Miracle-dz/UniFAR-FTUs huggingface dataset:
Faster RCNN based on Feature Fusion and its Application in Steel Surface Defect Detection

Surface defects are an inevitable problem in steel production and processing. To solve the problems of error detection, leakage detection and low accuracy of traditional manual methods for steel surface defect detection, this paper proposes a steel surface defect detection algorithm based on Faster RCNN, a classical model in the field of computer vision object detection. The proposed model uses ResNet50 as its backbone and introduces FPN to fuse the multi-layer feature maps of the backbone to improve the detection capability for defects of different scales. The experimental results on NEU-DET dataset show that the proposed model in this paper has different detection accuracies for six different types of defects in the dataset, and the overall mAP reaches 0.708. In addition, the model execution speed reaches 43.3 frame/s, which meets the applications in industrial scenarios.
Optimization and effect of varying catalyst concentration and trans-esterification temperature on the yield of biodiesel production from palm kernel oil and groundnut oil

The negative environmental impact generated by fossil fuel has resulted in the demand to search for alternative routes of renewable sources of energy, such as biodiesel, that have unlimited duration while having little or no hazardous impact. In this study, trans-esterification of palm kernel oil and groundnut oil was carried out using sodium methoxide (CH3ONa) as a catalyst. The effect of varying Sodium Methoxide (CH3ONa) catalyst concentrations of (0.25, 0.5, 1.0, 1.5, and 2.0) % w/v at trans-esterification temperatures of (50, 55, and 60) oC on the yield of biodiesel from groundnut oil and palm kernel oil was determined. This was to identify the catalyst concentration and trans-esterification temperature with optimal process yield. The process gave optimum biodiesel yields of 98% and 84% by volume of groundnut oil and palm kernel oil at reaction conditions of 0.5%w/v CH3ONa as catalyst, trans-esterification temperature of 55oC, 360 rpm mixing rate and a reaction time of 90 minutes. The biodiesel produced was analyzed for fuel properties using the ASTM standard, and the results obtained were as follows; specific gravity (0.8835, 0.8815 at 15oC), flash point (98, 124) oC, and viscosity (5.2, 7.6) mm2S-1 for palm kernel oil and groundnut oil respectively.
Optimal scheduling of energy storage resources

It is likely that electricity storage will play a significant role in the balancing of future energy systems. A major challenge is then that of how to assess the contribution of storage to capacity adequacy, i.e.\ to the ability of such systems to meet demand. This requires an understanding of how to optimally schedule multiple storage facilities. The present paper studies this problem in the cases where the objective is the minimisation of expected energy unserved (EEU) and also a form of weighted EEU in which the unit cost of unserved energy is higher at higher levels of unmet demand. We also study how the contributions of individual stores may be identified for the purposes of their inclusion in electricity capacity markets.
Incremental and Parallel Machine Learning Algorithms With Automated Learning Rate Adjustments

The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning algorithms incorporating the line search method, which automatically and algorithmically finds appropriate learning rates at run-time. One algorithm is based on the incremental subgradient algorithm, which sequentially and cyclically uses each of the parts of the objective function; the other is based on the parallel subgradient algorithm, which uses parts independently in parallel. These algorithms can be applied to constrained nonsmooth convex optimization problems appearing in tasks of learning support vector machines without adjusting the learning rates precisely. The proposed line search method can determine learning rates to satisfy weaker conditions than the ones used in the existing machine learning algorithms. This implies that the two algorithms are generalizations of the existing incremental and parallel subgradient algorithms for solving constrained nonsmooth convex optimization problems. We show that they generate sequences that converge to a solution of the constrained nonsmooth convex optimization problem under certain conditions. The main contribution of this paper is the provision of three kinds of experiment showing that the two algorithms can solve concrete experimental problems faster than the existing algorithms. First, we show that the proposed algorithms have performance advantages over the existing ones in solving a test problem. Second, we compare the proposed algorithms with a different algorithm Pegasos, which is designed to learn with a support vector machine efficiently, in terms of prediction accuracy, value of the objective function, and computational time. Finally, we use one of our algorithms to train a multilayer neural network and discuss its applicability to deep learning.
Numerical Approximation of Optimal Convex Shapes

