Miracle-dz/UniFAR-FTUs huggingface dataset:
Algorithms And Programming On The Minimal Combinations Of Weights Of Projective Hypersurfaces.

This paper designs an alogrithm to compute the minimal combinations of finite sets in Euclidean spaces, and applys the algorithm of study the moment maps and geometric invariant stability of hypersurfaces. The classical example of cubic curves is repeated by the algorithm. Furhtermore the alogrithm works for cubic surfaces. For given affinely indepdent subsets of monomials, the algorithm can output the unique unstable points of the Morse strata if it exists. Also there is a discussion on the affinely dependent sets of monomials.
A rigidity theorem for holomorphic disks in Teichmüller space

In this paper, we discuss a rigidity property for holomorphic disks in Teichm\"uller space. In fact, we give a refinement of Tanigawa's rigidity theorem. We will also treat the rigidity property of holomorphic disks for complex manifolds. We observe the rigidity property is valid for bounded strictly pseudoconvex domains with $C^{2}$-boundaries, but the rigidity property does not hold for product manifolds.
Explicit heat kernel on generalized cones

The authors compute explicitly the heat kernel on the surface of cones as well as on their generalizations. A procedure similar to the Fourier transform is employed in order to combine two Green’s functions: one for the Bessel equation on the positive half-line and another for the Laplacian on graph networks. An analogue of the Poisson summation formula is derived from the residue theorem applied to the Green’s function. Numerical computations are also implemented to determine some geometric quantity via the asymptotic expansion of the spectral function as t goes to zero.
Self-similar spatially homogeneous cosmologies: orthogonal perfect fluid and vacuum solutions

It is known that the symptotic states of a large class of spatially homogeneous cosmological models, near the big bang and at late times, are described by exact self-similar solutions. With this as motivation the authors find all spatially homogeneous solutions of the Einstein field equations which have an orthogonal perfect fluid as source, or are vacuum, and admit a similarity group H4 which acts transitively on spacetime.
High-frequency sampling of multivariate CARMA processes

High-frequency sampled multivariate continuous time autoregressive moving average processes are investigated. We obtain asymptotic expansion for the spectral density of the sampled MCARMA process $(Y_{n\Delta})_{n \in \mathbb{Z}}$ as $\Delta \downarrow 0$, where $(Y_t)_{t \in \mathbb{R}}$ is an MCARMA process. We show that the properly filtered process is a vector moving average process, and determine the asymptotic moving average representation of it, thus generalizing the results by Brockwell et al. in the univariate case to the multivariate model. The determination of the moving average representation of the filtered process, important for the analysis of high-frequency data, is difficult for any fixed positive $\Delta$. However, the results established here provide a useful and insightful approximation when $\Delta$ is very small.
Steady-state analysis of closed-loop switching circuit by calculating convolution integral in the steady state

This paper discusses the convolution integral of the circuit variable and the transfer function in the steady state of a circuit. It is shown that the integral can easily be calculated by the Shooting method when the transfer function to be calculated has a simple form. Using the proposed method of calculation, the steady-state operation is analyzed for the periodic switching circuit which is controlled by the closed loop, such as the switching converter. A method is proposed that precisely determines the steady-state operation of the overall circuit, while precisely analyzing the steady-state operation of the loop circuit. The proposed method differs from the conventional method in that the circuit, including the loop circuit not analyzed but the loop-control circuit is represented by a transfer function separately from the overall circuit and the steady-state response is determined by the convolu-tional integral. Consequently, for closed-loop switching circuits of various structures, the operation can be determined precisely without enlarging the circuit scale to be analyzed. Another point compared to the past method is that the operation specifications for the circuit can be handled with a better transparency.
Analysis of wasp-waist hysteresis loops

Wasp-waist and pot-belly hysteresis loops have been observed in many materials. When only the major loop is reported, the results are insufficient to establish which processes are involved. We present two models for wasp-waist materials that produce virtually indistinguishable major loops, but show that first-order reversal curves can be used to separate the effects. In the simplest model, we take a soft magnetic material and a hard material and exchange couple them. When the exchange is positive, the loop is conventional. However, for negative (antiferromagnetic) exchange, the wasp-waist loop is obtained. Negative coupling of two materials with different switching field distributions leads to pot-bellied loops.
Generically trivial derived categories

