Open Questions Research Articles

Fast Building Instance Proxy Reconstruction for Large Urban Scenes.

Digitalization of large-scale urban scenes (in particular buildings) has been a long-standing open problem, which attributes to the challenges in data acquisition, such as incomplete scene coverage, lack of semantics, low efficiency, and low reliability in path planning. In this paper, we address these challenges in urban building reconstruction from aerial images, and we propose an effective workflow and a few novel algorithms for efficient 3D building instance proxy reconstruction for large urban scenes. Specifically, we propose a novel learning-based approach to instance segmentation of urban buildings from aerial images followed by a voting-based algorithm to fuse the multi-view instance information to a sparse point cloud (reconstructed using a standard Structure from Motion pipeline). Our method enables effective instance segmentation of the building instances from the point cloud. We also introduce a layer-based surface reconstruction method dedicated to the 3D reconstruction of building proxies from extremely sparse point clouds. Extensive experiments on both synthetic and real-world aerial images of large urban scenes have demonstrated the effectiveness of our approach. The generated scene proxy models can already provide a promising 3D surface representation of the buildings in large urban scenes, and when applied to aerial path planning, the instance-enhanced building proxy models can significantly improve data completeness and accuracy, yielding highly detailed 3D building models.

On 3-Coloring Circle Graphs

Given a graph $G$ with a fixed vertex order $\prec$, one obtains a circle graph $H$ whose vertices are the edges of $G$ and where two such edges are adjacent if and only if their endpoints are pairwise distinct and alternate in $\prec$. Therefore, the problem of determining whether $G$ has a $k$-page book embedding with spine order $\prec$ is equivalent to deciding whether $H$ can be colored with $k$ colors. Finding a $k$-coloring for a circle graph is known to be NP-complete for $k \geq 4$ [9] and trivial for $k \leq 2$. For $k = 3$, Unger (1992) claims an efficient algorithm that finds a 3-coloring in $O(n \log n)$ time, if it exists. Given a circle graph $H$, Unger's algorithm (1) constructs a 3-\textsc{Sat} formula $\Phi$ that is satisfiable if and only if $H$ admits a 3-coloring and (2) solves $\Phi$ by a backtracking strategy that relies on the structure imposed by the circle graph. However, the extended abstract misses several details and Unger refers to his PhD thesis (in German) for details. In this paper we argue that Unger's algorithm for 3-coloring circle graphs is not correct and that 3-coloring circle graphs should be considered as an open problem. We show that step (1) of Unger's algorithm is incorrect by exhibiting a circle graph and its representation whose formula $\Phi$ is satisfiable but that is not 3-colorable. We further show that Unger's backtracking strategy for solving $\Phi$ in step (2) may produce incorrect results and give empirical evidence that it exhibits a runtime behaviour that is not consistent with the claimed running time.

A framework for measuring the training efficiency of a neural architecture

Measuring Efficiency in neural network system development is an open research problem. This paper presents an experimental framework to measure the training efficiency of a neural architecture. To demonstrate our approach, we analyze the training efficiency of Convolutional Neural Networks and Bayesian equivalents on the MNIST and CIFAR-10 tasks. Our results show that training efficiency decays as training progresses and varies across different stopping criteria for a given neural model and learning task. We also find a non-linear relationship between training stopping criteria, training Efficiency, model size, and training Efficiency. Furthermore, we illustrate the potential confounding effects of overtraining on measuring the training efficiency of a neural architecture. Regarding relative training efficiency across different architectures, our results indicate that CNNs are more efficient than BCNNs on both datasets. More generally, as a learning task becomes more complex, the relative difference in training efficiency between different architectures becomes more pronounced.