This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem. Moreover, we prove the convergence of discretizations in two-dimensional situations. A numerical algorithm is devised that iteratively solves the discrete formulation. Numerical experiments show that optimal convex shapes are generally non-smooth and that three-dimensional problems require an appropriate relaxation of the convexity condition.
A theorem on even pancyclic bipartite digraphs

We prove that a strongly connected balanced bipartite directed graph of order $2a\geq 6$ with partite sets $X$ and $Y$ contains cycles of every length $2, 4, \ldots , 2a$, provided $d(x)+d(y)\geq 3a$ for every pair of vertices $x$, $y$ either both in $X$ or both in $Y$.
Anatomical Aspects of Neurogenic Bladder and the Approach in Its Management: A Narrative Review

The contraction of the detrusor muscle causes the urinary bladder and its mass peristaltic movement, leading to micturition. The vesical plexus of nerves, composed of fibers from the inferior hypogastric plexus, supplies the urinary bladder. The brain plays a crucial part in developing and maintaining bladder control, although its specific involvement in urgency and urine leakage is not well understood. The critical components in the neural control of the bladder and its regulation are the pontine micturition center (located in the mediodorsal aspect of the pons) and the Onuf's nucleus, also known as the sacral micturition center (located between the sacral S2 and S4 segments). The most important cause of a neurogenic bladder is damage or lesions of the spinal cord affecting the pontine micturition center, Onuf's nucleus, or damage to the motor neurons between the pontine and the sacral centers of micturition. Neurogenic bladder can be of several types based on the location of the lesions, such as the autonomous bladder, spastic bladder, atonic bladder, and cortical bladder, all were presented with a unique clinical picture. The classical approach to a case of neurogenic bladder involves a complete assessment of the neurologic system and of pelvic anatomy, while neurogenic bladder rehabilitation may include a bladder retraining program involving intermittent catheterization, timed voiding, medications, and lifestyle modifications. This review article attempts to correlate the neurogenic bladder with various anatomical aspects related to the micturition center in the brain and spinal cord and their control over the urinary bladder, as well as the classical approach toward such a case of neurogenic bladder.
Hitting time and mixing time bounds of Stein's factors

For any discrete target distribution, we exploit the connection between Markov chains and Stein's method via the generator approach and express the solution of Stein's equation in terms of expected hitting time. This yields new upper bounds of Stein's factors in terms of the parameters of the Markov chain, such as mixing time and the gradient of expected hitting time. We compare the performance of these bounds with those in the literature, and in particular we consider Stein's method for discrete uniform, binomial, geometric and hypergeometric distribution. As another application, the same methodology applies to bound expected hitting time via Stein's factors. This article highlights the interplay between Stein's method, modern Markov chain theory and classical fluctuation theory.
Limits of canonical forms on towers of Riemann surfaces

Abstract We prove a generalized version of Kazhdan’s theorem for canonical forms on Riemann surfaces. In the classical version, one starts with an ascending sequence { S n → S } {\{S_{n}\rightarrow S\}} of finite Galois covers of a hyperbolic Riemann surface S, converging to the universal cover. The theorem states that the sequence of forms on S inherited from the canonical forms on S n {S_{n}} ’s converges uniformly to (a multiple of) the hyperbolic form. We prove a generalized version of this theorem, where the universal cover is replaced with any infinite Galois cover. Along the way, we also prove a Gauss–Bonnet-type theorem in the context of arbitrary infinite Galois covers.
Continuous Inventory Models of Diffusion Type: Long-term Average Cost Criterion

