Miracle-dz/UniFAR-FTUs huggingface dataset:
On the hollow enclosed by convex sets

For n ≤ d, a family F = {C0, C1, . , Cn} of compact convex sets in R d is called an n-critical family provided any n members of F have a non-empty intersection, but ⋂n i=0 Ci = ∅. If n = d then a lemma on the intersection of convex sets due to Klee implies that the d + 1 members of the d-critical family enclose a ‘hollow’ in R, a bounded connected component of R \ ⋃n i=0 Ci. Here we prove that the closure of the convex hull of a hollow in R d is a d-simplex. Besides the Helly-theorem on intervals in R a less notable property is that two disjoint intervals can be separated by a point, in other words, there is a ‘hollow’ (an interval) between them, a gap, which cannot be bridged with two intervals having empty intersection. This separation or gap property, trivial as it is, helps characterize the intersection patterns of convex sets in R in terms of ‘interval graphs’. Actually, the gap property implies the foremost necessary condition that an interval graph must be chordal, namely, each cycle of length more than three has a chord (see [5]). Just as Helly’s theorem is established in R, for every d ≥ 1, the separation or gap property has extensions to higher dimension. A family of compact convex sets C0, C1, . , Cn ⊂ R d is called here an n-critical family if ⋂ i6=j Ci 6= ∅, for every j = 0, 1, . , n, but ⋂n i=0 Ci = ∅. The denotation ‘critical’ 2 becomes clear when in some finite family of sets with empty intersection we consider a ‘smallest’ subset with the same property, a ‘critical subfamily’. Convexity and compactness in the definition of a critical family was chosen here with combinatorial geometry applications in mind (see [13]). However, in intersection or covering theorems of topology, when a finite or infinite family of sets appears, the compactness requirement of the members might be relaxed (see [17]), and the condition ⋂n i=0 Ci = ∅ is usually replaced with its contrapositive that ⋃n i=0 Ci is a convex set, which denies the hollow (see [14]). Meanwhile, the primary condition that ⋂ i6=j Ci 6= ∅, for every j = 0, 1, . , n, is unchanged and displays a topology variation of n-criticality in the different contexts. The role of n-critical families (or its variations) in Euclidean spaces was recognized by Klee [14, 15], Berge [3], and Ghouila-Houri [9] in the study of intersection properties of convex sets. These properties are closely related Since September 1, 2019 the Alfréd Rényi Institute of Mathematics does not belong to the Hungarian Academy of Sciences. Supported by the National Research, Development and Innovation Fund (TUDFO/51757/2019-ITM, Thematic Excellence Program) and National Research, Development and Innovation Office, NKFIH, K-13152. 1
Multi-Objective LQG Design with Primal-Dual Method

The objective of this paper is to investigate a multi-objective linear quadratic Gaussian (LQG) control problem. Specifically, we examine an optimal control problem that minimizes a quadratic cost over a finite time horizon for linear stochastic systems subject to control energy constraints. To tackle this problem, we propose an efficient bisection line search algorithm that outperforms other approaches such as semidefinite programming in terms of computational efficiency. The primary idea behind our algorithm is to use the Lagrangian function and Karush–Kuhn–Tucker (KKT) optimality conditions to address the constrained optimization problem. The bisection line search is employed to search for the Lagrange multiplier. Furthermore, we provide numerical examples to illustrate the efficacy of our proposed methods.
Feasibility Assessment of Multitasking in MRI Neuroimaging Analysis: Tissue Segmentation, Cross-Modality Conversion and Bias correction

