Reviewerly/exHarmony huggingface dataset:
Oracle Computability and Turing Reducibility in the Calculus of Inductive Constructions

We develop synthetic notions of oracle computability and Turing reducibility in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. As usual in synthetic approaches, we employ a definition of oracle computations based on meta-level functions rather than object-level models of computation, relying on the fact that in constructive systems such as CIC all definable functions are computable by construction. Such an approach lends itself well to machine-checked proofs, which we carry out in Coq. There is a tension in finding a good synthetic rendering of the higher-order notion of oracle computability. On the one hand, it has to be informative enough to prove central results, ensuring that all notions are faithfully captured. On the other hand, it has to be restricted enough to benefit from axioms for synthetic computability, which usually concern first-order objects. Drawing inspiration from a definition by Andrej Bauer based on continuous functions in the effective topos, we use a notion of sequential continuity to characterise valid oracle computations. As main technical results, we show that Turing reducibility forms an upper semilattice, transports decidability, and is strictly more expressive than truth-table reducibility, and prove that whenever both a predicate p and its complement are semi-decidable relative to an oracle q, then p Turing-reduces to q.
Lexical simplification in learner translation: A corpus-based approach

The advance of corpus-based methodology in translation studies has greatly enhanced our understanding of the nature of translational language. While most research efforts have focused on identifying the unique features of translations carried out by professionals, comparatively fewer studies have investigated the linguistic features of student translations. In this corpus-based study, we examine if learner translations carried out by Hong Kong students exhibit lexical simplification features vis-à-vis comparable written texts. The study is based on two comparable corpora: the International Corpus of English in Hong Kong (ICE-HK) and the Parallel Learner Translation Corpus (PLTC) compiled at The Hong Kong Polytechnic University. Following Laviosa (1998), we compare four main lexical features (lexical density, type-token ratio, core vocabulary coverage, and list head coverage) to investigate if student translations show a simplification trend. The results demonstrate that Chinese-to-English translation is not lexically simpler than English as a Second Language (ESL) writing. Furthermore, it is lexically denser than ESL writing. Our study aims to provide new insights into learner translation as a form of constrained communication.
Transport via Partial Galois Connections and Equivalences

Multiple types can represent the same concept. For example, lists and trees can both represent sets. Unfortunately, this easily leads to incomplete libraries: some set-operations may only be available on lists, others only on trees. Similarly, subtypes and quotients are commonly used to construct new type abstractions in formal verification. In such cases, one often wishes to reuse operations on the representation type for the new type abstraction, but to no avail: the types are not the same. To address these problems, we present a new framework that transports programs via equivalences. Existing transport frameworks are either designed for dependently typed, constructive proof assistants, use univalence, or are restricted to partial quotient types. Our framework (1) is designed for simple type theory, (2) generalises previous approaches working on partial quotient types, and (3) is based on standard mathematical concepts, particularly Galois connections and equivalences. We introduce the notions of partial Galois connection and equivalence and prove their closure properties under (dependent) function relators, (co)datatypes, and compositions. We formalised the framework in Isabelle/HOL and provide a prototype.
A Few Key Probability Theory Results

The materials presented in this book are undeniably technical in nature. We established numerous theoretical conclusions by relying on classical probability theory results. Although these conclusions are well-known, many of us often struggle to recall the exact details. Notably, these conclusions are sometimes quoted from papers or books without specifying their applicability to a given context, making it challenging to ensure that the required conditions are met. Chapter 17 compiles some of these cited conclusions from the previous chapters to facilitate reference and ensure clarity regarding their specific contexts.
Modified Likelihood Ratio Test

While achieving a profound understanding of the limiting distribution of the likelihood ratio test under mixture models is indeed a grand success, translating this knowledge into concrete data analysis procedures can be challenging. One potential approach is to adhere to the fundamental principle of the likelihood ratio test but make slight adjustments to develop effective procedures. The modified likelihood ratio test for homogeneity is a product of this approach, grounded in a deep comprehension of two forms of problematic partial non-identifiability within the finite mixture model. By introducing a penalty term to the log likelihood function, the modified likelihood ratio test mitigates one of these issues, restoring a degree of regularity. Chapter 11 is dedicated to providing a detailed analysis of the limiting distribution for the modified likelihood ratio test for homogeneity.
Experimenting with an Intrinsically-Typed Probabilistic Programming Language in Coq