This paper establishes conditions for optimality of an $(s,S)$ ordering policy for the minimization of the long-term average cost of one-dimensional diffusion inventory models. The class of such models under consideration have general drift and diffusion coefficients and boundary points that are consistent with the notion that demand should tend to decrease the inventory level. Characterization of the cost of a general $(s,S)$ policy as a function $F$ of two variables naturally leads to a nonlinear optimization problem over the ordering levels $s$ and $S$. Existence of an optimizing pair $(s_*,S_*)$ is established for these models. Using the minimal value $F_*$ of $F$, along with $(s_*,S_*)$, a function $G$ is identified which is proven to be a solution of a quasi-variational inequality provided a simple condition holds. At this level of generality, optimality of the $(s_*,S_*)$ ordering policy is established within a large class of ordering policies such that local martingale and transversality conditions involving $G$ hold. For specific models, optimality of an $(s,S)$ policy in the general class of admissible policies can be established using comparison results. This most general optimality result is shown for the classical drifted Brownian motion inventory model with holding and fixed plus proportional ordering costs and for a geometric Brownian motion inventory model with fixed plus level-dependent ordering costs. However, for a drifted Brownian motion process with reflection at $\{0\}$, a new class of non-Markovian policies is introduced which have lower costs than the $(s,S)$ policies. In addition, interpreting reflection at $\{0\}$ as "just-in-time" ordering, a necessary and sufficient condition is given that determines when just-in-time ordering is better than traditional $(s,S)$ policies.
Ginger Compress Therapy – A Painless Solution for Kidney Failure Patients

Chronic kidney disease (CKD) is one of the most outgrowing diseases of all, and globally, about 10% of the world's population is affected. Chronic kidney disease (CKD) occurs when the kidney can no longer perform its function to full capacity. There are currently two treatment options for CKD: dialysis and transplantation. Both existing treatment options have their demerits, including high cost, pain, sleep disturbances, restlessness, graft rejection, and much more. Zingiber officinale, also commonly known as ginger, is one of the most commonly used household herbs and a potential medicinal herb. It contains various phytochemicals such as essential oils, phenolic compounds, alkaloids, glycosides, flavonoids, terpenoids, saponin, tannin, protein, and carbohydrates. Ginger has been reported for multiple medicinal properties such as antibacterial, antioxidant, anti-inflammatory, immune-modulatory, anti-hypertensive, anti-arthritic, hepatoprotective, and nephroprotective. The nephroprotective properties of ginger are less explored than their other therapeutic properties. Few research data suggest that the aqueous extracts of ginger lowered blood glucose, serum, urea, and creatinine levels in diabetic-induced rats. It also helped to restore the changes in the kidney due to toxicity. Thus, it protects renal tissues from structural damage caused by hypoglycemia, inhibits cholesterol absorption due to oxidative stress, and also boosts the kidney's defense mechanism. The in silico work performed on 64 phytochemicals against the Vitamin D3 receptor target protein of CKD showed the binding efficiency of phytochemicals against this target. Diterpene (Lactone) has shown a better binding score with optimal ADMET properties. Ginger compress therapy is a very simple treatment process, using pieces of ginger boiled in hot water, after which a towel is soaked in this ginger water and spread over the lower portion of the patient's back for around 30 minutes. After this, the area must be rubbed with a few drops of gingelly oil. Currently, many Siddha and Ayurveda practitioners in India and many other countries use this therapy to cure numerous patients. Deeper research into this therapy could enhance efficiency and provide a scientific approach.
Speed of convergence towards attracting sets for endomorphisms of P^k

Let f be a non-invertible holomorphic endomorphism of P^k having an attracting set A. We show that, under some natural assumptions, A supports a unique invariant positive closed current \tau, of the right bidegree and of mass 1. Moreover, if R is a current supported in a small neighborhood of A then its push-forwards by f^n converge to \tau exponentially fast. We also prove that the equilibrium measure on A is hyperbolic.
Topics in Ramsey Theory