We study generic objects in triangulated categories and characterize the finite dimensional algebras $A$ such that the derived categories $D(\Mod A)$ are generically trivial. This is an analogue of a result of Crawley-Boevey for module categories. As a consequence, we show that $D(\Mod A)$ is generically trivial if and only if the category of perfect complexes $K^b(\proj A)$ is locally finite.
Cell-free DNA as a Promising Diagnostic Biomarker in Prostate Cancer: A Systematic Review and Meta-Analysis

Objective . The detection of cell-free DNA (cfDNA) as a part of “liquid biopsy” of prostate cancer (PCa) has been widely explored. However, its diagnostic value for PCa remains controversial. Based on the data from the latest literature published in the past decade, the present review was conducted to clarify the diagnostic value of cfDNA in PCa. Methods . The related studies were systematically searched in the databases of PubMed, Embase, Web of Science, and Cochrane Library from January 1, 2010 to December 1, 2020. Sensitivity (SEN), specificity (SPE), and other relative parameters were pooled using a random model. Results . 14 eligible studies with 1049 PCa patients and 973 controls were selected based on the inclusion and exclusion criteria. Results demonstrated that cfDNA showed favorable SPE (0.89, 95% CI: 0.79, 0.94) but unsatisfied SEN (0.56, 95% CI: 0.43, 0.68) in the PCa diagnosis. The positive likelihood ratios (PLR), negative likelihood ratios (NLR), and diagnostic odds ratios (DOR) were 5.1 (95% CI: 3.1, 8.5), 0.49 (95% CI: 0.39, 0.63), and 10 (95% CI: 6, 17), respectively. The summary receiver operating characteristic graph (SROC) with an area under the curve (AUC) of 0.80 (95% CI: 0.76, 0.83) was constructed which indicated favorable diagnostic accuracy for PCa. Results of the subgroup analysis and metaregression analysis reminded “ethnicity” and “methylation” might be sources of heterogeneity. The potential publication bias was not found using Deek’s funnel plot asymmetry test ( p > 0 . 05). Conclusions . Our meta-analysis illustrated that the cfDNA could undertake a promising role in the PCa diagnosis.
Products of two proportional primes

In RSA cryptography numbers of the form $pq$, with $p$ and $q$ two distinct proportional primes play an important role. For a fixed real number $r>1$ we formalize this by saying that an integer $pq$ is an RSA-integer if $p$ and $q$ are primes satisfying $p<q\le rp$. Recently Dummit, Granville and Kisilevsky showed that substantially more than a quarter of the odd integers of the form $pq$ up to $x$, with $p, q$ both prime, satisfy $p\equiv q\equiv 3\pmod{4}$. In this paper we investigate this phenomenon for RSA-integers. We establish an analogue of a strong form of the prime number theorem with the logarithmic integral replaced by a variant. From this we derive an asymptotic formula for the number of RSA-integers $\le x$ which is much more precise than an earlier one derived by Decker and Moree in 2008.
A New Image Affine-Invariant Region Detector and Descriptor

To solve the problems that exist in present affine-invariant region detection and description methods, a new affine-invariant region detector and descriptor are proposed in this paper. First, affine-invariant regions in an image are detected using a connected-region based method. And then a vector composed of a group of affine invariant moments is adopted to descript the regions. Experiments show the effectiveness and robustness of the method. It is also very fast.
Sobolev–Lorentz capacity and its regularity in the Euclidean setting