Neuroimaging is essential in brain studies for the diagnosis and identification of disease, structure, and function of the brain in its healthy and disease states. Literature shows that there are advantages of multitasking with some deep learning (DL) schemes in challenging neuroimaging applications. This study examines the feasibility of using multitasking in three different applications, including tissue segmentation, cross-modality conversion, and bias-field correction. These applications reflect five different scenarios in which multitasking is explored and 280 training and testing sessions conducted for empirical evaluations. Two well-known networks, U-Net as a well-known convolutional neural network architecture, and a closed architecture based on the conditional generative adversarial network are implemented. Different metrics such as the normalized cross-correlation coefficient and Dice scores are used for comparison of methods and results of the different experiments. Statistical analysis is also provided by paired t-test. The present study explores the pros and cons of these methods and their practical impacts on multitasking in different implementation scenarios. This investigation shows that bias correction and cross-modality conversion applications are significantly easier than the segmentation application, and having multitasking with segmentation is not reasonable if one of them is identified as the main target application. However, when the main application is the segmentation of tissues, multitasking with cross-modality conversion is beneficial, especially for the U-net architecture.
Objective Robustness in Deep Reinforcement Learning

We study objective robustness failures, a type of out-of-distribution robustness failure in reinforcement learning (RL). Objective robustness failures occur when an RL agent retains its capabilities out-of-distribution yet pursues the wrong objective. This kind of failure presents different risks than the robustness problems usually considered in the literature, since it involves agents that leverage their capabilities to pursue the wrong objective rather than simply failing to do anything useful. We provide the ﬁrst explicit empirical demonstrations of objective robustness failures and present a partial characterization of its causes.
Emergence and algorithmic information dynamics of systems and observers

One of the challenges of defining emergence is that one observer’s prior knowledge may cause a phenomenon to present itself as emergent that to another observer appears reducible. By formalizing the act of observing as mutual perturbations between dynamical systems, we demonstrate that the emergence of algorithmic information does depend on the observer’s formal knowledge, while being robust vis-a-vis other subjective factors, particularly: the choice of programming language and method of measurement; errors or distortions during the observation; and the informational cost of processing. This is called observer-dependent emergence (ODE). In addition, we demonstrate that the unbounded and rapid increase of emergent algorithmic information implies asymptotically observer-independent emergence (AOIE). Unlike ODE, AOIE is a type of emergence for which emergent phenomena will be considered emergent no matter what formal theory an observer might bring to bear. We demonstrate the existence of an evolutionary model that displays the diachronic variant of AOIE and a network model that displays the holistic variant of AOIE. Our results show that, restricted to the context of finite discrete deterministic dynamical systems, computable systems and irreducible information content measures, AOIE is the strongest form of emergence that formal theories can attain. This article is part of the theme issue ‘Emergent phenomena in complex physical and socio-technical systems: from cells to societies’.
Modeling Text-visual Mutual Dependency for Multi-modal Dialog Generation

Multi-modal dialog modeling is of growing interest. In this work, we propose frameworks to resolve a specific case of multi-modal dialog generation that better mimics multi-modal dialog generation in the real world, where each dialog turn is associated with the visual context in which it takes place. Specifically, we propose to model the mutual dependency between text-visual features, where the model not only needs to learn the probability of generating the next dialog utterance given preceding dialog utterances and visual contexts, but also the probability of predicting the visual features in which a dialog utterance takes place, leading the generated dialog utterance specific to the visual context. We observe significant performance boosts over vanilla models when the mutual dependency between text and visual features is modeled. Code is available at https://github.com/ShannonAI/OpenViDial.
Verdi: Quality Estimation and Error Detection for Bilingual Corpora

Translation Quality Estimation is critical to reducing post-editing efforts in machine translation and to cross-lingual corpus cleaning. As a research problem, quality estimation (QE) aims to directly estimate the quality of translation in a given pair of source and target sentences, and highlight the words that need corrections, without referencing to golden translations. In this paper, we propose Verdi, a novel framework for word-level and sentence-level post-editing effort estimation for bilingual corpora. Verdi adopts two word predictors to enable diverse features to be extracted from a pair of sentences for subsequent quality estimation, including a transformer-based neural machine translation (NMT) model and a pre-trained cross-lingual language model (XLM). We exploit the symmetric nature of bilingual corpora and apply model-level dual learning in the NMT predictor, which handles a primal task and a dual task simultaneously with weight sharing, leading to stronger context prediction ability than single-direction NMT models. By taking advantage of the dual learning scheme, we further design a novel feature to directly encode the translated target information without relying on the source context. Extensive experiments conducted on WMT20 QE tasks demonstrate that our method beats the winner of the competition and outperforms other baseline methods by a great margin. We further use the sentence-level scores provided by Verdi to clean a parallel corpus and observe benefits on both model performance and training efficiency.
Reputation Bootstrapping for Composite Services Using CP-Nets

