Proper Curve Research Articles

Continuous Rotation Group Equivariant Network Inspired by Neural Population Coding

Neural population coding can represent continuous information by neurons with a series of discrete preferred stimuli, and we find that the bell-shaped tuning curve plays an important role in this mechanism. Inspired by this, we incorporate a bell-shaped tuning curve into the discrete group convolution to achieve continuous group equivariance. Simply, we modulate group convolution kernels by Gauss functions to obtain bell-shaped tuning curves. Benefiting from the modulation, kernels also gain smooth gradients on geometric dimensions (e.g., location dimension and orientation dimension). It allows us to generate group convolution kernels from sparse weights with learnable geometric parameters, which can achieve both competitive performances and parameter efficiencies. Furthermore, we quantitatively prove that discrete group convolutions with proper tuning curves (bigger than 1x sampling step) can achieve continuous equivariance. Experimental results show that 1) our approach achieves very competitive performances on MNIST-rot with at least 75% fewer parameters compared with previous SOTA methods, which is efficient in parameter; 2) Especially with small sample sizes, our approach exhibits more pronounced performance improvements (up to 24%); 3) It also has excellent rotation generalization ability on various datasets such as MNIST, CIFAR, and ImageNet with both plain and ResNet architectures.

Conditions of Existence and Uniqueness of Limit Cycle for Grid-Connected VSC With PLL

This paper investigates the large disturbance stability of single voltage source converter (VSC) connected to the infinite bus system through the transmission line. One conservative stable region is obtained via the direct method of Lyapunov. Based on the Poincaré Theorem, it is interesting to find there might exist limit cycle between the obtained stable boundary and the angle of unstable equilibrium point (UEP). Accordingly, the nonlinear damping effect on the system stability is defined, and one limit cycle exists when the positive and negative damping effect over one period is mutually balanced. A conservative existence condition of limit cycle is further derived by constructing a proper piece-wise curve to approximate one specified unstable system trajectory. The derived analytical existence condition can directly predict the limit cycle without numerical simulations. Finally, the paper also proves that the studied dynamic system has at most one limit cycle, and if it exists, it is unstable.

Fatigue assessment of steel tube-to-flange welded joints with reinforcement ribs subjected to multiaxial loads according to the Peak Stress Method

In fatigue design of welded structures, the Peak Stress Method (PSM) is a FE-oriented tool to estimate the Notch Stress Intensity Factors (NSIFs). In compliance with proper fatigue design curves validated against more than 1300 experimental data, the PSM allows to estimate the fatigue lifetime of welded structures made of either aluminium alloys or structural steels and subjected to uniaxial and multiaxial loadings. Moreover, an interactive analysis tool has also been developed in Ansys® Mechanical to automate PSM application on welded structures and support the FE analyst. In this work, the fatigue strength of complex steel tube-to-flange welded joints with reinforcement ribs has been experimentally investigated under pure bending, pure torsion and in-phase as well as out-of-phase combined bending-torsion loadings. The tested joint consists of a steel SHS tube having 6.3 mm thickness, which is joined at both ends to a 15-mm-thick flange. In addition, tube and flanges are joined by fillet welding to 6-mm-thick steel reinforcement ribs. A test rig has been designed in order to perform the experimental fatigue tests, taking advantage of two hydraulic actuators. The experimental fatigue results have been compared with fatigue lifetime estimations performed using the automated PSM tool.

Preparation of Fe3O4@pectin nanocomposite hydrogel with high heating efficiency for hyperthermia applications

In this paper, magnetic nanoparticles (Fe3O4) were prepared by the co-precipitation method. The synthesized magnetic nanoparticles were added to the biocompatible polymer, pectin, for synthesizing Fe3O4@pectin (F@P) nanocomposite hydrogels. The structural, morphological, and magnetic characterizations were performed by X-ray diffraction (XRD), scanning electron microscopy (SEM), Fourier transform infrared (FTIR), and vibrating sample magnetometer (VSM) techniques. The XRD pattern confirmed the existence of the cubic phase of Fe3O4 nanoparticles. The FTIR spectra revealed the incorporation of pectin on the surface of Fe3O4 nanoparticles. The VSM measurement shows the proper magnetization curve of F@P nanocomposites, and good saturation magnetization value (∼33 emu/g). The results of hyperthermia temperature reveal an excellent heating efficiency of F@P nanocomposite hydrogel. The heating efficiency was quantified by a specific absorption rate (SAR) value and was obtained as 214 W/g for F@P nanocomposite hydrogels. This good hyperthermia result with biocompatible polymer (pectin) and hydrogel structure can be used for developing cancer treatment studies.

