Miracle-dz/UniFAR-FTUs huggingface dataset:
A Study of Projections of 2-Bouquet Graphs

We extend the concepts of trivializing and knotting numbers for knots to spatial graphs and 2-bouquet graphs, in particular. Furthermore, we calculate the trivializing and knotting numbers for projections and pseudodiagrams of 2-bouquet spatial graphs based on the number of precrossings and the placement of the precrossings in the pseudodiagram of the spatial graph.
Non-trivial solutions of local and non-local Neumann boundary-value problems

We prove new results on the existence, non-existence, localization and multiplicity of non-trivial solutions for perturbed Hammerstein integral equations. Our approach is topological and relies on the classical fixed-point index. Some of the criteria involve a comparison with the spectral radius of some related linear operators. We apply our results to some boundary-value problems with local and non-local boundary conditions of Neumann type. We illustrate in some examples the methodologies used.
On the finiteness of minimal and maximal spectra

In this article, it is proved that the minimal spectrum of a commutative ring is quasi-compact with respect to the flat topology. Consequently, all of the related results of Kaplansky, Anderson, Gilmer-Heinzer and Bahmanpour et al on minimal primes are deduced as special cases of this result. Dually, some similar results are also obtained for maximal ideals.
A non-exponential extension of Sanov’s theorem via convex duality

Abstract This work is devoted to a vast extension of Sanov’s theorem, in Laplace principle form, based on alternatives to the classical convex dual pair of relative entropy and cumulant generating functional. The abstract results give rise to a number of probabilistic limit theorems and asymptotics. For instance, widely applicable non-exponential large deviation upper bounds are derived for empirical distributions and averages of independent and identically distributed samples under minimal integrability assumptions, notably accommodating heavy-tailed distributions. Other interesting manifestations of the abstract results include new results on the rate of convergence of empirical measures in Wasserstein distance, uniform large deviation bounds, and variational problems involving optimal transport costs, as well as an application to error estimates for approximate solutions of stochastic optimization problems. The proofs build on the Dupuis–Ellis weak convergence approach to large deviations as well as the duality theory for convex risk measures.
On the growth of Sobolev norms for NLS on 2- and 3-dimensional manifolds

Using suitable modified energies we study higher order Sobolev norms' growth in time for the nonlinear Schrodinger equation (NLS) on a generic $2d$ or $3d$ compact manifold. In $2d$ we extend earlier results that dealt only with cubic nonlinearities, and get polynomial in time bounds for any higher order nonlinearities. In $3d$, we prove that solutions to the cubic NLS grow at most exponentially, while for sub-cubic NLS we get polynomial bounds on the growth of the $H^2$-norm.
Toward a framework for assessing the quality of students’ social scientific reasoning

ABSTRACT This study aims to describe components and levels of upper secondary social science students’ reasoning about social problems. We consulted conceptualizations of social scientific reasoning in sociology textbooks and social science education literature, analyzed student papers, and conducted focus groups with social science teachers and teacher educators to define social scientific reasoning by proficiency levels and identify common flaws in students’ reasoning. The papers were written by upper secondary social science students from eight schools in the Netherlands. We defined social scientific reasoning in terms of three components (describing, explaining, and solving problems) and five reasoning activities (causal analysis; use of social scientific concepts, models, and theories; use of evidence; use of perspectives and reflections on them; and comparing). We described these reasoning activities in three proficiency levels supported by practical examples and rubrics for students’ reasoning. These insights can inform teachers and teacher educators in monitoring students’ progression and designing teaching materials and activities that can promote students’ social scientific reasoning.
On error distance of received words with fixed degrees to Reed-Solomon code

Under polynomial time reduction, the maximum likelihood decoding of a linear code is equivalent to computing the error distance of a received word. It is known that the decoding complexity of standard Reed-Solomon codes at certain radius is at least as hard as the discrete logarithm problem over certain large finite fields. This implies that computing the error distance is hard for standard Reed-Solomon codes. Using some elegant algebraic constructions, we are able to determine the error distance of received words whose degree is k+1 to the Standard Reed-Solomon code or Primitive Reed-Solomon code exactly. Moreover, we can precisely determine the error distance of received words of degree k+2 to the Standard Reed-Solomon codes. As a corollary, we can simply get the results of Zhang-Fu-Liao and Wu-Hong on the deep hole problem of Reed-Solomon codes.
The Core Ingram Conjecture for non-recurrent critical points

