Miracle-dz/UniFAR-FTUs huggingface dataset:
Relevance Judgment Convergence Degree - A Measure of Inconsistency among Assessors for Information Retrieval

Relevance judgment of human assessors is inherently subjective and dynamic when evaluation datasets are created for Information Retrieval (IR) systems. However, a small group of experts’ relevance judgment results are usually taken as ground truth to “objectively” evaluate the performance of the IR systems. Recent trends intend to employ a group of judges, such as outsourcing, to alleviate the potentially biased judgment results stemmed from using only a single expert’s judgment. Nevertheless, different judges may have different opinions and may not agree with each other, and the inconsistency in human relevance judgment may affect the IR system evaluation results. In this research, we introduce a Relevance Judgment Convergence Degree (RJCD) to measure the quality of queries in the evaluation datasets. Experimental results reveal a strong correlation coefficient between the proposed RJCD score and the performance differences between the two IR systems.
An Unsupervised Learning Approach for Spectrum Allocation in Terahertz Communication Systems

We propose a new spectrum allocation strategy, aided by unsupervised learning, for multiuser terahertz communication systems. In this strategy, adaptive sub-band bandwidth is considered such that the spectrum of interest can be divided into sub-bands with unequal bandwidths. This strategy reduces the variation in molecular absorption loss among the users, leading to the improved data rate performance. We first formulate an optimization problem to determine the optimal sub-band bandwidth and transmit power, and then propose the unsupervised learning-based approach to obtaining the near-optimal solution to this problem. In the proposed approach, we first train a deep neural network (DNN) while utilizing a loss function that is inspired by the Lagrangian of the formulated problem. Then using the trained DNN, we approximate the near-optimal solutions. Numerical results demonstrate that comparing to existing approaches, our proposed unsupervised learning-based approach achieves a higher data rate, especially when the molecular absorption coefficient within the spectrum of interest varies in a highly non-linear manner.
Parameter uniform numerical method for singularly perturbed two parameter parabolic problem with discontinuous convection coefficient and source term

In this article, we have considered a time-dependent two-parameter singularly perturbed parabolic problem with discontinuous convection coefficient and source term. The problem contains the parameters $\epsilon$ and $\mu$ multiplying the diffusion and convection coefficients, respectively. A boundary layer develops on both sides of the boundaries as a result of these parameters. An interior layer forms near the point of discontinuity due to the discontinuity in the convection and source term. The width of the interior and boundary layers depends on the ratio of the perturbation parameters. We discuss the problem for ratio $\displaystyle\frac{\mu^2}{\epsilon}$. We used an upwind finite difference approach on a Shishkin-Bakhvalov mesh in the space and the Crank-Nicolson method in time on uniform mesh. At the point of discontinuity, a three-point formula was used. This method is uniformly convergent with second order in time and first order in space. Shishkin-Bakhvalov mesh provides first-order convergence; unlike the Shishkin mesh, where a logarithmic factor deteriorates the order of convergence. Some test examples are given to validate the results presented.
Content-Based Landmark Retrieval Combining Global and Local Features using Siamese Neural Networks

In this work, we present a method for landmark retrieval that utilizes global and local features. A Siamese network is used for global feature extraction and metric learning, which gives an initial ranking of the landmark search. We utilize the extracted feature maps from the Siamese architecture as local descriptors, the search results are then further refined using a cosine similarity between local descriptors. We conduct a deeper analysis of the Google Landmark Dataset, which is used for evaluation, and augment the dataset to handle various intra-class variances. Furthermore, we conduct several experiments to compare the effects of transfer learning and metric learning, as well as experiments using other local descriptors. We show that a re-ranking using local features can improve the search results. We believe that the proposed local feature extraction using cosine similarity is a simple approach that can be extended to many other retrieval tasks.
A high-resolution dynamical view on momentum methods for over-parameterized neural networks