Fuel Consumption Efficiency Enhancement of Synchronous Diesel Generator Operating at Adjustable Speed using Adaptive Inertia Weight Particle Swarm Optimization Algorithm

Diesel generator is a reliable source of electricity, but requires quite high operational costs, especially for fuel. This paper describes a technique for reducing fuel consumption in Diesel Engine Synchronous Generator systems. The system is originally a Constant Speed Diesel Synchronous Generator (CSD-SG), but during certain conditions, the speed is reduced to minimize fuel consumption by adjusting the Specific Fuel Consumption (SFC) map. SFC is defined as the amount of fuel consumed by a diesel engine generator for each unit of power output. It shows various numbers depending on the speed and operating power. In this paper, we use the Adaptive Inertia Weight Particle Swarm Optimization (AIWPSO) algorithm to select of the proper SFC curve at a certain speed and operating power. AIWPSO employs an adaptive inertial weight adjustment method, which enables this algorithm to achieve faster convergence than conventional Particle Swarm Optimisation (PSO) algorithms. The system is embedded with AC/DC/AC power electronics converter to regulate the frequency. Data set of 1000 kVA Cummins diesel engine generator from the oil and gas company in Central Java, Indonesia was taken for simulations. The results show that the AIWPSO algorithm calculates the fuel consumption as 1,678 liters per day on a typical condition, whereas the previous method, the linear line needs 1,693 liters per day. Therefore, using AIWPSO method can save up to 450 liters of fuel per month. The simulation results show that the proposed method can improve fuel efficiency compared to the previous model.

Study on the Phase Angle Master Curve of the Polyurethane Mixture with Dense Gradation

The phase angle master curve of the PU mixture is a new research field that is urgently needed to characterize the viscoelastic of the PU mixture under different conditions. In this paper, five master curve models, five shift factor equations, and four error minimization methods were introduced to fitting the phase angle master curve of the PU mixture. The results analysis indicated that the master curves fitted by different error minimization methods had small differences when the loading frequency was higher than 10−3 Hz. The R2 maximization as the main constraint and the others as the additional constraints were recommended as the error minimization method. The combination of the Christensen Anderson and Marasteanu model (CAM) and kaelble shift factor equation was recommended for fitting the phase angle master curve of the PU mixture. The phase angle master curve of the PU mixture did not follow the “Bell” shape of the asphalt mixture. The PU mixture with smaller temperature susceptibility would still be subject to the PU at higher temperatures and was closer to that of the viscoelastic material. The phase angle master curve construction was analyzed for the first time and proper master curve fitting parameters were recommended for pavement performance predicting and analyzing.

Stably semiorthogonally indecomposable varieties

A triangulated category is said to be indecomposable if it admits no nontrivial semiorthogonal decompositions. We introduce a definition of a noncommutatively stably semiorthogonally indecomposable (NSSI) variety. This propery implies, among other things, that each smooth proper subvariety has indecomposable derived category of coherent sheaves, and that if $Y$ is NSSI, then for any variety $X$ all semiorthogonal decompositions of $X \times Y$ are induced from decompositions of $X$. We prove that any variety whose Albanese morphism is finite is NSSI, and that the total space of a fibration over NSSI base with NSSI fibers is also NSSI. We apply this indecomposability to deduce that there are no phantom subcategories in some varieties, including surfaces $C \times \mathbb{P}^1$, where $C$ is any smooth proper curve of positive genus.

A study of different tapering windowing functions and referencing curve for the improvement of sound field using wave-field synthesis

Wavefield synthesis is a well-known sound field reproduction technique. The correct synthesis of the desired sound field ideally requires a continuous source distribution over an enclosed surface. Due to practical limitations, a finite length of secondary source array is used. This results in distortion in the reproduced sound field due to the diffraction effect from the edge loudspeakers. To alleviate this problem, tapering window functions are utilized. In this paper, the influence of various windowing functions on the reproduced fields for different secondary source geometry and virtual source type is studied, and different parameters are used to make a quantitative comparison between the performance of different windowing functions. Further, the effect of the different referencing curves for the synthesis of correct amplitude is also presented. From the simulation results, it was found that the Tukey window function provides a wider sweet spot area with a minimal amplitude ringing effect. The selection of a proper referencing curve depends on the array geometry and the type of virtual source.

Optimization of enzyme-linked immunosorbent assay kit protocol to detect trimethylamine N-oxide levels in humans.