We study inverse limit spaces of tent maps, and the Ingram Conjecture, which states that the inverse limit spaces of tent maps with different slopes are non-homeomorphic. When the tent map is restricted to its core, so there is no ray compactifying on the inverse limit space, this result is referred to as the Core Ingram Conjecture. We prove the Core Ingram Conjecture when the critical point is non-recurrent and not preperiodic.
Convergence of Star Product: From Examples to a General Framework

We recall some of the fundamental achievements of formal deformation quantization to argue that one of the most important remaining problems is the question of convergence. Here we discuss different approaches found in the literature so far. The recent developments of finding convergence conditions are then outlined in three basic examples: the Weyl star product for constant Poisson structures, the Gutt star product for linear Poisson structures, and the Wick type star product on the Poincare disc.
Critical Percolation and the Minimal Spanning Tree in Slabs

The minimal spanning forest on ℤd is known to consist of a single tree for d ≤ 2 and is conjectured to consist of infinitely many trees for large d. In this paper, we prove that there is a single tree for quasi‐planar graphs such as ℤ2 × {0,…,k}d−2. Our method relies on generalizations of the “gluing lemma” of Duminil‐Copin, Sidoravicius, and Tassion. A related result is that critical Bernoulli percolation on a slab satisfies the box‐crossing property. Its proof is based on a new Russo‐Seymour‐Welsh‐type theorem for quasi‐planar graphs. Thus, at criticality, the probability of an open path from 0 of diameter n decays polynomially in n. This strengthens the result of Duminil‐Copin et al., where the absence of an infinite cluster at criticality was first established. © 2017 Wiley Periodicals, Inc.
PipaSet and TEAS: A Multimodal Dataset and Annotation Platform for Automatic Music Transcription and Expressive Analysis Dedicated to Chinese Traditional Plucked String Instrument Pipa

Music information retrieval (MIR) is developing these years rapidly. As the fundamental MIR tasks, automatic music transcription (AMT) and expressive analysis (EA) are gaining momentum in both Western and non-European music. However, the annotated datasets for non-Eurogenic instruments remain scarce in terms of quantity and feature diversity, so that general evaluations and data-driven models on various tasks cannot be well explored. As one of the most popular traditional plucked string instruments in Asia, which is barely studied in the MIR community, pipa has lots of distinctive national and local characteristics, including the fake nails, intrinsic pitch deviation, rubato, as well as sophisticated playing techniques, that greatly enhance the music expressiveness. Our work aims to systematically clarify a complete creation procedure of a pipa solo dataset with audio, musical notation and multiview video modalities. The use of 4-track string vibration signals captured by optical sensors paves a path to the high quality annotations. Furthermore, a transcription and expressiveness annotation system (TEAS) was transparently implemented to ensure the scalability of dataset. Three expressive analysis approaches in this system were newly proposed and evaluated in the paper. Finally, a series of the existing and emerging MIR tasks enabled by this dataset were enumerated and two AMT models were simply investigated for future exploration.
Infinite measure renewal theorem and related results

We present abstract conditions under which a special flow over a probability preserving map with a non‐integrable roof function is Krickeberg mixing. Our main condition is a version of the local central limit theorem for the underlying map. We check our assumptions for independent and identically distributed random variables (renewal theorem with infinite mean) and for suspensions over Pomeau–Manneville maps.
On the survival probability in the Matheron - De Marsily model

We are interested in the behaviour of the range and of the first return time to the origin of random walks in random scenery. As a byproduct a precise estimate of the survival probability in the Matheron and de Marsily model is obtained. Our result confirms the conjectures announced by Majumdar and Redner.
Bacteriological Study on Surgical Site Infection in Rangpur Medical College and Hospital

