Miracle-dz/UniFAR-FTUs huggingface dataset:
Weak Convergence Methods for Approximation of Path-dependent Functionals

This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient condition for the convergence of the path-dependent functional underlying weak convergent processes to the functional of the original process. In the second part, we study the weak convergence of Markov chain approximation to the underlying process when it is given by a solution of stochastic differential equation. Finally, we combine the results of the two parts to provide approximation of option pricing for discretely monitoring barrier option underlying stochastic volatility model. Different from the existing literatures, the weak convergence analysis is obtained by means of metric computations in the Skorohod topology together with the continuous mapping theorem. The advantage of this approach is that the functional under study may be a function of stopping times, projection of the underlying diffusion on a sequence of random times, or maximum/minimum of the underlying diffusion.
Fractionalized non-self-dual solutions in the CP N-1 model

We study non-self-dual classical solutions in the CP(N-1) model with Z_N twisted boundary conditions on the spatially compactified cylinder. These solutions have finite, and fractional, classical action and topological charge, and are `unstable' in the sense that the corresponding fluctuation operator has negative modes. We propose a physical interpretation of these solutions as saddle point configurations whose contributions to a resurgent semi-classical analysis of the quantum path integral are imaginary non-perturbative terms which must be cancelled by infrared renormalon terms generated in the perturbative sector.
Ultra-Wideband Millimeter-Wave Bidirectional Circularly Polarized Monopole Antenna Array Using a Sequentially Rotated Feeding Technique

In this communication, an ultrawideband millimeter-wave (mm-Wave) bidirectional circularly polarized (CP) monopole antenna array with sequential rotation feeding (SRF) technique is proposed. First, a broadband CP monopole antenna element is realized by utilizing the asymmetric ground plane, C-shaped ring, and rectangular stub structure. A microstrip to coplanar waveguide (CPW) transition structure is designed to feed the antenna element. Then, the SRF technique is adopted to further improve the axial ratio (AR) bandwidth of the 2 <inline-formula> <tex-math notation="LaTeX">$\times2$ </tex-math></inline-formula> CP subarray. Finally, a <inline-formula> <tex-math notation="LaTeX">$4\times4$ </tex-math></inline-formula> CP array is designed to further enhance the gain for mm-Wave applications. Measured results show that the proposed <inline-formula> <tex-math notation="LaTeX">$4\times4$ </tex-math></inline-formula> CP array exhibits the −10 dB impedance bandwidth of 102.7%, 3 dB AR bandwidths of 100.7%/101.3% in the <inline-formula> <tex-math notation="LaTeX">$+\textit {z}/-\textit {z}$ </tex-math></inline-formula>-direction, and the peak gain of 15.6 dBic.
A Good Data Augmentation Policy is not All You Need: A Multi-Task Learning Perspective

Data augmentation, which improves the diversity of datasets by applying image transformations, has become one of the most effective techniques in visual representation learning. Usually, the design of augmentation policies faces a diversity-difficulty trade-off. On the one hand, a simple augmentation leads to a low training set diversity, which can not improve model performance significantly. On the other hand, an excessively hard augmentation has an overlarge regularization effect which harms model performance. Recently, automatic augmentation methods have been proposed to address this issue by searching the optimal data augmentation policy from a predefined searching space. However, these methods still suffer from heavy searching overhead or complex optimization objectives. In this paper, instead of searching the optimal augmentation policy, we propose to break the diversity-difficulty trade-off from a multi-task learning perspective. By formulating model learning on the augmented images and the original images as the auxiliary task and the primary task in multi-task learning respectively, the hard augmentation does not directly influence the training of the primary branch and thus its negative influence can be alleviated. Hence, neural networks can learn valuable semantic information even with a totally random augmentation policy. Experimental results on ten datasets for four tasks demonstrate the superiority of our method over the other twelve methods. Codes have been released in https://github.com/ArchipLab-LinfengZhang/data-augmentation-multi-task.
Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue

In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.
Agglomeration in a preferential attachment random graph with edge-steps

In this paper we investigate geometric properties of graphs generated by a preferential attachment random graph model with edge-steps. More precisely, at each time $t\in\mathbb{N}$, with probability $p$ a new vertex is added to the graph (a vertex-step occurs) or with probability $1-p$ an edge connecting two existent vertices is added (an edge-step occurs). We prove that the global clustering coefficient decays as $t^{-\gamma(p)}$ for a positive function $\gamma$ of $p$. We also prove that the clique number of these graphs is, up to sub-polynomially small factors, of order~$t^{(1-p)/(2-p)}$.
Magnetorotational collapse of very massive stars to black holes in full general relativity