The serum level of trimethylamine N-oxide (TMAO), a gut microbiota metabolite associated with diabetes, cancer, inflammatory and neurological diseases, can be determined by the micro-enzyme-linked immunosorbent assay (ELISA) method. However, we had problems obtaining accurate standard curves with the original kit protocol from Bioassay Technology Laboratory. We aimed to acquire proper standard curves by modifying the kit protocol in this study. First, we evaluated the human TMAO ELISA kit protocols and other human ELISA kits. We maintained the incubation times longer and increased the wash cycle. Moreover, we incubated the standards containing biotinylated antibody in the wells alone. Then we washed the wells and added streptavidin-HRP for the second incubation step. The data of original and modified ELISA kit protocol were analyzed with Student's t-test. We measured higher absorbance with lower standard solution concentration in experiments that followed the original kit protocol. After investigating other human TMAO ELISA kits, we noticed that the SunRed Biotechnology Company and MyBioSource companies suggested similar protocols to the Bioassay Technology Laboratory company. The ELK Biotechnology ELISA protocol was different from others. However, since there is no biotinylated antibody in the standard solution in the ELK biotechnology kit, we changed some steps by examining other human ELISA protocols from different companies. After performing the modified protocol, we found that the absorbances of the standard solutions were consistent with their concentrations, and we obtained an accurate standard curve. Higher R2 values and lower absolute difference of standard concentrations were found in the modified kit protocol. The human TMAO ELISA protocol, which we modified in this study, will enable researchers to obtain more reliable results and prevent them from failing time and resources.

Group-theoreticity of numerical invariants and distinguished subgroups of configuration space groups

Let $\Sigma$ be a set of prime numbers which is either of cardinality one or equal to the set of all prime numbers. In this paper, we prove that various objects that arise from the geometry of the configuration space of a hyperbolic curve over an algebraically closed field of characteristic zero may be reconstructed group-theoretically from the pro-$\Sigma$ fundamental group of the configuration space. Let $X$ be a hyperbolic curve of type $(g,r)$ over a field $k$ of characteristic zero. Thus, $X$ is obtained by removing from a proper smooth curve of genus $g$ over $k$ a closed subscheme [i.e., the "divisor of cusps"] of $X$ whose structure morphism to Spec$(k)$ is finite étale of degree $r$; $2g-2+r>0$. Write $X_n$ for the $n$-th configuration space associated to $X$, i.e., the complement of the various diagonal divisors in the fiber product over $k$ of $n$ copies of $X$. Then, when $k$ is algebraically closed, we show that the triple $(n,g,r)$ and the generalized fiber subgroups—i.e., the subgroups that arise from the various natural morphisms $X_n \to X_m$ $[m$ < $n]$, which we refer to as generalized projection morphisms—of the pro-$\Sigma$ fundamental group $\Pi_n$ of $X_n$ may be reconstructed group-theoretically from $\Pi_n$ whenever $n \geq 2$. This result generalizes results obtained previously by the first and third authors and A. Tamagawa to the case of arbitrary hyperbolic curves [i.e., without restrictions on $(g,r)$]. As an application, in the case where $(g,r)= (0,3)$ and $n \geq 2$, we conclude that there exists a direct product decomposition Out$(\Pi_n) = {\mathrm{GT}^{\Sigma}} \times \mathfrak{S}_{n + 3}$ —where we write "Out$(-)$" for the group of outer automorphisms [i.e., without any auxiliary restrictions!] of the profinite group in parentheses and ${\mathrm{GT}^{\Sigma}}$ (respectively, $\mathfrak{S}_{n + 3}$) for the pro-$\Sigma$ Grothendieck-Teichmüller group (respectively, symmetric group on $n + 3$ letters). This direct product decomposition may be applied to obtain a simplified purely group-theoretic equivalent definition—i.e., as the centralizer in ${\rm Out}(\Pi_n)$ of the union of the centers of the open subgroups of ${\rm Out}(\Pi_n)$—of ${\mathrm{GT}^{\Sigma}}$. One of the key notions underlying the theory of the present paper is the notion of a pro-$\Sigma$ log-full subgroup—which may be regarded as a sort of higher-dimensional analogue of the notion of a pro-$\Sigma$ cuspidal inertia subgroup of a surface group—of $\Pi_n$. In the final section of the present paper, we show that, when $X$ and $k$ satisfy certain conditions concerning "weights", the pro-$l$ log-full subgroups may be reconstructed group-theoretically from the natural outer action of the absolute Galois group of $k$ on the geometric pro-$l$ fundamental group of $X_n$.

The clinical meaning of the area under a receiver operating characteristic curve for the evaluation of the performance of disease markers.