Background: Surgical site infections (SSIs) is a major problem in both developed and developing countries. In developing countries like Bangladesh, infection in surgical patients has been appearing as a serious risk due to insurgence of drug resistance. Surgical site infections (SSIs) contribute significantly to increased health care costs in terms of prolonged hospital stay and lost working days. The problem was largely unexplored in Rangpur Medical College and Hospital, Rangpur. Objective: The aim of the study was to evaluate the bacteriological study on surgical site infections in Rangpur Medical College & Hospital. Methods: This cross-sectional observational study was conducted in the Department of Surgery at Rangpur Medical College Hospital. 72 patients of all ages, sex who developed surgical site infection were included through purposive sampling for observation and clinical follow up and wound swab was microbiologically evaluated. Results: Of the 72 cases, SSI developed 30.6% (22) following elective surgery and 69.4% (50) following emergency surgery. 7 cases were associated with co-morbid conditions like diabetes mellitus (2), malignancy (4) and tuberculosis (1). Most common organisms were Escherichia coli (30 /54) followed by Staphylococcous aureus (14/54), Pseudomonas (07/54) and Klebsiella (03/54). The antibiogram pattern of the organism isolated from wound swab of SSIs were analyzed with commonly used antibiotics. Resistance of Escherichia coli to Amoxycillin, Cotrimoxazole, Doxycycline and Nalidixic acid were 100%, 91.5%, 71.4% and 60.5% respectively. In case of, Staphylococcus aureus 87.5% were resistant to penicillin and Cotrimoxazole. Resistance of Pseudomonas spp. to Ciprofloxacin, Ceftazidime and Gentamicin were 31.2%. 6.3% and 50% respectively. In case of Klebsiella spp, it showed that 100% strains were resistant to Amoxycillin like Esch. coli but all strains were sensitive to both Ceftriaxon and Imipenem. Conclusion: The study emphasizes the need for the evidence-based infection control and antibiotic prescription policies in the hospital. J Rang Med Col. September 2022; Vol. 7, No. 2:12-19
Unramified Godement-Jacquet theory for the spin similitude group

Suppose $F$ is a non-archimedean local field. The classical Godement-Jacquet theory is that one can use Schwartz-Bruhat functions on $n \times n$ matrices $M_n(F)$ to define the local standard $L$-functions on $\mathrm{GL}_n$. The purpose of this partly expository note is to give evidence that there is an analogous and useful "approximate" Godement-Jacquet theory for the standard $L$-functions on the special orthogonal groups $\mathrm{SO}(V)$: One replaces $\mathrm{GL}_n(F)$ with $\mathrm{GSpin}(V)(F)$ and $M_n(F)$ with $\mathrm{Clif}(V)(F)$, the Clifford algebra of $V$. More precisely, we explain how a few different local unramified calculations for standard $L$-functions on $\mathrm{SO}(V)$ can be done easily using Schwartz-Bruhat functions on $\mathrm{Clif}(V)(F)$. We do not attempt any of the ramified or global theory of $L$-functions on $\mathrm{SO}(V)$ using Schwartz-Bruhat functions on $\mathrm{Clif}(V)$.
Outage and Throughput Analysis of UAV-Assisted NOMA Relay Systems With Indoor and Outdoor Users

Nonorthogonal multiple access (NOMA) and unmanned aerial vehicle (UAV) are two promising technologies for the fifth generation (5G) and beyond networks. On the other hand, the transition environment from outdoor to indoor is an important problem in practical wireless communication. In this article, we mathematically study a multiantenna UAV-assisted communication system where a multiantenna base station (BS) communicates with indoor and outdoor users through a multiantenna UAV using the power-domain NOMA technique. The metric used to evaluate the system performance are outage probability (OP) and throughput of indoor and outdoor users under different communication urban environments. Moreover, the impacts of the UAV's altitude and location and the line-of-sight probability on system performance are also considered. We give the exact and asymptotic closed-form OP expressions and then optimize the transmission rate to maximize the throughput of each user and the overall system throughput. Numerical results show that better system performance can be achieved by controlling the altitudes and location of the UAV, selecting an appropriate transmission rate, or equipping BS and UAV with more antennas. Monte Carlo simulation results are provided to demonstrate the performance of the investigated system and the accuracy of the developed analytical results.
Doss almost periodic functions, Besicovitch-Doss almost periodic functions and convolution products