Bounds on the superconducting transition temperature

I summarize recent progress on obtaining rigorous upper bounds on superconducting transition temperature [Formula: see text] in two dimensions independent of pairing mechanism or interaction strength. These results are derived by finding a general upper bound for the superfluid stiffness for a multi-band system with arbitrary interactions, with the only assumption that the external vector potential couples to the kinetic energy and not to the interactions. This bound is then combined with the universal relation between the superfluid stiffness and the Berezinskii–Kosterlitz–Thouless [Formula: see text] in 2D. For parabolic dispersion, one obtains the simple result that [Formula: see text], which has been tested in recent experiments. More generally, the bounds are expressed in terms of the optical spectral weight and lead to stringent constraints for the [Formula: see text] of low-density, strongly correlated superconductors. Results for [Formula: see text] bounds for models of flat-band superconductors, where the kinetic energy vanishes and the vector potential must couple to interactions, are briefly summarized. Upper bounds on [Formula: see text] in 3D remains an open problem, and I describe how questions of universality underlie the challenges in 3D.

Better Hardness Results for the Minimum Spanning Tree Congestion Problem

AbstractIn the spanning tree congestion problem, given a connected graph G, the objective is to compute a spanning tree T in G that minimizes its maximum edge congestion, where the congestion of an edge e of T is the number of edges in G for which the unique path in T between their endpoints traverses e. The problem is known to be $$\mathbb{N}\mathbb{P}$$ N P -hard, but its approximability is still poorly understood, and it is not even known whether the optimum solution can be efficiently approximated with ratio o(n). In the decision version of this problem, denoted $${\varvec{K}-\textsf {STC}}$$ K - STC , we need to determine if G has a spanning tree with congestion at most K. It is known that $${\varvec{K}-\textsf {STC}}$$ K - STC is $$\mathbb{N}\mathbb{P}$$ N P -complete for $$K\ge 8$$ K ≥ 8 , and this implies a lower bound of 1.125 on the approximation ratio of minimizing congestion. On the other hand, $${\varvec{3}-\textsf {STC}}$$ 3 - STC can be solved in polynomial time, with the complexity status of this problem for $$K\in { \left\{ 4,5,6,7 \right\} }$$ K ∈ 4 , 5 , 6 , 7 remaining an open problem. We substantially improve the earlier hardness results by proving that $${\varvec{K}-\textsf {STC}}$$ K - STC is $$\mathbb{N}\mathbb{P}$$ N P -complete for $$K\ge 5$$ K ≥ 5 . This leaves only the case $$K=4$$ K = 4 open, and improves the lower bound on the approximation ratio to 1.2. Motivated by evidence that minimizing congestion is hard even for graphs of small constant radius, we also consider $${\varvec{K}-\textsf {STC}}$$ K - STC restricted to graphs of radius 2, and we prove that this variant is $$\mathbb{N}\mathbb{P}$$ N P -complete for all $$K\ge 6$$ K ≥ 6 .

Optimizing predictive models for evaluating the F-temperature index in predicting the π-electron energy of polycyclic hydrocarbons, applicable to carbon nanocones

In the fields of mathematics, chemistry, and the physical sciences, graph theory plays a substantial role. Using modern mathematical techniques, quantitative structure-property relationship (QSPR) modeling predicts the physical, synthetic, and natural properties of substances based only on their chemical composition. For a chemical graph, the temperature of a vertex is a local property introduced by Fajtlowicz (1988). A temperature-based graphical descriptor is structured based on temperatures of vertices. Involving a non-zero real parameter β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document}, the general F-temperature index Tβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\beta }$$\\end{document} is a temperature index having strong efficacy. In this paper, we employ discrete optimization and regression analysis to find optimal value(s) of β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document} for which the prediction potential of Tβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\beta }$$\\end{document} and the total π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi$$\\end{document}-electron energy Eπ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{\\pi }$$\\end{document} of polycyclic hydrocarbons is the strongest. This, in turn, answers an open problem proposed by Hayat & Liu (2024). Applications of the optimal values for Tβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\beta }$$\\end{document} are presented a two-parametric family of carbon nanocones in predicting their Eπ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{\\pi }$$\\end{document} with significantly higher accuracy.

A proof of gross' conjecture on 2‐automorphic 2‐groups

AbstractBuilding upon previous results, a classification is given of finite ‐groups whose elements of order are all fused. This particularly confirms a conjecture of Gross proposed in 1976 on 2‐automorphic 2‐groups, which are 2‐groups with involutions forming a single fusion class. As a consequence, two open problems regarding AT‐groups and FIF‐groups are solved.