The area under a receiver operating characteristic (ROC) curve (AUC) is a popular measure of pure diagnostic accuracy that is independent from the proportion of diseased subjects in the analysed sample. However, its actual usefulness in the clinical context has been questioned, because it does not seem to be directly related to the actual performance of a diagnostic marker in identifying diseased and non-diseased subjects in real clinical settings. This study evaluates the relationship between the AUC and the proportion of correct classifications (global diagnostic accuracy, GDA) in relation to the shape of the corresponding ROC curves. We demonstrate that AUC represents an upward-biased measure of GDA at an optimal accuracy cut-off for balanced groups. The magnitude of bias depends on the shape of the ROC plot and on the proportion of diseased and non-diseased subjects. In proper curves, the bias is independent from the diseased/non-diseased ratio and can be easily estimated and removed. Moreover, a comparison between 2 partial AUCs can be replaced by a more powerful test for the corresponding whole AUCs. Applications to 3 real datasets are provided: a marker for a hormone deficit in children, 2 tumour markers for malignant mesothelioma, and 2 gene expression profiles in ovarian cancer patients. The AUC is a measure of accuracy with potential clinical relevance for the evaluation of disease markers. The clinical meaning of ROC parameters should always be evaluated with an analysis of the shape of the corresponding ROC curve.

Characterization of proper curves and proper helix lying on $S_{1}^2(r)$

In this paper, we analyse the proper curve $\gamma(s)$ lying on the pseudo-sphere. We develop an orthogonal frame $\lbrace V_{1}, V_{2}, V_{3} \rbrace$ along the proper curve, lying on pseudosphere. Next, we find the condition for $\gamma(s)$ to become $V_{k} -$ slant helix in Minkowski space. Moreover, we find another curve $\beta(\bar{s})$ lying on pseudosphere or hyperbolic plane heaving $V_{2} = \bar{V_{2}}$ for which $\lbrace \bar{V_{1}},\bar{V_{2}},\bar{V_{3}} \rbrace$, an orthogonal frame along $\beta(\bar{s})$. Finally, we find the condition for curve $\gamma(s)$ to lie in a plane.

Inclination of Mandibular Molars and Alveolar Bone in Untreated Adults and Its Relationship with Facial Type

To date, there is no solid agreement on the relationship between mandibular molars, mandibular alveolar bone, and vertical facial types. Therefore, we aim to assess the buccolingual inclination of mandibular first molars and respective alveolar bones and their relationship with different vertical skeletal patterns. The CBCT data from fifty-four untreated Caucasian adult patients (12 males and 42 females, 18–65 years old) were obtained from a private orthodontic practice. We measured the inclination of the tooth and alveolar bone of the right and left mandibular first molars using CBCT. From the two-dimensional lateral cephalometric radiographic images extracted from CBCT, we assessed FMA, SN-GoGn, and PFH:AFH. All subjects showed lingual inclinations of the mandibular molars and alveolar bones which were significantly correlated with each other. However, there was no significant correlation between the inclination of alveolar bone and vertical facial types. Our study supports the conclusion that a proper curve of Wilson is physiological and should be maintained during orthodontic treatment.

Special values of L-functions on regular arithmetic schemes of dimension 1

We construct a well-behaved Weil-étale complex for a large class of Z-constructible sheaves on a regular irreducible scheme U of finite type over Z and of dimension 1. We then give a formula for the special value at s=0 of the L-function associated to any Z-constructible sheaf on U in terms of Euler characteristics of Weil-étale cohomology; for smooth proper curves, we obtain the formula of [GS20]. We deduce a special value formula for Artin L-functions of integral representations twisted by a singular irreducible scheme X of finite type over Z and of dimension 1. This generalizes and improves all results in [Tra16]; as a special case, we obtain a special value formula for the arithmetic zeta function of X.

The Brauer–Manin obstruction for constant curves over global function fields

Let 𝔽 be a finite field and C,D smooth, geometrically irreducible, proper curves over 𝔽 and set K=𝔽(D). We consider Brauer–Manin and abelian descent obstructions to the existence of rational points and to weak approximation for the curve C⊗ 𝔽 K. In particular, we show that Brauer–Manin is the only obstruction to weak approximation and the Hasse principle in the case that the genus of D is less than that of C. We also show that we can identify the points corresponding to non-constant maps D→C using Frobenius descents.