Due to the simplicity and efficiency of the first-order gradient method, it has been widely used in training neural networks. Although the optimization problem of the neural network is non-convex, recent research has proved that the first-order method is capable of attaining a global minimum for training over-parameterized neural networks, where the number of parameters is significantly larger than that of training instances. Momentum methods, including heavy ball method (HB) and Nesterov's accelerated method (NAG), are the workhorse first-order gradient methods owning to their accelerated convergence. In practice, NAG often exhibits better performance than HB. However, current research fails to distinguish their convergence difference in training neural networks. Motivated by this, we provide convergence analysis of HB and NAG in training an over-parameterized two-layer neural network with ReLU activation, through the lens of high-resolution dynamical systems and neural tangent kernel (NTK) theory. Compared to existing works, our analysis not only establishes tighter upper bounds of the convergence rate for both HB and NAG, but also characterizes the effect of the gradient correction term, which leads to the acceleration of NAG over HB. Finally, we validate our theoretical result on three benchmark datasets.
Revisiting Random Points: Combinatorial Complexity and Algorithms

Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new concentration result on the number of pairs of points of $P$ at a distance at most $r$ -- we show that this number lies in an interval that contains only $O(n \log n)$ numbers. We also present simple linear time algorithms to construct the Delaunay triangulation, Euclidean MST, and the convex hull of the points of $P$. The MST algorithm is an interesting divide-and-conquer algorithm which might be of independent interest. We also provide a new proof that the expected complexity of the Delaunay triangulation of $P$ is linear -- the new proof is simpler and more direct, and might be of independent interest. Finally, we present a simple $\tilde{O}(n^{4/3})$ time algorithm for the distance selection problem for $d=2$.
Causality in cardiorespiratory signals in pediatric cardiac patients

Four different Granger causality-based methods - one linear and three nonlinear (Granger Causality, Kernel Granger Causality, large-scale Nonlinear Granger Causality, and Neural Network Granger Causality) were used for assessment and causal-based quantification of the respiratory sinus arrythmia (RSA) in the group of pediatric cardiac patients, based on the single-lead ECG and impedance pneumography signals (the latter as the tidal volume curve equivalent). Each method was able to detect the dependency (in terms of causal inference) between respiratory and cardiac signals. The correlations between quantified RSA and the demographic parameters were also studied, but the results differ for each method. Clinical relevance- The presented methods (among which NNGC seems to be the most valid) allow for quantification of RSA and study of dependency between tidal volume and RR intervals which may help to better understand association between respiratory and cardiovascular systems in different populations.
The geometry of immobilizing sets of objects

When an object is grasped by a set of fingers, it is important to know the best positions to place them. An immobilizing set is a set of points on the object at which a firm grasp of the object is achieved, that is, where the object cannot be moved within the grasp. In this thesis a study of immobilizing sets of points for planar figures and tetrahedra is undertaken. A new proof of Czyzowicz, Stojmenovic and Urrutia’s theorem giving necessary and sufficient geometric conditions for immobilizing a triangle is obtained. The same method of proof is employed to obtain proofs of statements on immobilizing sets of polygonal planar objects. In three dimensions, a detailed study of immobilizing sets of a tetrahedron is carried out. A 3 × 3 matrix A is defined for each quadruple of points, one from the interior of each face of the tetrahedron using a good choice of outward normal vectors to the faces of the tetrahedron. A necessary and sufficient condition on the quadruple of points to immobilize the tetrahedron is that the matrix A is symmetric. An analysis of the eigenvalues of symmetric matrix A leads to a new proof of Bracho, Mayer, Fetter and Montejano’s theorem. This proof is adapted to give another treatment of necessary and sufficient conditions characterizing immobilizing sets of a triangle. The set of centroids, set of circumcenters and set of orthocenters of the faces of a tetrahedron are shown to immobilize it in appropriate cases. It is shown that a set of four immobilizing points one in each face of the tetrahedron has five degrees of freedom and immobilizing sets of a tetrahedron having two fixed points have one degree of freedom. An analysis of the orientation of the tetrahedron whose vertices are the points in an immobilizing set of a given tetrahedron reveals the existence of immobilizing sets of a regular tetrahedron which are co-planar. In higher dimensions, a method of generating sets of points for which the matrix A is symmetric from another such set is presented and some geometrical properties arising from the symmetry of A are analysed.
Site adaptation with machine learning for a Northern Europe gridded solar radiation product