We propose a novel framework to bootstrap the reputation of on-demand service compositions. On-demand compositions are usually context-aware and have little or no direct consumer feedback. The reputation bootstrapping of single or atomic services do not consider the topology of the composition and relationships among reputation-related factors. We apply Conditional Preference Networks (CP-nets) of reputation-related factors for each of component services in a composition. The reputation of a composite service is bootstrapped by the composition of CP-nets. We consider the history of invocation among component services to determine reputation-interdependence in a composition. The composition rules are constructed using the composition topology and four types of reputation-influence among component services. A heuristic-based Q-learning approach is proposed to select the optimal set of reputation-related CP-nets. Experimental results prove the efficiency of the proposed approach.
Adsorption of Methyl Orange from Aqueous Solution on Hydrothermal Synthesized Mg–Al Layered Double Hydroxide

In this study, we presented the efficiently adsorptive removal of organic dye, methyl orange (MO), from aqueous solution with the hydrothermal synthesized Mg–Al layered double hydroxide (LDH). The as-obtained product was characterized by X-ray diffraction (XRD), Fourier transformation infrared spectroscopy (FTIR), and scanning electron microscopy (SEM). The adsorption characteristics of MO onto the Mg–Al LDH were evaluated in a batch adsorption process and systematically investigated by different experimental parameters, such as initial dye concentration, contact time, and solution pH. The adsorption kinetics were analyzed by pseudofirst-order, pseudosecond-order, Elovich, intraparticle diffusion, and Boyd models, which were well-described by the pseudosecond-order model. The equilibrium adsorption data were interpreted using the Langmuir, Freundlich, and Temkin isotherm models, which fitted well to both the Langmuir and Freundlich models. The monolayer adsorption capacity of the Mg–Al LDH toward MO was f.
The HulC: Confidence Regions from Convex Hulls

We develop and analyze the HulC, an intuitive and general method for constructing confidence sets using the convex hull of estimates constructed from subsets of the data. Unlike classical methods which are based on estimating the (limiting) distribution of an estimator, the HulC is often simpler to use and effectively bypasses this step. In comparison to the bootstrap, the HulC requires fewer regularity conditions and succeeds in many examples where the bootstrap provably fails. Unlike subsampling, the HulC does not require knowledge of the rate of convergence of the estimators on which it is based. The validity of the HulC requires knowledge of the (asymptotic) median-bias of the estimators. We further analyze a variant of our basic method, called the Adaptive HulC, which is fully data-driven and estimates the median-bias using subsampling. We show that the Adaptive HulC retains the aforementioned strengths of the HulC. In certain cases where the underlying estimators are pathologically asymmetric the HulC and Adaptive HulC can fail to provide useful confidence sets. We propose a final variant, the Unimodal HulC, which can salvage the situation in cases where the distribution of the underlying estimator is (asymptotically) unimodal. We discuss these methods in the context of several challenging inferential problems which arise in parametric, semi-parametric, and non-parametric inference. Although our focus is on validity under weak regularity conditions, we also provide some general results on the width of the HulC confidence sets, showing that in many cases the HulC confidence sets have near-optimal width.
Impact of the Presence of Carbon Monoxide and Carbon Dioxide on Gas Oil Hydrotreatment: Investigation on Liquids from Biomass Cotreatment with Petroleum Cuts