We perform axisymmetric simulations of the magnetorotational collapse of very massive stars in full general relativity. Our simulations are applicable to the collapse of supermassive stars with masses M > or approx. 10{sup 3}M{sub {center_dot}} and to very massive Population III stars. We model our initial configurations by n=3 polytropes, uniformly rotating near the mass-shedding limit and at the onset of radial instability to collapse. The ratio of magnetic to rotational kinetic energy in these configurations is chosen to be small (1% and 10%). We find that such magnetic fields do not affect the initial collapse significantly. The core collapses to a black hole, after which black-hole excision is employed to continue the evolution long enough for the hole to reach a quasistationary state. We find that the black-hole mass is M{sub h}=0.95M and its spin parameter is J{sub h}/M{sub h}{sup 2}=0.7, with the remaining matter forming a torus around the black hole. The subsequent evolution of the torus depends on the strength of the magnetic field. We freeze the spacetime metric ('Cowling approximation') and continue to follow the evolution of the torus after the black hole has relaxed to quasistationary equilibrium. In the absence of magnetic fields, the torusmore » settles down following ejection of a small amount of matter due to shock heating. When magnetic fields are present, the field lines gradually collimate along the hole's rotation axis. MHD shocks and the magnetorotational instability generate MHD turbulence in the torus and stochastic accretion onto the central black hole. When the magnetic field is strong, a wind is generated in the torus, and the torus undergoes radial oscillations that drive episodic accretion onto the hole. These oscillations produce long-wavelength gravitational waves potentially detectable by the Laser Interferometer Space Antenna. The final state of the magnetorotational collapse always consists of a central black hole surrounded by a collimated magnetic field and a hot, thick accretion torus. This system is a viable candidate for the central engine of a long-soft gamma-ray burst. « less
Joint Design of SAR Waveform and Imaging Filters Based on Target Information Maximization

In this paper, a joint design of both transmit waveform and imaging filters for synthetic aperture radar (SAR) is proposed to improve its information acquisition capability. First, the mutual information between SAR image and target scattering characteristics is considered as the performance metric, and its equivalent analytical version is derived in the 2-D frequency domain. The design is formulated as an optimization problem with an energy condition and a similarity constraint. Then, to tackle the resultant non-convex problem, by referring to the Dinkelbach's method, an algorithm is derived to find the desired solution via a cyclic maximization procedure alternating between three subproblems. Based on minorization-maximization, a unified optimization method with an increasing penalty on constraint violation is proposed to solve all subproblems. Convergence of the developed algorithm is analytically proved. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed design.
A 5LCHB Inverter for PV Transformerless Applications With Reduced Leakage Ground Current

Transformerless inverters for photovoltaic systems are widely used as it features low cost, volume, and weight. Thus, in recent years, its study has been of great interest to the research community. In this paper a transformerless cascade multilevel inverter for photovoltaic applications with leakage ground current compensation capability is presented. The proposed solution involves a second-order LC output filter with a particular connection, which is referred to as the DC-link-tied LC output filter. This solution is aimed to deal with the leakage-ground current issue, regardless of the considered PWM strategy. The mathematical model of the system involving such a particular LC output passive filter configuration is presented, out of which, both the differential-mode and the common-mode models are obtained. These models are used to explain the leakage-ground current improvement of the proposed DC-link-tied LC output filter. This hardware solution is evaluated under different modulation schemes to contrast the converter output response and the leakage-ground current performance. Finally, simulation and experimental results are performed using a 1 kW academic prototype to assess the performance of the proposed DC-link-tied LC output filter used in a transformerless inverter application.
Role of RAS signaling in ovarian cancer