Although the formalization of probabilistic programs already has several applications in the fields of security proofs and artificial intelligence, formal verification experiments are still underway to support the many features of probabilistic programming. We report on the formalization in the Coq proof assistant of a syntax and a denotational semantics for a probabilistic programming language with sampling, scoring, and normalization. We use dependent types in a crucial way since our syntax is intrinsically-typed and since the semantic values are essentially dependent records. Thanks to the features of Coq, we can use notations that hide the details of type inference when writing examples. The resulting formalization is usable to reason about simple probabilistic programs.
Likelihood Ratio Test for Homogeneity

Despite the successful application of the C( $$\alpha $$ ) test, statisticians continue to explore the utility of the likelihood ratio test for homogeneity under finite mixture models. For those who opt for the likelihood ratio test, a crucial undertaking involves determining the distribution or the limiting distribution of this test. This task becomes exceedingly challenging when the parameter space for subpopulations is unbounded. One solution to this challenge was proposed, albeit it required a seemingly unnecessary separation condition. However, after numerous dedicated efforts, a comprehensive and satisfying solution emerged. Chapter 10 does not go over the grand solution, but is dedicated to providing answers to specific scenarios where concrete results are attainable. This chapter serves to demystify the complexities associated with this formidable task.
Priority Planning for Robots via Fuzzy Logic Controller

In this paper, a novel solution for resolving path planning conflicts for multiple robots by considering the priority levels of the robots is proposed. The proposed algorithm integrated fuzzy logic controller inspired by International Regulations for Preventing Collisions at Sea (COLREGs) traffic rules with a collision area membership function that identifies suitable traffic procedures for each robot to take, into the existing local and global planner and to address the problem of robot navigation in narrow environments. The proposed algorithm was validated using a simulation that used parameters from a Pioneer 3DX robot and a 2D scanned world map. The robots that were used, and the proposed planning algorithm, are generic and could be applied in various real scenarios, such as production facilities, warehouses and product delivery. The results of the simulation experiments demonstrate that this algorithm can effectively solve the problem of ensuring that robots with higher priority pass through narrow areas first.
Robust loss function for class imbalanced semantic segmentation and image classification

Real world datasets are often unbalanced. Such an imbalance in data can limit the performance of modern deep learning based solutions by introducing a bias in the trained model. In particular, the trained model show weak performance on sub tasks or classes where the data availability is sparse. In this work, we address such a data imbalance problem and propose a novel modification to the existing cross-entropy loss function to mitigate the issue. Our proposed loss function can amplify the loss gradients generated during the back-propagation step. In particular, we penalize the predictions of the model which can result in higher loss values and gradients. We compare our proposed loss function with several recently proposed approaches and show superior performance. Our experiments show that proposed approach achieves state of the art performance on log-tailed image classification on CIFAR100/10-LT and Imagenet-LT datasets and on semantic segmentation task on Citiscapes dataset.
SA-reCBS: Multi-robot task assignment with integrated reactive path generation

In this paper, we study the multi-robot task assignment and path-finding problem (MRTAPF), where a number of robots are required to visit all given tasks while avoiding collisions with each other. We propose a novel two-layer algorithm SA-reCBS that cascades the simulated annealing algorithm and conflict-based search to solve this problem. Compared to other approaches in the field of MRTAPF, the advantage of SA-reCBS is that without requiring a pre-bundle of tasks to groups with the same number of groups as the number of robots, it enables a part of robots needed to visit all tasks in collision-free paths. We test the algorithm in various simulation instances and compare it with state-of-the-art algorithms. The result shows that SA-reCBS has a better performance with a higher success rate, less computational time, and better objective values.
Least-square Fitting on the Circle using Optimal Control

Filtering of circular data from noisy measurements is well known to be a hard problem because of the ambiguity of the wrapped phase and further complicated by the constraint that filtered states need to be on the circle. Probabilistic models focus on specifying the dynamics of the random phase and then estimate these states recursively using Bayes' formula, while deterministic approaches normally define a cost function containing the error between the states and measurements and then minimize it over all allowed state paths. In this paper, we construct a deterministic filter on the circle by minimizing the least square error based on Pontryagin's minimum principle, where the optimal state trajectory is described by a bilinear differential equation with deterministic optimal control input. The effectiveness of the proposed filter is shown through numerical experiments.
Quantum state and detector tomography with known rank

Quantum state tomography and quantum detector tomography are two main problems in quantum system identification. In this paper, we study state tomography and detector tomography with prior knowledge about the true rank of the unknown state/detector. In this case, we propose a sufficient condition for static (non-adaptive) tomography algorithms to achieve the optimal infidelity scaling O(1/N) on the number of state copies N. Then we present two examples of such static quantum state tomography and quantum detector tomography algorithms. Numerical examples demonstrate the effectiveness of our algorithms.
Optimal control of multiple drones for obstacle avoidance