Gridded global horizontal irradiance (GHI) databases are fundamental for analysing solar energy applications' technical and economic aspects, particularly photovoltaic applications. Today, there exist numerous gridded GHI databases whose quality has been thoroughly validated against ground-based irradiance measurements. Nonetheless, databases that generate data at latitudes above 65$^{\circ}$ are few, and those available gridded irradiance products, which are either reanalysis or based on polar orbiters, such as ERA5, COSMO-REA6, or CM SAF CLARA-A2, generally have lower quality or a coarser time resolution than those gridded irradiance products based on geostationary satellites. Among the high-latitude gridded GHI databases, the STR\r{A}NG model developed by the Swedish Meteorological and Hydrological Institute (SMHI) is likely the most accurate one, providing data across Sweden. To further enhance the product quality, the calibration technique called"site adaptation"is herein used to improve the STR\r{A}NG dataset, which seeks to adjust a long period of low-quality gridded irradiance estimates based on a short period of high-quality irradiance measurements. This study, differing from the conventional statistical approaches, adopts machine learning for site adaptation. Nine machine-learning algorithms have been analysed and compared with conventional statistical ones to identify Sweden's most favourable technique for site adaptation. Three weather stations of SMHI are used for training and validation. The results show that, due to the spatio-temporal heterogeneity in model performance, no universal model can be identified, which suggests that site adaptation is a location-dependent procedure.
Monodromy of four‐dimensional irreducible compatible systems of Q$\mathbb {Q}$

Let F$F$ be a totally real field and n⩽4$n\leqslant 4$ a natural number. We study the monodromy groups of any n$n$ ‐dimensional strictly compatible system {ρλ}λ$\lbrace \rho _\lambda \rbrace _\lambda$ of λ$\lambda$ ‐adic representations of F$F$ with distinct Hodge–Tate numbers such that ρλ0$\rho _{\lambda _0}$ is irreducible for some λ0$\lambda _0$ . When F=Q$F=\mathbb {Q}$ , n=4$n=4$ , and ρλ0$\rho _{\lambda _0}$ is fully symplectic, the following assertions are obtained. (i)The representation ρλ$\rho _\lambda$ is fully symplectic for almost all λ$\lambda$ . (ii)If in addition the similitude character μλ0$\mu _{\lambda _0}$ of ρλ0$\rho _{\lambda _0}$ is odd, then the system {ρλ}λ$\lbrace \rho _\lambda \rbrace _\lambda$ is potentially automorphic and the residual image ρ¯λ(GalQ)$\bar{\rho }_\lambda (\operatorname{Gal}_\mathbb {Q})$ has a subgroup conjugate to Sp4(Fℓ)$\mathrm{Sp}_4(\mathbb {F}_\ell )$ for almost all λ$\lambda$ .
DarkMix: Mixture Models for the Detection and Characterization of Dark Matter Halos

Dark matter simulations require statistical techniques to properly identify and classify their halos and structures. Nonparametric solutions provide catalogs of these structures but lack the additional learning of a model-based algorithm and might misclassify particles in merging situations. With mixture models, we can simultaneously fit multiple density profiles to the halos that are found in a dark matter simulation. In this work, we use the Einasto profile to model the halos found in a sample of the Bolshoi simulation, and we obtain their location, size, shape, and mass. Our code is implemented in the R statistical software environment and can be accessed on https://github.com/LluisHGil/darkmix.
Selectively Combining Multiple Coverage Goals in Search-Based Unit Test Generation