This paper studies the Sobolev-Lorentz capacity and its regularity in the Euclidean setting for $n \ge 1$ integer. We extend here our previous results on the Sobolev-Lorentz capacity obtained for $n \ge 2. $ Moreover, for $n \ge 2$ integer we obtain a few new results concerning the $n,1$ relative and global capacities. We obtain sharp estimates for the $n,1$ relative capacity of the concentric condensers $(\overline{B}(0,r), B(0,1))$ for all $r$ in $[0,1). $ As a consequence we obtain the exact value of the $n,1$ capacity of a point relative to all its bounded open neighborhoods from ${\mathbf{R}}^n$ when $n \ge 2. $ We also show that this aforementioned constant is the value of the $n,1$ global capacity of any point from ${\mathbf{R}}^n,$ where $n \ge 2$ is integer. This allows us to give a new proof of the embedding $H_{0}^{1,(n,1)}(\Omega) \hookrightarrow C(\overline{\Omega}) \cap L^{\infty}(\Omega),$ where $\Omega \subset {\mathbf{R}}^n$ is open and $n \ge 2$ is an integer. In the penultimate section of our paper we prove a new weak convergence result for bounded sequences in the non-reflexive spaces $H^{1,(p,1)}(\Omega)$ and $H_{0}^{1,(p,1)}(\Omega). $ The weak convergence result concerning the spaces $H^{1,(p,1)}(\Omega)$ is valid whenever $1<p<\infty,$ while the weak convergence result concerning the spaces $H_{0}^{1,(p,1)}(\Omega)$ is valid whenever $1 \le n<p<\infty$ or $1<n=p<\infty. $ As a consequence of the weak convergence result concerning the spaces $H_{0}^{1,(p,1)}(\Omega),$ in the last section of our paper we show that the relative and the global $(p,1)$ and $p,1$ capacities are Choquet whenever $1 \le n<p<\infty$ or $1<n=p<\infty. $
Optical coherence tomography in the diagnosis of myocardial infarction with non-obstructive coronary arteries

Myocardial infarction with non-obstructive coronary arteries (MINOCA) is a working diagnosis and requires identification of the underlying causes to optimize treatment, improve prognosis, and prevent the recurrence of myocardial infarction. According to the literature, the prognosis of patients diagnosed with MINOCA is comparable to the group of patients with myocardial infarction (MI) and significant stenosis of the coronary arteries. Intracoronary imaging is a crucial diagnostic tool used in identifying epicardial causes of MINOCA that are not visible in coronary angiography. Optical coherence tomography (OCT) provides the highest spatial resolution, simultaneously allowing detailed visualization of plaque pathology in individuals with MINOCA and identifying the cause of MI in up to 80% of patients. Common causes of a MINOCA may include plaque disruption, spontaneous coronary artery dissection (SCAD), coronary artery spasm, and coronary thromboembolism. The optimization of pharmacological treatment in this group of patients, especially dual antiplatelet therapy and statins, improves the prognosis. Data on the indications for invasive treatment of patients with MINOCA based on OCT findings are insufficient. There is a strong need for research comparing treatment strategies, especially in high-risk lesions visualized in OCT. The main aim of this review is to demonstrate the usefulness of OCT in determining the mechanism of MINOCA.
An Algorithm for Total Variation Inpainting Based on Nonlinear Multi-Grid Methods

Image inpainting refers to restoring a damaged image with missing information. The total variation (TV) inpainting model is one such method that simultaneously fills in the regions with available information from their surroundings and eliminates noises. The method works well with small narrow inpainting domains. However there remains an urgent need to develop fast iterative solvers, as the underlying problem sizes are large. In addition one needs to tackle the imbalance of results between inpainting and denoising. When the inpainting regions are thick and large, the procedure of inpainting works quite slowly and usually requires a significant number of iterations and leads inevitably to oversmoothing in the outside of the inpainting domain. To overcome these difficulties, we propose a solution for TV inpainting method based on the nonlinear multi-grid algorithm.
Hydrodynamic coefficients and forces on multihulls in shallow water with constant or variable depth

Abstract Numerical and hydro dynamical procedures are developed to compute bidimensional hydrodynamic coefficients and forces on multihulls associated with harmonic oscillations in shallow water with constant or variable depth. The forces are composed of two parts and include the sum of incident and diffracted forces and hydrodynamic reaction. The latter one is used to determinate the hydrodynamic coefficients (added mass and damping). The numerical method used is the Boundary Element Method. We can compute flow around multihulls sections. An application to cylindrical, right triangular and rectangular hull forms is presented.
The Representation, Recognition, and Locating of 3-D Objects