The control and path planning of multiple drones in a 3D space with obstacle avoidance is a complex challenge, subject to ongoing research. In this paper we propose an optimal control approach, with a baseline controller and filter running on the drones, and a prediction based optimization algorithm running remotely, as a supervisory controller. The supervisor is responsible for calculating the minimal deviation from the trajectory given by the baseline controllers, such that the obstacle is avoided. The approach is tested in simulations with nonlinear drone models in a realistic setting with noise and transmission delays.
Accounting for simulation errors in continuous-discrete Kalman filtering

In continuous-discrete Kalman filter implementations there is a tradeoff between the computational requirements for real time implementation, and errors incurred by selection of step size and method order in the simulation of the continuous time system model between sampling instances. Because the Kalman filter corrects errors in the state vector using output measurements, a systematic approach to account for the effects of simulation errors in the continuous-discrete Kalman filter allows the filter to be designed to deal with simulation errors in addition to conventional process (state) and measurement (output) noise.
Globally Convergent Policy Gradient Methods for Linear Quadratic Control of Partially Observed Systems

While the optimization landscape of policy gradient methods has been recently investigated for partially observed linear systems in terms of both static output feedback and dynamical controllers, they only provide convergence guarantees to stationary points. In this paper, we propose a new policy parameterization for partially observed linear systems, using a past input-output trajectory of finite length as feedback. We show that the solution set to the parameterized optimization problem is a matrix space, which is invariant to similarity transformation. By proving a gradient dominance property, we show the global convergence of policy gradient methods. Moreover, we observe that the gradient is orthogonal to the solution set, revealing an explicit relation between the resulting solution and the initial policy. Finally, we perform simulations to validate our theoretical results.
Adaptive mixture approximation for target tracking in clutter

Target tracking is a state estimation problem common in many practical scenarios like air traffic control, autonomous vehicles, marine radar surveillance and so on. In a Bayesian perspective, when phenomena like clutter are present, most existing tracking algorithms must deal with association hypotheses which may grow in number over time. In that case, the posterior state distribution can quickly become computationally intractable, and approximations must necessarily be introduced. In this work, the impact of the number of hypotheses and of reduction procedures is investigated both in terms of computational resources and tracking performances. For this purpose, a recently developed adaptive mixture model reduction algorithm is considered in order to assess its performances when applied to the problem of single object tracking in the presence of clutter and to provide some interesting insights into the addressed problem.
Sugeno-Type Fuzzy Ontology PI Controller for Proportional Electrohydraulic System

In this paper, an ontology representation of the Sougeno-type PI Fuzzy Logic Controller (FLC) is presented. The proposed controller is an extension of the Fuzzy Ontology Controller (FOC), where the new fuzzy annotations relevant to Sougeno-type fuzzy control are added to the ontology. The design of the fuzzy ontology is carried out in Protégé and it is hosted on a remote server in the Virtuoso database. Simulation results for the proportional electrohydraulic system are presented and compared to the PI and the SMC controller. The simulation results show that the proposed concept works, and achieves similar results to the PI controller. Experimental results are carried out on a proportional electrohydraulic system. Results show good tracking capabilities despite slow network communication between the server and experimental setup.
Exact Set-valued Estimation using Constrained Convex Generators for uncertain Linear Systems

Set-valued state estimation when in the presence of uncertainties in the model have been addressed in the literature essentially following three main approaches: i) interval arithmetic of the uncertain dynamics with the estimates; ii) factorizing the uncertainty into matrices with unity rank; and, iii) performing the convex hull for the vertices of the uncertainty space. Approach i) and ii) introduce a lot of conservatism because both disregard the relationship of the parameters with the entries of the dynamics matrix. On the other hand, approach iii) has a large growth on the number of variables required to represent the set or is approximated losing its main advantage in comparison with i) and ii). In this paper, with the application of autonomous vehicles in GPS-denied areas that resort to beacon signals for localization, we develop an exact (meaning no added conservatism) and optimal (smallest growth in the number of variables) closed-form definition for the convex hull of Convex Constrained Generators (CCGs). This results in a more efficient method to represent the minimum volume convex set corresponding to the state estimation. Given that reductions methods are still lacking in the literature for CCGs, we employ an approximation using ray-shooting that is comparable in terms of accuracy with methods for Constrained Zonotopes as the ones implemented in CORA. Simulations illustrate the greater accuracy of CCGs with the proposed convex hull operation in comparison to Constrained Zonotopes.
Fast IMU-based Dual Estimation of Human Motion and Kinematic Parameters via Progressive In-Network Computing*

