Conditional Linear Regression for Heterogeneous Covariances

Often machine learning and statistical models will attempt to describe the majority of the data. However, there may be situations where only a fraction of the data can be fit well by a linear regression model. Here, we are interested in a case where such inliers can be identified by a Disjunctive Normal Form (DNF) formula. We give a polynomial time algorithm for the conditional linear regression task, which identifies a DNF condition together with the linear predictor on the corresponding portion of the data. In this work, we improve on previous algorithms by removing a requirement that the covariances of the data satisfying each of the terms of the condition have to all be very similar in spectral norm to the covariance of the overall condition.
A modular equality for m$m$ ‐ovoids of elliptic quadrics

An m$m$ ‐ovoid of a finite polar space P$\mathcal {P}$ is a set O$\mathcal {O}$ of points such that every maximal subspace of P$\mathcal {P}$ contains exactly m$m$ points of O$\mathcal {O}$ . In the case when P$\mathcal {P}$ is an elliptic quadric Q−(2r+1,q)$\mathcal {Q}^-(2r+1, q)$ of rank r$r$ in Fq2r+2$\mathbb {F}_q^{2r+2}$ , we prove that an m$m$ ‐ovoid exists only if m$m$ satisfies a certain modular equality, which depends on q$q$ and r$r$ . This condition rules out many of the possible values of m$m$ . Previously, only a lower bound on m$m$ was known, which we slightly improve as a byproduct of our method. We also obtain a characterization of the m$m$ ‐ovoids of Q−(7,q)$\mathcal {Q}^{-}(7,q)$ for q=2$q = 2$ and (m,q)=(4,3)$(m, q) = (4, 3)$ .
Perceived Value of Time for Truck Operators

Value of time for trucks was estimated from stated preference data collected in California. Truckers were asked about a choice between an existing free road versus a toll facility for different combinations of travel time and cost. Estimation was based on the point of diversion at which the switch of facility occurred in the stated preference questions and also on the use of a modified logit model in which the coefficients to be estimated were assumed to be distributed lognormally across the population. Comparisons between data sets that were segmented according to business type, shipment size, and the method of driver compensation indicated that for-hire trucks tend to have higher values of time than private ones and the companies that pay drivers hourly wages have higher values of time than those who pay commissions or fixed salary.
Quadratic speedup of global search using a biased crossover of two good solutions

The minimisation of cost functions is crucial in various optimisation fields. However, identifying their global minimum remains challenging owing to the huge computational cost incurred. This work analytically expresses the computational cost to identify an approximate global minimum for a class of cost functions defined under a high-dimensional discrete state space. Then, we derive an optimal global search scheme that minimises the computational cost. Mathematical analyses demonstrate that a combination of the gradient descent algorithm and the selection and crossover algorithm--with a biased crossover weight--maximises the search efficiency. Remarkably, its computational cost is of the square root order in contrast to that of the conventional gradient descent algorithms, indicating a quadratic speedup of global search. We corroborate this proposition using numerical analyses of the travelling salesman problem. The simple computational architecture and minimal computational cost of the proposed scheme are highly desirable for biological organisms and neuromorphic hardware.
Asymptotics of the eigenvalues of seven-diagonal Toeplitz matrices of a special form

We find uniform asymptotic formulas for all the eigenvalues of certain 7-diagonal symmetric Toeplitz matrices of large dimension. The entries of the matrices are real and we consider the case where the real-valued generating function such that its first five derivatives at the one endpoint of interval are equal zero. This is not the simple-loop case considered earlier. We obtain nonlinear equations for the eigenvalues. It should be noted that our equations have a more complicated structure than the equations for the simple loop case.
Young and Young–Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states

Motivated by the need for greater understanding of systems that involve interfaces between a nematic liquid crystal, a solid substrate and a passive gas that include nematic–substrate–gas three-phase contact lines, we analyse a two-dimensional static ridge of nematic resting on a solid substrate in an atmosphere of passive gas. Specifically, we obtain the first complete theoretical description for this system, including nematic Young and Young–Laplace equations, and then, making the assumption that anchoring breaking occurs in regions adjacent to the contact lines, we use the nematic Young equations to determine the continuous and discontinuous transitions that occur between the equilibrium states of complete wetting, partial wetting and complete dewetting. In particular, in addition to continuous transitions analogous to those that occur in the classical case of an isotropic liquid, we find a variety of discontinuous transitions, as well as contact-angle hysteresis, and regions of parameter space in which there exist multiple partial wetting states that do not occur in the classical case.
Convergence and Equilibria Analysis of a Networked Bivirus Epidemic Model

This paper studies a networked bivirus model, in which two competing viruses spread across a network of interconnected populations; each node represents a population with a large number of individuals. The viruses may spread through possibly different network structures, and an individual cannot be simultaneously infected with both viruses. Focusing on convergence and equilibria analysis, a number of new results are provided. First, we show that for networks with generic system parameters, there exist a finite number of equilibria. Exploiting monotone systems theory, we further prove that for bivirus networks with generic system parameters, then convergence to an equilibrium occurs for all initial conditions, except possibly for a set of measure zero. Given the network structure of one virus, a method is presented to construct an infinite family of network structures for the other virus that results in an infinite number of equilibria in which both viruses coexist. Necessary and sufficient conditions are derived for the local stability/instability of boundary equilibria, in which one virus is present and the other is extinct. A sufficient condition for a boundary equilibrium to be almost globally stable is presented. Then, we show how to use monotone systems theory to generate conclusions on the ordering of stable and unstable equilibria, and in some instances identify the number of equilibria via rapid simulation testing. Last, we provide an analytical method for computing equilibria in networks with only two nodes, and show that it is possible for a bivirus network to have an unstable coexistence equilibrium and two locally stable boundary equilibria.
Improving usual Naive Bayes classifier performances with Neural Naive Bayes based models

Naive Bayes is a popular probabilistic model appreciated for its simplicity and interpretability. However, the usual form of the related classifier suffers from two major problems. First, as caring about the observations' law, it cannot consider complex features. Moreover, it considers the conditional independence of the observations given the hidden variable. This paper introduces the original Neural Naive Bayes, modeling the parameters of the classifier induced from the Naive Bayes with neural network functions. This allows to correct the first problem. We also introduce new Neural Pooled Markov Chain models, alleviating the independence condition. We empirically study the benefits of these models for Sentiment Analysis, dividing the error rate of the usual classifier by 4.5 on the IMDB dataset with the FastText embedding.
CoLLIE: Continual Learning of Language Grounding from Language-Image Embeddings

This paper presents CoLLIE: a simple, yet effective model for continual learning of how language is grounded in vision. Given a pre-trained multimodal embedding model, where language and images are projected in the same semantic space (in this case CLIP by OpenAI), CoLLIE learns a transformation function that adjusts the language embeddings when needed to accommodate new language use. This is done by predicting the difference vector that needs to be applied, as well as a scaling factor for this vector, so that the adjustment is only applied when needed. Unlike traditional few-shot learning, the model does not just learn new classes and labels, but can also generalize to similar language use and leverage semantic compositionality. We verify the model’s performance on two different tasks of identifying the targets of referring expressions, where it has to learn new language use. The results show that the model can efficiently learn and generalize from only a few examples, with little interference with the model’s original zero-shot performance.