Ramsey theory is the study of conditions under which mathematical objects show order when partitioned. Ramsey theory on the integers concerns itself with partitions of $[1,n]$ into $r$ subsets and asks the question whether one (or more) of these $r$ subsets contains a $k$-term member of $\mathcal{F}$, where $[1,n]=\{1,2,3,\ldots,n\}$ and $\mathcal{F}$ is a certain family of subsets of $\mathbb{Z}^+$. When $\mathcal{F}$ is fixed to be the set of arithmetic progressions, the corresponding Ramsey-type numbers are called the van der Waerden numbers. I started the project choosing $\mathcal{F}$ to be the set of semi-progressions of scope $m$. A semi-progression of scope $m\in \mathbb{Z}^+$ is a set of integers $\{x_1,x_2,\ldots,x_k\}$ such that for some $d\in\mathbb{Z}^+$, $x_{i}-x_{i-1}\in\{d,2d,\ldots,md\}$ for all $i\in\{2,3,\ldots,k\}$. The exact values of Ramsey-type functions corresponding to semi-progressions are not known. We use $SP_m(k)$ to denote these numbers as a Ramsey-type function of $k$ for a fixed scope $m$. During this project, I used the probabilistic method to get an exponential lower bound for any fixed $m$. The first chapter starts with a brief introduction to Ramsey theory and then explains the problem considered. In the second chapter, I give the results obtained on semi-progressions. In the third chapter, I will discuss the lower bound obtained on $Q_1(k)$. When $\mathcal{F}$ is chosen to be quasi-progressions of diameter $n$, the corresponding Ramsey-type numbers obtained are denoted as $Q_n(k)$. The last chapter gives an exposition of advanced probabilistic techniques, in particular concentration inequalities and how to apply them.
The integrative model of ICT effects on Adolescents’ well-being (iMEW): The synthesis of theories from developmental psychology, media and communications, and health

ABSTRACT Information and communication technologies (ICTs) have become commonplace in adolescents’ lives, and they have grown in importance during the COVID-19 pandemic, when online communication became standard for many parts of life. This brings the need for developmental psychology to revise and update its theories for these new societal challenges. It is beneficial to look at these changes from an interdisciplinary perspective to enrich developmental psychology with knowledge from other fields. This theoretical article proposes the Integrative Model of ICT Effects on Adolescents’ Well-being (iMEW), which integrates the Problem Behaviour Theory from developmental psychology and the Differential Susceptibility to Media Effects Model from media and communications. It draws inspiration from the Ecological Systems Theory and the Health Belief Model. The new model brings a more comprehensive understanding to adolescents’ development and the effects of ICTs on their well-being. It is also helpful for the empirical research because it can serve as a roadmap for research that focuses on the effects of ICT.
An Extension of a Theorem of Duffin and Schaeffer in Diophantine Approximation

Duffin and Schaeffer have generalized the classical theorem of Khintchine in metric Diophantine approximation in the case of any error function under the assumption that all the rational approximants are irreducible. This result is extended to the case where the numerators and the denominators of the rational approximants are related by a congruential constraint stronger than coprimality.
Local-global principles for Weil–Châtelet divisibility in positive characteristic

Abstract We extend existing results characterizing Weil-Châtelet divisibility of locally trivial torsors over number fields to global fields of positive characteristic. Building on work of González-Avilés and Tan, we characterize when local-global divisibility holds in such contexts, providing examples showing that these results are optimal. We give an example of an elliptic curve over a global field of characteristic 2 containing a rational point which is locally divisible by 8, but is not divisible by 8 as well as examples showing that the analogous local-global principle for divisibility in the Weil-Châtelet group can also fail.
Verification of the Firoozbakht conjecture for primes up to four quintillion

If $p_k$ is the k-th prime, the Firoozbakht conjecture states that the sequence $(p_k)^{1/k}$ is strictly decreasing. We use the table of first-occurrence prime gaps in combination with known bounds for the prime-counting function to verify the Firoozbakht conjecture for primes up to four quintillion $(4\times10^{18})$.
A Hybrid Finite-Dimensional RHC for Stabilization of Time-Varying Parabolic Equations

The present work is concerned with the stabilization of a general class of time-varying linear parabolic equations by means of a finite-dimensional receding horizon control (RHC). The stability and suboptimality of the unconstrained receding horizon framework is studied. The analysis allows the choice of the squared $\ell_1$-norm as control cost. This leads to a nonsmooth infinite-horizon problem which provides stabilizing optimal controls with a low number of active actuators over time. Numerical experiments are given which validate the theoretical results and illustrate the qualitative differences between the $\ell_1$- and $\ell_2$-control costs.
The Korteweg–de Vries equation and its symmetry-preserving discretization