Unit testing is a critical part of software development process, ensuring the correctness of basic programming units in a program (e.g., a method). Search-based software testing (SBST) is an automated approach to generating test cases. SBST generates test cases with genetic algorithms by specifying the coverage criterion (e.g., branch coverage). However, a good test suite must have different properties, which cannot be captured by using an individual coverage criterion. Therefore, the state-of-the-art approach combines multiple criteria to generate test cases. As combining multiple coverage criteria brings multiple objectives for optimization, it hurts the test suites’ coverage for certain criteria compared with using the single criterion. To cope with this problem, we propose a novel approach named smart selection. Based on the coverage correlations among criteria and the coverage goals’ subsumption relationships, smart selection selects a subset of coverage goals to reduce the number of optimization objectives and avoid missing any properties of all criteria. We conduct experiments to evaluate smart selection on 400 Java classes with three state-of-the-art genetic algorithms. On average, smart selection outperforms combining all goals on of the classes having significant differences between the two approaches.
Dataset Obfuscation: Its Applications to and Impacts on Edge Machine Learning

Obfuscating a dataset by adding random noises to protect the privacy of sensitive samples in the training dataset is crucial to prevent data leakage to untrusted parties for edge applications. We conduct comprehensive experiments to investigate how the dataset obfuscation can affect the resultant model weights - in terms of the model accuracy, Frobenius-norm (F-norm)-based model distance, and level of data privacy - and discuss the potential applications with the proposed Privacy, Utility, and Distinguishability (PUD)-triangle diagram to visualize the requirement preferences. Our experiments are based on the popular MNIST and CIFAR-10 datasets under both independent and identically distributed (IID) and non-IID settings. Significant results include a trade-off between the model accuracy and privacy level and a trade-off between the model difference and privacy level. The results indicate broad application prospects for training outsourcing in edge computing and guarding against attacks in Federated Learning among edge devices.
A Parallel Technique for Multi-objective Bayesian Global Optimization: Using a Batch Selection of Probability of Improvement

Bayesian global optimization (BGO) is an efficient surrogate-assisted technique for problems involving expensive evaluations. A parallel technique can be used to parallelly evaluate the true-expensive objective functions in one iteration to boost the execution time. An effective and straightforward approach is to design an acquisition function that can evaluate the performance of a bath of multiple solutions, instead of a single point/solution, in one iteration. This paper proposes five alternatives of \emph{Probability of Improvement} (PoI) with multiple points in a batch (q-PoI) for multi-objective Bayesian global optimization (MOBGO), taking the covariance among multiple points into account. Both exact computational formulas and the Monte Carlo approximation algorithms for all proposed q-PoIs are provided. Based on the distribution of the multiple points relevant to the Pareto-front, the position-dependent behavior of the five q-PoIs is investigated. Moreover, the five q-PoIs are compared with the other nine state-of-the-art and recently proposed batch MOBGO algorithms on twenty bio-objective benchmarks. The empirical experiments on different variety of benchmarks are conducted to demonstrate the effectiveness of two greedy q-PoIs ($\kpoi_{\mbox{best}}$ and $\kpoi_{\mbox{all}}$) on low-dimensional problems and the effectiveness of two explorative q-PoIs ($\kpoi_{\mbox{one}}$ and $\kpoi_{\mbox{worst}}$) on high-dimensional problems with difficult-to-approximate Pareto front boundaries.
DP2-VAE: Differentially Private Pre-trained Variational Autoencoders

Modern machine learning systems achieve great success when trained on large datasets. However, these datasets usually contain sensitive information (e.g. medical records, face images), leading to serious privacy concerns. Differentially private generative models (DPGMs) emerge as a solution to circumvent such privacy concerns by generating privatized sensitive data. Similar to other differentially private (DP) learners, the major challenge for DPGM is also how to achieve a subtle balance between utility and privacy. We propose DP$^2$-VAE, a novel training mechanism for variational autoencoders (VAE) with provable DP guarantees and improved utility via \emph{pre-training on private data}. Under the same DP constraints, DP$^2$-VAE minimizes the perturbation noise during training, and hence improves utility. DP$^2$-VAE is very flexible and easily amenable to many other VAE variants. Theoretically, we study the effect of pretraining on private data. Empirically, we conduct extensive experiments on image datasets to illustrate our superiority over baselines under various privacy budgets and evaluation metrics.
Novel Supernumerary Robotic Limb based on Variable Stiffness Actuators for Hemiplegic Patients Assistance