The problem of recognizing and locating rigid objects in 3-D space is important for applications of robotics and naviga tion. We analyze the task requirements in terms of what information needs to be represented, how to represent it, what kind of paradigms can be used to process it, and how to implement the paradigms. We describe shape surfaces by curves and patches, which we represent by linear primitives, such as points, lines, and planes. Next we describe algo rithms to construct this representation from range data. We then propose the paradigm of recognizing objects while locat ing them. We analyze the basic constraint of rigidity that can be exploited, which we implement as a prediction and verifi cation scheme that makes efficient use of the representation. Results are presented for data obtained from a laser range finder, but both the shape representation and the matching algorithm are general and can be used for other types of data, such as ultrasound, stereo, and tactile.
Bimodules over $\mathop {\rm VN}\nolimits (G)$, harmonic operators and the non-commutative Poisson boundary

Starting with a left ideal $J$ of $L^1(G)$ we consider its annihilator $J^{\perp}$ in $L^{\infty}(G)$ and the generated ${\rm VN}(G)$-bimodule in $\mathcal{B}(L^2(G))$, ${\rm Bim}(J^{\perp})$. We prove that ${\rm Bim}(J^{\perp})=({\rm Ran }J)^{\perp}$ when $G$ is discrete, compact or abelian, where ${\rm Ran }J$ is a suitable saturation of $J$ in the trace class. We define jointly harmonic functions and jointly harmonic operators and show that, for these classes of groups, the space of jointly harmonic operators is the ${\rm VN}(G)$-bimodule generated by the space of jointly harmonic functions. Using this, we give a proof of the following result of Izumi and Jaworski - Neufang: the non-commutative Poisson boundary is isomorphic to the crossed product of the space of harmonic functions by $G$.
The cavity method for counting spanning subgraphs subject to local constraints

Using the theory of negative association for measures and the notion of random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically tree-like graphs. Specifically, the corresponding free entropy density is shown to converge along any sequence of graphs whose random weak limit is a tree, and the limit is directly expressed in terms of the unique solution to a limiting cavity equation. On a Galton-Watson tree, the latter simplifies into a recursive distributional equation which can be solved explicitely. As an illustration, we provide an explicit-limit formula for the $b-$matching number of an Erd\H{o}s-Renyi random graph with fixed average degree and diverging size, for any $b\in\mathbb N$.
Some memories of the Dover Heights field station, 1946–1954

The author describes the first eight years of his astronomical career. His collaboration with John Bolton, Gordon Stanley, Kevin West fold and Dick McGee at the Dover Heights field station resulted in the detection and optical identification of the first radio sources outside the solar system. The first radio spectra, angular sizes and source variability measurements were made during this interval.
Poisson structures for two nonholonomic systems with partially reduced symmetries

We consider nonholonomic systems which symmetry groups consist of two subgroups one of which represents rotations about the axis of symmetry. After nonholonomic reduction by another subgroup the corresponding vector fields on partially reduced phase space are linear combinations of the Hamiltonian and symmetry vector fields. The reduction of the Poisson bivectors associated with the Hamiltonian vector fields to canonical form is discussed.
Type Theory and Universal Grammar

The paper takes a look at the history of the idea of universal grammar and compares it with multilingual grammars, as formalized in the Grammatical Framework, GF. The constructivist idea of formalizing math­ematics piece by piece, in a weak logical framework, rather than trying to reduce everything to one single strong theory, is the model that guides the development of grammars in GF.
Preoperative Biologics Exposure Predisposes Ulcerative Colitis Patients to a Distinct Delayed Postoperative Ileus Syndrome After Colectomy