U and Th zonation in apatite observed by synchrotron X-ray fluorescence tomography and implications for the (U–Th) ∕ He system

Abstract. Synchrotron X-ray fluorescence microtomography can non-destructively image the three-dimensional distribution of several trace elements in whole apatite crystals at the resolution of 1 µm3. This allows for precise determination of the physical geometry of a crystal and the quantification of the relative abundance of the radioactive parent nuclides uranium and thorium with high fidelity. We use these data to develop a more precise alpha ejection correction for (U–Th) / He thermochronology and high-resolution models of apatite crystals that are the foundation for a new generation of three-dimensional diffusion modeling. The application of synchrotron radiation to non-destructive imaging of minerals used for geochronology sheds light on causes of long-standing unresolved problems in the field that are rooted in previously unmeasurable parent nuclide zonation, especially the pervasive overdispersion of single-crystal ages.

Pitfalls in Machine Learning for Computer Security

With the growing processing power of computing systems and the increasing availability of massive datasets, machine learning algorithms have led to major breakthroughs in many different areas. This development has influenced computer security, spawning a series of work on learning-based security systems, such as for malware detection, vulnerability discovery, and binary code analysis. Despite great potential, machine learning in security is prone to subtle pitfalls that undermine its performance and render learning-based systems potentially unsuitable for security tasks and practical deployment. In this paper, we look at this problem with critical eyes. First, we identify common pitfalls in the design, implementation, and evaluation of learning-based security systems. We conduct a study of 30 papers from top-tier security conferences within the past 10 years, confirming that these pitfalls are widespread in the current security literature. In an empirical analysis, we further demonstrate how individual pitfalls can lead to unrealistic performance and interpretations, obstructing the understanding of the security problem at hand. As a remedy, we propose actionable recommendations to support researchers in avoiding or mitigating the pitfalls where possible. Furthermore, we identify open problems when applying machine learning in security and provide directions for further research.

Construction of Asymmetric Orthogonal Arrays With High Strength

ABSTRACTOrthogonal arrays (OAs) are a key research focus in combinatorial design theory and experimental design theory. They play a very important role in an increasing number of interdisciplinary fields, such as computer science, cryptography, multipartite quantum states and quantum information. And the open problems in many fields are closely related to the construction of orthogonal arrays with high strength and large size. At present, some open problems have been solved by using orthogonal arrays. There is an urgent need for developing such orthogonal arrays. This article introduces a general method for obtaining asymmetric orthogonal arrays with high strength. The proposed method is straightforward and constructive. The constructed OAs can be utilized to generate more OAs. Some selective OAs are tabulated for practical applications.

On general fiber product rings, Poincaré series and their structure

The present paper deals with the investigation of the structure of general fiber product rings R × T S , where R, S and T are local rings with common residue field. We show that the Poincaré series of any R-module over the fiber product ring R × T S is bounded by a rational function. In addition, we give a description of depth ( R × T S ) , which is an open problem in this theory. As a biproduct, using the characterization of the Betti numbers over R × T S obtained, we provide certain cases of the Cohen-Macaulayness of R × T S and, in particular, we show that R × T S is always non-regular. Some positive answers for the Buchsbaum-Eisenbud-Horrocks and Total rank conjectures over R × T S are also established.

On the blow-up for a Kuramoto–Velarde type equation

It is known that the Kuramoto-Velarde equation is globally well-posed on Sobolev spaces in the case when the parameters γ1 and γ2 involved in the non-linear terms verify γ2=γ12 or γ2=0. In the complementary case of these parameters, the global existence or blow-up of solutions is a completely open (and hard) problem. Motivated by this fact, in this work we consider a non-local version of the Kuramoto-Velarde equation. This equation allows us to apply a Fourier-based method and, within the framework γ2≠γ12 and γ2≠0, we show that large values of these parameters yield a blow-up in finite time of solutions in the Sobolev norm. As a complement to it, we address an alternative result on the finite-time blow-up of smooth solutions by considering a virial-type estimate.