Many applications involve humans in the loop, where continuous and accurate human motion monitoring provides valuable information for safe and intuitive human-machine interaction. Portable devices such as inertial measurement units (IMUs) are applicable to monitor human motions, while in practice often limited computational power is available locally. The human motion in task space coordinates requires not only the human joint motion but also the nonlinear coordinate transformation depending on the parameters such as human limb length. In most applications, measuring these kinematics parameters for each individual requires undesirably high effort. Therefore, it is desirable to estimate both, the human motion and kinematic parameters from IMUs. In this work, we propose a novel computational framework for dual estimation in real-time exploiting in-network computational resources. We adopt the concept of field Kalman filtering, where the dual estimation problem is decomposed into a fast state estimation process and a computationally expensive parameter estimation process. In order to further accelerate the convergence, the parameter estimation is progressively computed on multiple networked computational nodes. The superiority of our proposed method is demonstrated by a simulation of a human arm, where the estimation accuracy is shown to converge faster than with conventional approaches.
Set-Membership Estimator for Multisensor Systems: A Collector-Based Approach

This paper considers a distributed state estimation problem of a multisensor linear time-invariant system affected by bounded disturbances and measurement noises. We propose a zonotopic state estimation scheme called collector, which generates a directed rooted tree from the underlying graph by designating a node to collect information. Based on this idea, multi-hop decomposition is implemented, and properties of multi-hop decomposition under this framework are discussed. Furthermore, this paper presents a solution for treating one node as a collector. In the end, a case study is used to illustrate the effectiveness of the proposed estimator.
The Weighted Kalman Filter

This paper proposes a new version of the Kalman filter, referred to as weighted Kalman filter (WKF). In the WKF some recent results on the weighted linearization of nonlinear systems are exploited to incorporate modifications in the equations of the extended Kalman filter (EKF). More specifically, the computation of the Jacobian matrices at the current mean of the estimated state is replaced by the multiple integral over the state space of the Jacobian matrix functions multiplied by a weighting function. Similar modifications are introduced in the equations used to account for the available nonlinear model and compute the so-called a priori state and output estimates. The weighting function is chosen to be a multivariable Gaussian function where the generalized variance is selected as proportional to the current covariance matrix of the state estimate. An illustrative example is used to describe the step-by-step derivation of the WKF equations and compare its performance against the EKF in terms of convergence properties and estimation error performance.
Analysis of Interpolating Regression Models and the Double Descent Phenomenon

A regression model with more parameters than data points in the training data is overparametrized and has the capability to interpolate the training data. Based on the classical bias-variance tradeoff expressions, It is commonly assumed that models which interpolate noisy training data are poor to generalize. In some cases, this is not true. The best models obtained are overparametrized and the testing error exhibits the double descent behavior as the model order increases. In this contribution, we provide some analysis to explain the double descent phenomenon, first reported in the machine learning literature. We focus on interpolating models derived from the minimum norm solution to the classical least-squares problem and also briefly discuss model fitting using ridge regression. We derive a result based on the behavior of the smallest singular value of the regression matrix that explains the peak location and the double descent shape of the testing error as a function of model order.
Traversability Aware graph-based Subterranean Exploration with Unmanned Aerial Vehicles*

Subterranean exploration and mapping for search and rescue robotics have become an emerging research direction since the DARPA organized Subterranean Challenge. As part of development efforts within the team CoSTAR (Collaborative SubTerranean Autonomous Robots) in the Sub-T challenge, this work establishes a novel traversable graph-based exploration strategy that utilizes frontiers for local navigation and a fast collision risk-aware graph building for global navigation. The exploration strategy extracts frontiers in an unknown area that contribute to safe navigation while maximizing information gain for the robot. The exploration problem is further bifurcated into local and global exploration for faster decision-making at junctions with the goal of rapidly exploring the area. The local exploration guarantees collision-free straight-line paths to informative frontiers for rapid forward navigation, while global re-positioning utilizes a traversable graph subject to geometrical collision checks within the occupancy map. The pathfinding in a graph is addressed using a heuristic, which combines risk margins and travel costs to assist in short yet safe paths to the global frontier in case of a dead end in local exploration. The presented exploration strategy is developed with the goal of making exploration algorithms platform agnostic in order to be able to use it with aerial, as well as ground robots. The proposed method is also evaluated against different state-of-the-art exploration planners in simulated fixed-time budget-based exploration missions on an Unmanned Aerial Vehicle (UAV) in order to benchmark the capabilities and highlight the novelty.