Background Postoperative ileus (POI) remains the most common complication after colectomy for inflammatory bowel disease (IBD). Delayed POI (DPOI) can develop late (>14 days) after colectomy in clinical settings, with unknown etiology. The aim of this study was to address a novel entity of POI after colectomy for ulcerative colitis (UC). Material/Methods The data of 263 UC patients who underwent colectomy from Jan 1, 2013 to May 31, 2021 were collected. DPOI was defined as POI occurring on or after postoperative day (POD) 14 with apparent resolution from obligatory POI. Univariate and multivariate analysis were conducted to identify the risk factors for DPOI. Results The rate of canonical prolonged POI and DPOI were 11.7% (31/263) and 9.9% (26/263), respectively. The pathophysiological process of DPOI demonstrated an ileus-dysbiosis-recovery triad. Two DPOI cases were diagnosed with UC-related severe enteritis and underwent re-laparotomy. Multivariate analysis showed preoperative biologics exposure was an independent risk factor for DPOI (OR 3.100 95% CI 1.261–7.619, P=0.018) and the number of biologics session/course moderately predicted the occurrence of DPOI (AUC=0.639, 95% CI=0.578–0.697, P=0.0129). Conclusions A distinct pattern of ileus was identified in a tertiary IBD center. Clarification of this syndrome complemented the spectrum of post-IPAA complications and offered experience to treat this condition.
A Method to Calculate Conserved Currents and Fermionic Force for the Lanczos Approximation to the Overlap Dirac Operator

The overlap Dirac operator obeys the Ginsparg-Wilson equation and offers a possibility to introduce chiral symmetry on the lattice. Evaluating the overlap operator is numerically very expensive and one has to rely on approximation methods. At finite chemical potential the overlap operator can be efficiently computed with the two-sided Lanczos algorithm. To calculate conserved currents on the lattice, or to evaluate the fermionic force in HMC calculations, one needs to compute derivatives of the Dirac operator with respect to gauge fields. In this paper we present a method to simultaneously compute the action of the overlap operator and its derivative on a source vector.
Optical bistable behavior involving photonic crystals nonlinear cavity

We present an analytical model and numerical experiments to describe optimal bistable switching involving photonic crystals nonlinear cavity. The involving photonic crystals nonlinear cavity is particularly suitable for large-scale all-optical integration. It is interesting to show that the refractive index of the system can be altered by the incident intensity when the incident frequency is tuned to the evanescent mode and the cavity contains a nonlinear Kerr medium. The response of this system to high-intensity incident waves is studied in detail. A cavity host a localized mode at 1.55 um with a Q of 4000 and a mode volume of 0.055 um3, we predict the onset of bistable reflection at incident powers of ~40 mW. The downstream reflections lead to hysteresis loops in the reflectivity that are topologically distinct from conventional Lorentzian-derived loops characteristic of isolated Fabry-Perot cavities. We provide a stability argument that reveals the unstable branches of these unique hysteresis loops, and we illustrate some of the rich bistable behaviors that can be engineered with such downstream sources, this fact may be used to obtain more flexibility in designing nonlinear devices.
Reflection and transmission of gravity waves at non-uniform stratification layers

The present study focuses on the interaction of gravity waves in the atmosphere with the tropopause. As the vertical extent of the latter is small compared to the density scale height, wave propagation is described by the Taylor-Goldstein equation as derived from the linearised Boussinesq approximation. Of particular interest in the construction of gravity wave parameterisations for the upper atmosphere are the transmission and reflection properties of the tropopause as these determine the upward fluxes of energy and momentum carried by internal waves. A method is presented that decomposes internal waves explicitly into upward and downward propagating contributions, thus giving direct access to transmission and reflection coefficients of finite regions of non-uniform stratification in a stationary atmosphere. The scheme utilizes a piecewise constant approximation for the background stratification and matches up- and downward propagating plane wave solutions in each layer through physically meaningful coupling conditions. As a result, transmission and reflection coefficients follow immediately.
THE AKNS HIERARCHY REVISITED: A VERTEX OPERATOR APPROACH AND ITS LIE-ALGEBRAIC STRUCTURE

A novel approach — based upon vertex operator representation — is devised to study the AKNS hierarchy. It is shown that this method reveals the remarkable properties of the AKNS hierarchy in relatively simple, rather natural and particularly effective ways. In addition, the connection of this vertex operator based approach with Lie-algebraic integrability schemes is analyzed and its relationship with τ-function representations is briefly discussed.