Социально-философское исследование проблемы классификации правовых оценок и правовых ценностей

The scientific article presents the results of socio-philosophical study of one of the unresolved problems in many evaluation-value theories, namely, the problem of creating a unified classification of values and evaluations. In this context, the problem of classification of legal values and legal evaluations is not an exception. Classification of legal values as opposed to the classification of legal evaluations is a sufficiently researched topic in modern philosophy of law and jurisprudence. However, in social philosophy the issue of classification of the concepts of “legal values” and “legal assessments” has not been the subject of a separate study. In order to conduct this classification, it is necessary to thoroughly understand the content of these concepts. Legal values and legal assessments are defined by means of the generic concepts of “social values” and “social assessments”. In addition to the classical definition in the socio-philosophical study of legal values and legal assessments, contextual definition and comparative analysis are applied. As a result, the problem of classification of legal assessments and legal values is solved through social-philosophical understanding of existing classifications of these concepts and proposing their own variants of classification.

Scheduling a single machine with multiple due dates per job

AbstractIn this paper, we consider single-machine scheduling with multiple due dates per job. This is motivated by several industrial applications, where it is not important by how much we miss a due date. Instead the relevant objective is to minimize the number of missed due dates. Typically, this situation emerges whenever fixed delivery appointments are chosen in advance, such as in the production of individualized pharmaceuticals or when customers can only receive goods at certain days in the week, due to constraints in their warehouse operation. We compare this previously unexplored problem with classical due date scheduling, for which it is a generalization. We show that single-machine scheduling with multiple due dates is NP-hard in the strong sense if processing times are job dependent. If processing times are equal for all jobs, then single-machine scheduling with multiple due dates is at least as hard as the long-standing open problem of weighted tardiness with equal processing times and release dates $$1 \mid r_j, p_j = p \mid \sum w_j T_j$$ 1 ∣ r j , p j = p ∣ ∑ w j T j . Finally, we focus on the case of equal processing times and provide several polynomially solvable special cases as well as an exact branch-and-bound algorithm and heuristics for the general case. Experiments show that our branch-and-bound algorithm compares well to modern exact methods to solve problem $$1 \mid r_j, p_j = p \mid \sum w_{j} T_{j}$$ 1 ∣ r j , p j = p ∣ ∑ w j T j .

Primordial Perturbations Including Second-Order Derivatives of the Inflationary Potential

In inflationary cosmology, the form of the potential is still an open problem. In this work, second-order effects of the inflationary potential are evaluated and related to the known formula for the primordial perturbations at a wide range of scales. We found effects that may help to unravel the unknown inflationary potential form and impose new constraints on the parameters that define this potential. In particular, we demonstrate that even slight deviations in the inflationary potential can lead to significant differences in the calculated spectra if inflation persists sufficiently long and the normal modes of perturbations are affected by these variations.

A REIDEMEISTER THEOREM FOR SOLID RIBBON TORUS LINKS

Abstract A complete Reidemeister characterisation of welded links is a long-standing open problem. We present a Reidemeister theorem for a related class of four-dimensional links: solid ribbon torus links, that is, immersed solid tori in $\mathbb {R}^4$ with only ribbon singularities, considered up to generalised ribbon isotopy.

Wave Speeds for a Time-Periodic Bistable Three-Species Lattice Competition System

In this paper, we consider propagation direction (which can be used to predict which species will occupy the habitat or win the competition eventually) of a bistable wave for a three-species time-periodic lattice competition system with bistable nonlinearity, aiming to address an open problem. As a first step, by transforming the competition system to a cooperative one, we study the asymptotic behavior for the bistable wave profile and then prove the uniqueness of the bistable wave speed. Secondly, we utilize comparison principle and build up two couples of upper and lower solutions to judge the sign of the bistable wave speed which partially provides the answer to the open problem. As an application, we reduce the time-periodic system to a space–time homogeneous system, we obtain the corresponding criteria and carry out numerical simulations to illustrate the availability of our results. Moreover, an interesting phenomenon we have found is that the two weak competitors can wipe out the strong competitor under some circumstances.