A potential valorization pathway for liquids obtained from lignocellulosic biomass could be their cohydrotreatment with petroleum cuts to produce transportation fuels. Thus, under hydrotreating conditions, biomass compounds are converted through HDO and decarbylation/decarboxylation reactions, leading to the production of CO, CO2, and water. Therefore, it seems essential to consider the impact of COx on the performance of an HDT catalyst in the conversion of a straight run gas oil (SRGO), working under industrial conditions. The conversion of the SRGO was performed at 330 °C, LHSV = 1 h−1, and 5 MPa on a commercial CoMo/Al2O3 sulfided catalyst in the presence of various concentrations of COx (0.0 < molar flow of CO or CO2 < 13.4 mmol/h). The introduction of COx inhibits the HDS and HDN reactions and, to a lesser extent, the hydrogenation of aromatics. Water gas shift and methanation reactions compete with HDT reactions, methane being the major product, and WGS equilibria govern the distribution of the rem.
DAAIN: Detection of Anomalous and Adversarial Input using Normalizing Flows

Despite much recent work, detecting out-of-distribution (OOD) inputs and adversarial attacks (AA) for computer vision models remains a challenge. In this work, we introduce a novel technique, DAAIN, to detect OOD inputs and AA for image segmentation in a unified setting. Our approach monitors the inner workings of a neural network and learns a density estimator of the activation distribution. We equip the density estimator with a classification head to discriminate between regular and anomalous inputs. To deal with the high-dimensional activation-space of typical segmentation networks, we subsample them to obtain a homogeneous spatial and layer-wise coverage. The subsampling pattern is chosen once per monitored model and kept fixed for all inputs. Since the attacker has access to neither the detection model nor the sampling key, it becomes harder for them to attack the segmentation network, as the attack cannot be backpropagated through the detector. We demonstrate the effectiveness of our approach using an ESPNet trained on the Cityscapes dataset as segmentation model, an affine Normalizing Flow as density estimator and use blue noise to ensure homogeneous sampling. Our model can be trained on a single GPU making it compute efficient and deployable without requiring specialized accelerators.
BaMBNet: A Blur-aware Multi-branch Network for Defocus Deblurring

The defocus deblurring raised from the finite aperture size and exposure time is an essential problem in the computational photography. It is very challenging because the blur kernel is spatially varying and difficult to estimate by traditional methods. Due to its great breakthrough in low-level tasks, convolutional neural networks (CNNs) have been introduced to the defocus deblurring problem and achieved significant progress. However, they apply the same kernel for different regions of the defocus blurred images, thus it is difficult to handle these nonuniform blurred images. To this end, this study designs a novel blur-aware multi-branch network (BaMBNet), in which different regions (with different blur amounts) should be treated differentially. In particular, we estimate the blur amounts of different regions by the internal geometric constraint of the DP data, which measures the defocus disparity between the left and right views. Based on the assumption that different image regions with different blur amounts have different deblurring difficulties, we leverage different networks with different capacities (\emph{i.e.} parameters) to process different image regions. Moreover, we introduce a meta-learning defocus mask generation algorithm to assign each pixel to a proper branch. In this way, we can expect to well maintain the information of the clear regions while recovering the missing details of the blurred regions. Both quantitative and qualitative experiments demonstrate that our BaMBNet outperforms the state-of-the-art methods. Source code will be available at https://github.com/junjun-jiang/BaMBNet.
Optimal Spectral Recovery of a Planted Vector in a Subspace