Functional Form of The Zenga Curve Based on Rohde’s Version of the Lorenz Curve

The Zenga curve is a tool to measure income inequality that represents the income ratio between the bottom income group and the top income group. A proper Zenga curve is a Zenga curve that can detect variations in the Ratio. In this paper, we derive the functional form of the Zenga curve from Rohde's Lorenz curve model. The result of this paper is that the functional form of the Zenga curve from Rohde's version of the Lorenz curve model is a constant. It cannot represent the truly happening phenomenon of inequality.

Simultaneous 3D dithering of multiple images by curves

We present a method to simultaneously dither multiple images by space curves, seen from multiple views. The space curves are a-priori designed to create varying coverages over a contrasting background, when projected in the different directions. By carefully placing the proper curves at specific pixel locations, the desired dithering effect of multiple images can be achieved, as one 3D model consisting of only space curves, and from multiple directions.The presented approach employs dark space curves of finite width over light background. The dithering of two or three different B&W images from two or three different directions is demonstrated, using computer simulations as well as 3D printed results.

A Hub and Spoke Learning Program in Bariatric Surgery in a Small Region of Italy.

BackgroundMetabolic and bariatric surgery (BS) are considered life-changing and life-saving treatments for obese patients. The Italian Society of Obesity Surgery (SICOB) requires at least 25 operations per year to achieve the standard of care in the field. Despite the increasing need to treat obese patients, some small southern regions of Italy, such as Molise, do not have enough experience in bariatric procedures to be allowed to perform them. Therefore, our aim was to run a Hub and Spoke Program with a referral center in BS to treat obese patients and provide a proper learning curve in BS in Molise.MethodsIn 2020, the “A. Cardarelli Hospital” in Campobasso, Molise, started a formal “Learning Model of Hub and Spoke Collaboration” with the Hub center “Ospedale Del Mare”, Naples. A multidisciplinary approach was achieved. Patients were supervised and operated under the supervision and tutoring of the referral center. We retrospectively reviewed our prospectively collected database from February 2020 to August 2021 in order to analyze the safety and effectiveness of our learning program.ResultsIn total, 13 (3 men and 10 women) patients underwent BS with the mean age of 47.08 years and a presurgery BMI of 41.79. Seven (53.84%) patients were the American Society of Anesthesiologist (ASA) II, and 6 (46.16%) patients were ASA III. Twelve (92.31%) procedures were laparoscopic sleeve gastrectomies, 1 (7.69%) patient underwent endoscopic BioEnterics Intragastric Balloon (BIB) placement. One (8.33%) sleeve gastrectomy was associated to gastric band removal. Mean surgical time was 110.14 ± 23.54 min. The mean length of stay was 4.07 ± 2.40 days. No Clavien-Dindo ≥ III and mortality were reported. The follow-up program showed a mean decrease of 11.82 in terms of body mass index (BMI) value. The last 5 procedures were performed by the whole equips from “A. Cardarelli” under external tutoring without any impact on complication rate.ConclusionThe setup of a proper Hub and Spoke Program may allow to perform BS to provide the standard of care. This approach may reduce health costs and related patient migration.

Picard ranks of K3 surfaces over function fields and the Hecke orbit conjecture

Let \({\mathscr {X}} \rightarrow C\) be a non-isotrivial and generically ordinary family of K3 surfaces over a proper curve C in characteristic \(p \ge 5\). We prove that the geometric Picard rank jumps at infinitely many closed points of C. More generally, suppose that we are given the canonical model of a Shimura variety \({\mathcal {S}}\) of orthogonal type, associated to a lattice of signature (b, 2) that is self-dual at p. We prove that any generically ordinary proper curve C in \({\mathcal {S}}_{{\overline{{\mathbb {F}}}}_p}\) intersects special divisors of \({\mathcal {S}}_{{\overline{{\mathbb {F}}}}_p}\) at infinitely many points. As an application, we prove the ordinary Hecke orbit conjecture of Chai–Oort in this setting; that is, we show that ordinary points in \({\mathcal {S}}_{{\overline{{\mathbb {F}}}}_p}\) have Zariski-dense Hecke orbits. We also deduce the ordinary Hecke orbit conjecture for certain families of unitary Shimura varieties.

Reduction and lifting problem for differential forms on Berkovich curves

Given a complete real-valued field k of residue characteristic zero, we study properties of a differential form ω on a smooth proper k-analytic curve X. In particular, we associate to (X,ω) a natural tropical reduction datum combining tropical data of (X,ω) and algebra-geometric reduction data over the residue field k˜. We show that this datum satisfies natural compatibility condition, and prove a lifting theorem asserting that any compatible tropical reduction datum lifts to an actual pair (X,ω). In particular, we obtain a short proof of the main result of [2].