In the paper under review, we analyze the invariance of Doss almost periodicity and Besicovitch-Doss almost periodicity under the actions of convolution products. We thus continue our recent research studies \cite{fedorov-novi} and \cite{NSJOM-besik} by investigating the case in which the solution operator family $(R(t))_{t>0}$ under our consideration has special growth rates at zero and infinity. In contrast to \cite{NSJOM-besik}, the results obtained in this paper can be incorporated in the qualitative analysis of solutions to abstract (degenerate) inhomogeneous fractional differential equations in Banach spaces.
Homogeneous matchbox manifolds

We prove that a homogeneous matchbox manifold of any finite dimension is homeomorphic to a McCord solenoid, thereby proving a strong version of a conjecture of Fokkink and Oversteegen. The proof uses techniques from the theory of foliations that involve making important connections between homogeneity and equicontinuity. The results provide a framework for the study of equicontinuous minimal sets of foliations that have the structure of a matchbox manifold.
On weak Fraisse limits

Using the natural action of $S_\infty$ we show that a countable hereditary class $\cC$ of finitely generated structures has the joint embedding property (JEP) and the weak amalgamation property (WAP) if and only if there is a structure $M$ whose isomorphism type is comeager in the space of all countable, infinitely generated structures with age in $\cC$. In this case, $M$ is the weak Fra\"iss\'e limit of $\cC$. This applies in particular to countable structures with generic automorphisms and recovers a result by Kechris and Rosendal [\textit{Proc.\ Lond. \ Math.\ Soc. ,\ 2007}].
Discrete Multi-Objective Switching Topology Sliding Mode Control of Connected Autonomous Vehicles With Packet Loss

Information flow topology is crucial in the control of connected autonomous vehicles. It substantially influences the platoon's performance. This study provides a real-time switching topology technique for improving the platoon's performance under poor communication. First, a discrete sliding mode controller with a double power reaching law is designed for a nonlinear heterogeneous vehicle dynamic model with packet loss. Then, Lyapunov analysis is applied to ensure the platoon's stability and string stability. Finally, a two-step switching topology framework is introduced. The first step is to search for Pareto optimal topology offline with predicted imperfect communication scenarios. Then, the platoon's overall performance is optimised using a multi-objective evolutionary algorithm. In the second step, the optimal topology is selected and switched in real-time to reduce the control cost. The proposed method maximises the advantages of information flow topology. It deals with poor communication, improves the platoon's performance, and ensures stability. Numerical simulations were conducted to validate the proposed approach. Compared to a standard robust sliding mode controller, the suggested technique enhances platoon tracking ability by 97.73 percent, fuel efficiency by 9.96 percent, and driving comfort by 20.18 percent, respectively.
Unions of Lebesgue spaces and $A_1$ majorants

We study two questions. When does a function belong to the union of Lebesgue spaces and when does a function have an $A_1$ majorant? We show these questions are fundamentally related. For functions restricted to a fixed cube we prove that the following are equivalent: a function belongs to $L^p$ for some $p>1$; the function has an $A_1$ majorant; for any $p>1$ the function belongs to $L^p_w$ for some $A_p$ weight $w$. We also examine the case of functions defined on ${\mathbb R}^n$ and give characterizations of the union of $L^p_w$ over $w$ in $A_p$ and when a function has an $A_1$ majorant on all of ${\mathbb R}^n$.
Seismicity, Fault Architecture, and Slip Mode of the Westernmost Gofar Transform Fault