Recovering a planted vector v in an n-dimensional random subspace of R is a generic task related to many problems in machine learning and statistics, such as dictionary learning, subspace recovery, principal component analysis, and non-Gaussian component analysis. In this work, we study computationally efficient estimation and detection of a planted vector v whose l4 norm differs from that of a Gaussian vector with the same l2 norm. For instance, in the special case where v is an Nρ-sparse vector with Bernoulli–Gaussian or Bernoulli–Rademacher entries, our results include the following: (1) We give an improved analysis of a slight variant of the spectral method proposed by Hopkins, Schramm, Shi, and Steurer (2016), showing that it approximately recovers v with high probability in the regime nρ ≪ √ N . This condition subsumes the conditions ρ ≪ 1/ √ n or n √ ρ . √ N required by previous work up to polylogarithmic factors. We achieve l∞ error bounds for the spectral estimator via a leave-one-out analysis, from which it follows that a simple thresholding procedure exactly recovers v with Bernoulli–Rademacher entries, even in the dense case ρ = 1. (2) We study the associated detection problem and show that in the regime nρ ≫ √ N , any spectral method from a large class (and more generally, any low-degree polynomial of the input) fails to detect the planted vector. This matches the condition for recovery and offers evidence that no polynomial-time algorithm can succeed in recovering a Bernoulli–Gaussian vector v when nρ ≫ √ N . Email: cheng.mao@math.gatech. edu. Partially supported by NSF grants DMS-2053333 and DMS-2210734. Email: aswein@ucdavis.edu. Part of this work was done while with the Courant Institute at NYU, partially supported by NSF grant DMS-1712730 and by the Simons Collaboration on Algorithms and Geometry.
Harmonic Persistent Homology

We introduce harmonic persistent homology spaces for filtrations of finite simplicial complexes. As a result we can associate concrete subspaces of cycles to each bar of the barcode of the filtration. We prove stability of the harmonic persistent homology subspaces under small perturbations of functions defining them. We relate the notion of"essential simplices"introduced in an earlier work to identify simplices which play a significant role in the birth of a bar, with that of harmonic persistent homology. We prove that the harmonic representatives of simple bars maximizes the"relative essential content"amongst all representatives of the bar, where the relative essential content is the weight a particular cycle puts on the set of essential simplices.
Multi‐step reflection principle and barrier options

This paper examines a class of barrier options-multi-step barrier options, which can have any finite number of barriers of any level. We obtain a general, explicit expression of option prices of this type under the Black-Scholes model. Multi-step barrier options are not only useful in that they can handle barriers of different levels and time steps, but can also approximate options with arbitrary barriers. Moreover, they can be embedded in financial products such as deposit insurances based on jump models with simple barriers. Along the way, we derive multi-step reflection principle, which generalizes the reflection principle of Brownian motion.
Towards Lower Bounds on the Depth of ReLU Neural Networks

We contribute to a better understanding of the class of functions that can be represented by a neural network with ReLU activations and a given architecture. Using techniques from mixed-integer optimization, polyhedral theory, and tropical geometry, we provide a mathematical counterbalance to the universal approximation theorems which suggest that a single hidden layer is sufficient for learning any function. In particular, we investigate whether the class of exactly representable functions strictly increases by adding more layers (with no restrictions on size). As a by-product of our investigations, we settle an old conjecture about piecewise linear functions by Wang and Sun (2005) in the affirmative. We also present upper bounds on the sizes of neural networks required to represent functions with logarithmic depth.
A sequential approach for speed planning under jerk constraints

In this paper we discuss a sequential algorithm for the computation of a minimum-time speed profile over a given path, under velocity, acceleration and jerk constraints. Such a problem arises in industrial contexts such as automated warehouses, where LGVs need to perform assigned tasks as fast as possible in order to increase productivity. It can be reformulated as an optimization problem with a convex objective function, linear velocity and acceleration constraints, and non-convex jerk constraints, which, thus, represent the main source of difficulty. While existing non-linear programming (NLP) solvers can be employed for the solution of this problem, it turns out that the performance and robustness of such solvers can be enhanced by the sequential line-search algorithm proposed in this paper. At each iteration a feasible direction, with respect to the current feasible solution, is computed, and a step along such direction is taken in order to compute the next iterate. The computation of the feasible direction is based on the solution of a linearized version of the problem, and the solution of the linearized problem, through an approach which strongly exploits its special structure, represents the main contribution of this work. The efficiency of the proposed approach with respect to existing NLP solvers is proved through different computational experiments.