The Korteweg–de Vries equation is one of the most important nonlinear evolution equations in the mathematical sciences. In this article invariant discretization schemes are constructed for this equation both in the Lagrangian and in the Eulerian form. We also propose invariant schemes that preserve the momentum. Numerical tests are carried out for all invariant discretization schemes and related to standard numerical schemes. We find that the invariant discretization schemes give generally the same level of accuracy as the standard schemes with the added benefit of preserving Galilean transformations which is demonstrated numerically as well.
Implementation of the AC-based economic dispatch in the Russian electricity market

The Russian wholesale electricity market started to operate in its present form since 2006. Its unique specificity is the AC-based economic dispatch model underlying the market applications. Solution method for the day-ahead and balancing market applications was developed and implemented. Now it is employed by the commercial operator and the system operator of the Russian energy system. It is proved to be an adequate and reliable scheduling market technology
THE MASS SPECTRUM OF THE FIRST STARS

We perform cosmological hydrodynamics simulations with non-equilibrium primordial chemistry to obtain 59 minihalos that host first stars. The obtained minihalos are used as the initial conditions of local three-dimensional radiation hydrodynamics simulations to investigate the formation of the first stars. We find that two-thirds of the minihalos host multiple stars, while the other third has single stars. The mass of the stars found in our simulations are in the range of 1 M☉ ≲ M ≲ 300 M☉, peaking at several× 10 M☉. Most of the very massive stars of ≳ 140 M☉ are born as single stars, although not all of the single stars are very massive. We also find a few stars of ≲ 1 M☉ that are kicked by the gravitational three body interactions to the position distant from the center of mass. The frequency that a star forming minihalo contains a binary system is ∼50%. We also investigate the abundance pattern of the stellar remnants by summing up the contributions from the first stars in the simulations. Consequently, the pattern is compatible with that of the low metallicity damped Lyα systems or the extremely metal-poor (EMP) stars, if the mass spectrum obtained in our experiment is shifted to the low mass side by 0.2 dex. If we consider the case that an EMP star is born in the remnant of the individual minihalo without mixing with others, the chemical signature of the pair instability supernova is more prominent, because most of them are born as single stars.
Stable Cluster Variables

Richard Eager and Sebastian Franco introduced a change of basis transformation on the F-polynomials of Fomin and Zelevinsky, corresponding to rewriting them in the basis given by fractional brane charges rather than quiver gauge groups. This transformation seems to display a surprising stabilization property, apparently causing the first few terms of the polynomials at each step of the mutation sequence to coincide. Eager and Franco conjecture that this transformation will always cause the polynomials to converge to a formal power series as the number of mutations goes to infinity, at least for quivers possessing certain symmetries and along periodic mutation sequences respecting such symmetries. In this paper, we verify this convergence in the case of the Kronecker and Conifold quivers. We also investigate convergence in the $F_0$ quiver. We provide a combinatorial interpretation for the stable cluster variables in each appropriate case.
Inverse Magnetic Catalysis in the Polyakov--Nambu--Jona-Lasinio and Entangled Polyakov--Nambu--Jona-Lasinio Models

We investigate the QCD phase diagram at zero chemical potential and finite temperature in the presence of an external magnetic field within the three flavor Polyakov-Nambu-Jona-Lasinio and entangled Polyakov-Nambu-Jona-Lasinio models looking for the inverse magnetic catalysis. Two scenarios for a scalar coupling parameter dependent on the magnetic field intensity are considered. These dependencies of the coupling allow to reproduce qualitatively lattice QCD results for the quark condensates and for the Polyakov loop: due to the magnetic field the quark condensates are enhanced at low and high temperatures and suppressed for temperatures close to the transition temperatures while the Polyakov loop increases with the increasing of the magnetic field.