Statistical Distribution Theory and Fractional Calculus

This is an overview paper. This paper is an attempt to show that fractional calculus can be reached through statistical distribution theory. This paper brings together results on fractional integrals and fractional derivatives of the first and second kinds in the real and complex domains in the scalar, vector, and matrix-variate cases, and shows that all these results can be reached through statistical distribution theory. It is shown that the whole area of fractional integrals can be reached through distributions of products and ratios in the scalar variable case and distributions of symmetric products and symmetric ratios in the matrix-variate cases. While summarizing the materials, the real domain results are also listed side by side with the complex domain results so that a comparative study is possible. Fractional integrals and derivatives in the real domain mean that the parameters involved could be real or complex with appropriate conditions, the arbitrary function is real-valued, and the variables involved are all real. These in the complex domain mean that the parameters could be real or complex and the arbitrary function is still real-valued but the variables involved are in the complex domain. Fully complex domain means the variables as well as the arbitrary function are in the complex domain. Most of the materials on fractional integrals and fractional derivatives involving a single matrix or a number of matrices in the real or complex domain are of this author. Slight modifications of the results, compared with the published works in various papers, are there in various sections. In the paragraph on notations, the lemmas that are taken from this author’s own book on Jacobians are common with published works and hence the similarity index with this author’s works will be high. Section Matrix-Variate Joint Distributions and Fractional Integrals in Many Matrix-Variate Cases material on a statistical approach to Kiryakova’s multi-index fractional integral and its extension to the real scalar case of second kind integrals as well as extensions of first and second kind integrals to real and complex matrix-variate cases are believed to be new. Matrix differential operators are introduced in Section Fractional Derivatives and, with the help of these operators, fractional derivatives are constructed from the corresponding fractional integrals. These operators are applicable in a large variety of functions. Applicability is shown through identities created from scale transformed gamma random variables. Some concluding remarks are given and some open problems are pointed out in Section Concluding Remarks.

A Note on the Asymptotic Posterior Normality of Multivariate Latent Traits in an IRT Model for Polytomous Items of Mixed Format

The asymptotic posterior normality (APN) of the latent vector in an item response theory model is an important argument in modeling and inference. For a single latent trait, Chang and Stout proved its APN for binary items under general conditions, which generalized Chang for polytomous data and Kornely and Kateri for multivariate latent traits (MLT) and binary items. As MLT and polytomous items are nowadays common in psychometry, an APN-theory covering both simultaneously remains an open and ongoing problem. We generalize the APN-theory accordingly, providing thus a broader foundation for developments relying on APN. We also prove consistency of common estimators for the MLT, extending the according results of Chang and Kornely and Kateri.

Shotcreting with Cement–Sand Mixtures Under the Influence of an Electrostatic Field

One of the primary and still unresolved problems of shotcreting is the high rebound rate of the material, which reaches over 20% in “dry” shotcreting. There is a practical need to improve the very principle of shotcreting and methods for optimizing the movement of torch particles. Materials and Methods: The purpose of this study was to justify the use of the electrostatic treatment of cement–sand mortar in the process of performing shotcreting works using the dry method. It was proposed that the binder and then the finished mixture be ionized step-by-step (by passing it through a non-uniform electrostatic field formed by corona electrodes). As a result, the shotcrete will be held on the fence. Results: Analysis of the modeling results shows that the presence of an electrostatic field slows down the particle and reduces the kinetic energy of the rebound. After theoretical calculations, experiments were conducted, during which, the torch size and the plant productivity were changed, and the rebound mass was weighed. After application to the surface, prototypes were formed and subjected to strength tests. It was determined that gunning in a sharply non-uniform electric field demonstrates its practical and economic efficiency due to the uniform deposition of charged particles on the treated surface and low power consumption. Conclusions: It was established that the electrostatic treatment of a cement–sand mixture during application allows concrete particles to be retained on the shotcrete surface, the rebound of the material to be reduced and the strength of concrete to be increased.