Loss of upper extremity motor control and function is an unremitting symptom in post-stroke patients. This would impose hardships on accomplishing their daily life activities. Supernumerary robotic limbs (SRLs) were introduced as a solution to regain the lost Degrees of Freedom (DoFs) by introducing an independent new limb. The actuation systems in SRL can be categorized into rigid and soft actuators. Soft actuators have proven advantageous over their rigid counterparts through intrinsic safety, cost, and energy efficiency. However, they suffer from low stiffness, which jeopardizes their accuracy. Variable Stiffness Actuators (VSAs) are newly developed technologies that have been proven to ensure accuracy and safety. In this paper, we introduce the novel Supernumerary Robotic Limb based on Variable Stiffness Actuators. Based on our knowledge, the proposed proof-of-concept SRL is the first that utilizes Variable Stiffness Actuators. The developed SRL would assist post-stroke patients in bi-manual tasks, e.g., eating with a fork and knife. The modeling, design, and realization of the system are illustrated. The proposed SRL was evaluated and verified for its accuracy via predefined trajectories. The safety was verified by utilizing the momentum observer for collision detection, and several post-collision reaction strategies were evaluated through the Soft Tissue Injury Test. The assistance process is qualitatively verified through standard user-satisfaction questionnaire.
Achievable Refined Asymptotics for Successive Refinement Using Gaussian Codebooks

We study the mismatched successive refinement problem where one uses Gaussian codebooks to compress an arbitrary memoryless source with successive minimum Euclidean distance encoding under the quadratic distortion measure. Specifically, we derive achievable refined asymptotics under both the joint excess-distortion probability (JEP) and the separate excess-distortion probabilities (SEP) criteria. For both second-order and moderate deviations asymptotics, we consider two types of codebooks: the spherical codebook where each codeword is drawn independently and uniformly from the surface of a sphere and the i.i. d. Gaussian codebook where each component of each codeword is drawn independently from a Gaussian distribution. We establish the achievable second-order rate-region under JEP and we show that under SEP any memoryless source satisfying mild moment conditions is strongly successively refinable. When specialized to a Gaussian memoryless source (GMS), our results provide an alternative achievability proof with specific code design. We show that under JEP and SEP, the same moderate deviations constant is achievable. For large deviations asymptotics, we only consider the i.i. d. Gaussian codebook since the i.i. d. Gaussian codebook has better performance than the spherical codebook in this regime for the one layer mismatched rate-distortion problem (Zhou et al., 2019). We derive achievable exponents of both JEP and SEP and specialize our results to a GMS, which appears to be a novel result of independent interest.
An Optimal “It Ain’t Over Till It’s Over” Theorem

We study the probability of Boolean functions with small max influence to become constant under random restrictions. Let f be a Boolean function such that the variance of f is Ω(1) and all its individual influences are bounded by τ. We show that when restricting all but a ρ=Ω((log1/τ)−1) fraction of the coordinates, the restricted function remains nonconstant with overwhelming probability. This bound is essentially optimal, as witnessed by the tribes function =n/Clogn∘Clogn. We extend it to an anti-concentration result, showing that the restricted function has nontrivial variance with probability 1−o(1). This gives a sharp version of the “it ain’t over till it’s over” theorem due to Mossel, O’Donnell, and Oleszkiewicz. Our proof is discrete, and avoids the use of the invariance principle. We also show two consequences of our above result: (i) As a corollary, we prove that for a uniformly random input x, the block sensitivity of f at x is Ω(log1/τ) with probability 1−o(1). This should be compared with the implication of Kahn, Kalai and Linial’s result, which implies that the average block sensitivity of f is Ω(log1/τ). (ii) Combining our proof with a well-known result due to O’Donnell, Saks, Schramm and Servedio, one can also conclude that: Restricting all but a ρ=Ω(1/√log(1/τ) ) fraction of the coordinates of a monotone function f, then the restricted function has decision tree complexity Ω(τ−Θ(ρ)) with probability Ω(1).