Oceanic transform faults accommodate plate motions through both seismic and aseismic slips. However, deformation partition and slip mode interaction at these faults remain elusive mainly limited by rare observations. We use 1‐year ocean bottom seismometer data collected in 2008 to detect and locate earthquakes at the westernmost Gofar transform fault. The ultra‐fast slipping rate of Gofar results in ∼30,000 earthquakes during the observational period, providing an excellent opportunity to investigate interrelations between the slip mode, seismicity, and fault architecture at an unprecedented resolution. Earthquake distribution indicates that the ∼100‐km‐long Gofar transform fault is distinctly segmented into five zones, including one zone contouring a M6 earthquake that was captured by the experiment. Further, a barrier zone east of the M6 earthquake hosted abundant foreshocks preceding the M6 event and halted its active seismicity afterward. The barrier zone has two layers of earthquakes at depth, and they responded to the M6 earthquake differently. Additionally, a zone connecting to the East Pacific Rise had quasi‐periodic earthquake swarms. The seismicity segmentation suggests that the Gofar fault has multiple slip modes occurring in adjacent fault patches. Spatiotemporal characteristics of the earthquakes suggest that complex fault architecture and fluid–rock interaction play primary roles in modulating the slip modes at Gofar, possibly involving multiple concurrent physical processes.
A Generalized Fractional Calculus of Variations

We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, transversality conditions for free boundary value problems, and a generalized Noether type theorem.
On the Automorphism Tower of Free Nilpotent Groups

In this thesis I study the automorphism tower of free nilpotent groups. Our main tool in studying the automorphism tower is to embed every group as a lattice in some Lie group. Using known rigidity results the automorphism group of the discrete group can be embedded into the automorphism group of the Lie group. This allows me to lift the description of the derivation tower of the free nilpotent Lie algebra to obtain information about the automorphism tower of the free nilpotent group. The main result in this thesis states that the automorphism tower of the free nilpotent group $\Gamma(n,d)$ on $n$ generators and nilpotency class $d$, stabilizes after finitely many steps. If the nilpotency class is small compared to the number of generators we have that the height of the automorphism tower is at most 3.
Leveraging Android Automated Testing to Assist Crowdsourced Testing

Crowdsourced testing is an emerging trend in mobile application testing. The openness of crowdsourced testing provides a promising way to conduct large-scale and user-oriented testing scenarios on various mobile devices, while it also brings a problem, i.e., crowdworkers with different levels of testing experience severely threaten the quality of crowdsourced testing. Currently, many approaches have been proposed and studied to improve crowdsourced testing. However, these approaches do not fundamentally improve the ability of crowdworkers. In essence, the low-quality crowdsourced testing is caused by crowdworkers who are unfamiliar with the App Under Test (AUT) and do not know which part of the AUT should be tested. To address this problem, we propose a testing assistance approach, which leverages Android automated testing (i.e., dynamic and static analysis) to improve crowdsourced testing. Our approach constructs an Annotated Window Transition Graph (AWTG) model for the AUT by merging dynamic and static analysis results. Based on the AWTG model, our approach implements a testing assistance pipeline that provides the test task extraction, test task recommendation, and test task guidance to assist crowdworkers in testing the AUT. We experimentally evaluate our approach on real-world AUTs. The quantitative results demonstrate that our approach can effectively and efficiently assist crowdsourced testing. Besides, the qualitative results from a user study confirm the usefulness of our approach.
Approximate transmission conditions for a Poisson problem at mid-diffusion

AbstractThis work consists in the asymptotic analysis of the solution of Poisson equation in a bounded domain of RP (P = 2, 3) with a thin layer. We use a method based on hierarchical variational equations to derive an explicitly asymptotic expansion of the solution with respect to the thickness of the thin layer. We determine the first two terms of the expansion and prove the error estimate made by truncating the expansion after a finite number of terms. Next, using the first two terms of the asymptotic expansion, we show that we can model the effect of the thin layer by a problem with transmission conditions of order two.
On the Koszul cohomology of canonical and Prym‐canonical binary curves

In this paper we study Koszul cohomology and the Green and Prym–Green conjectures for canonical and Prym‐canonical binary curves. We prove that, if property Np holds for a canonical or a Prym‐canonical binary curve of genus g, then it holds for a generic canonical or Prym‐canonical binary curve of genus g + 1. We also verify the Green and Prym–Green conjectures for generic canonical and Prym‐canonical binary curves of low genus (6 ⩽ g ⩽ 15, g ≠ 8 for Prym‐canonical and 3 ⩽ g ⩽ 12 for canonical).