The RAS family of proteins is among the most frequently mutated genes in human malignancies. In ovarian cancer (OC), the most lethal gynecological malignancy, RAS, especially KRAS mutational status at codons 12, 13, and 61, ranges from 6–65% spanning different histo-types. Normally RAS regulates several signaling pathways involved in a myriad of cellular signaling cascades mediating numerous cellular processes like cell proliferation, differentiation, invasion, and death. Aberrant activation of RAS leads to uncontrolled induction of several downstream signaling pathways such as RAF-1/MAPK (mitogen-activated protein kinase), PI3K phosphoinositide-3 kinase (PI3K)/AKT, RalGEFs, Rac/Rho, BRAF (v-Raf murine sarcoma viral oncogene homolog B), MEK1 (mitogen-activated protein kinase kinase 1), ERK (extracellular signal-regulated kinase), PKB (protein kinase B) and PKC (protein kinase C) involved in cell proliferation as well as maintenance pathways thereby driving tumorigenesis and cancer cell propagation. KRAS mutation is also known to be a biomarker for poor outcome and chemoresistance in OC. As a malignancy with several histotypes showing varying histopathological characteristics, we focus on reviewing recent literature showcasing the involvement of oncogenic RAS in mediating carcinogenesis and chemoresistance in OC and its subtypes.
Boundary Value Problems in Lipschitz Domains for Equations with Drifts

In this work we establish solvability and uniqueness for the $D_2$ Dirichlet problem and the $R_2$ Regularity problem for second order elliptic operators $L=-{\rm div}(A\nabla\cdot)+b\nabla\cdot$ in bounded Lipschitz domains, where $b$ is bounded, as well as their adjoint operators $L^t=-{\rm div}(A^t\nabla\cdot)-{\rm div}(b\,\cdot)$. The methods that we use are estimates on harmonic measure, and the method of layer potentials. The nature of our techniques applied to $D_2$ for $L$ and $R_2$ for $L^t$ leads us to impose a specific size condition on ${\rm div}b$ in order to obtain solvability. On the other hand, we show that $R_2$ for $L$ and $D_2$ for $L^t$ are uniquely solvable, assuming only that $A$ is Lipschitz continuous (and not necessarily symmetric) and $b$ is bounded.
Necessities and luxuries in satisfying single lives

Despite the growing interest in single (unpartnered) individuals’ well-being, there is a lack of descriptive research providing a comprehensive understanding of what singles value in their lives. In this research, we adopted a budget allocation methodology to examine what domains are prioritized in single individuals’ construal of a satisfying single life. We recruited two samples of participants, one primarily consisting of singles from Europe and America (N = 851) and the other from Korea (N = 1012). Across the two samples, we found that singles gave high priority to being mentally and physically healthy and having good family relationships. Only when those essentials were accounted for did single individuals turn significant attention to other life domains such as having good friendships, available romantic connections, and sexual opportunities. These findings have implications for understanding single individuals’ life priorities and well-being and set the groundwork for further research on singlehood.
Off-Road Detection Analysis for Autonomous Ground Vehicles: A Review

When it comes to some essential abilities of autonomous ground vehicles (AGV), detection is one of them. In order to safely navigate through any known or unknown environment, AGV must be able to detect important elements on the path. Detection is applicable both on-road and off-road, but they are much different in each environment. The key elements of any environment that AGV must identify are the drivable pathway and whether there are any obstacles around it. Many works have been published focusing on different detection components in various ways. In this paper, a survey of the most recent advancements in AGV detection methods that are intended specifically for the off-road environment has been presented. For this, we divided the literature into three major groups: drivable ground and positive and negative obstacles. Each detection portion has been further divided into multiple categories based on the technology used, for example, single sensor-based, multiple sensor-based, and how the data has been analyzed. Furthermore, it has added critical findings in detection technology, challenges associated with detection and off-road environment, and possible future directions. Authors believe this work will help the reader in finding literature who are doing similar works.
The Expansion of each van der Waerden number $W(r, k)$ into Powers of $r$, when $r$ is the Number of Integer Colorings, determines a greatest lower Bound for all $k$ such that $W(r, k) < r^{k^{2}}$

Every positive integer greater than a positive integer $r$ can be written as an integer that is the sum of powers of $r$. Here we use this to prove the conjecture posed by Ronald Graham, B. Rothschild and Joel Spencer back in the nineteen nineties, that the van der Waerden number with $r$ colorings and with arithmetic progressions of $k$ terms, has a certain upper bound. Our proof does not need the application of double induction, constructive methods of proof or combinatorics, as applied to sets of integers that contain some van der Waerden number as an element. The proof instead derives from certain \emph{a priori} knowledge that is known about any positive integer when the integer is large. The mathematical methods we use are easily accessible by those whose field of specialization lies outside of combinatorial number theory, such as discrete mathematics, computational complexity, elementary number theory or analytic number theory.
Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces

We introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the later one provides a natural framework for developing a geometric version of small cancellation theory. Examples of such families naturally occur in groups acting on hyperbolic spaces including hyperbolic and relatively hyperbolic groups, mapping class groups, $Out(F_n)$, and the Cremona group. Other examples can be found among groups acting geometrically on $CAT(0)$ spaces, fundamental groups of graphs of groups, etc. We obtain a number of general results about rotating families and hyperbolically embedded subgroups; although our technique applies to a wide class of groups, it is capable of producing new results even for well-studied particular classes. For instance, we solve two open problems about mapping class groups, and obtain some results which are new even for relatively hyperbolic groups.
On the Sweep Map for k⃗-Dyck Paths

Garsia and Xin gave a linear algorithm for inverting the sweep map for Fuss rational Dyck paths in $D_{m,n}$ where $m=kn\pm 1$. They introduced an intermediate family $\mathcal{T}_n^k$ of certain standard Young tableaux. Then inverting the sweep map is done by a simple walking algorithm on a $T\in \mathcal{T}_n^k$. We find their idea naturally extends for $\mathbf{k}^\pm$-Dyck paths, and also for $\mathbf{k}$-Dyck paths (reducing to $k$-Dyck paths for the equal parameter case). The intermediate object becomes a similar type of tableau in $\mathcal{T}_\mathbf{k}$ of different column lengths. This approach is independent of the Thomas-Williams algorithm for inverting the general modular sweep map.
Feasibility of Insect Identification Based on Spectral Fringes Produced by Clear Wings

Due to the growing awareness that insects' diversity and populations are in decline, there is an increased need for monitoring insects. Entomological lidars and photonic sensors can monitor and remotely identify flying insects based on their backscattered signal in terms of oscillations-, polarization-, and spectral content. The backscattered light from insects is predominantly oscillatory and derives from the wings. This part of the signal is also more coherent and co-polarized than the light reflected from the insect's abdomen. Clear membranes can display soap-bubble colors due to thin-film interference, a feature that can be associated with the thickness of the wing. A hyperspectral camera can capture these wing interference patterns with hundreds of spectral bands and accurately identify the wing thickness. Here we investigate whether the spectral fringes can provide complementary information to aid remote species identification. We demonstrate that we can extract wing thickness and modulation depth information from spectral fringes of 87 species of common insect pollinators in Skåne, Sweden. The modulation depth of a fringe provides information related to insect wing thickness homogeneity, wrinkledness, or anti-reflectance features. Our results show that examined species display distinct modulation and wing thickness, and therefore such features can be used to improve the specificity of species identification of photonics sensors.
Online Glucose Analysis System With High Precision and Wide Detection Range for Fermentation Monitoring

Online glucose monitoring during the fermentation process is critical for evaluating the microbial metabolism state and reaction course, achieving precise process control for industrial efficiency enhancement. However, the fast, wide-range and highly accurate test technique always presents a challenge for state-of-the-art analytical instruments. In this work, we proposed an online glucose analysis system based on a homemade screen-printed enzymatic biosensor chip composed of Prussian blue (PB) nanocubes with a high sensitivity of 83.404 mA<inline-formula> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula>mM<inline-formula> <tex-math notation="LaTeX">$^{-1} \cdot $ </tex-math></inline-formula>cm<inline-formula> <tex-math notation="LaTeX">$^{-2}$ </tex-math></inline-formula>. To match the detection behavior of this chip, a specific signal conversion system was designed to realize the highly precise acquisition and treatment of nA-level currents by integrating hardware acquisition circuits and Kalman filtering algorithms. Focusing on the continuous change in glucose concentration during fermentation, an adaptive injection strategy for the sampling volume was proposed to achieve an ultrawide linear range from 1 to 180 g/L. The results show that the online analytical system exhibits excellent detection performance with high accuracy and low relative error of detection (< 2%) during the fermentation of sophorolipid and ethanol compared to high-performance liquid chromatography (HPLC) and commercial analyzers.
Effect of Heat–Moisture Treatment on the Physicochemical Properties, Structure, Morphology, and Starch Digestibility of Highland Barley (Hordeum vulgare L. var. nudum Hook. f) Flour

This study modified native highland barley (HB) flour by heat–moisture treatment (HMT) at different temperatures (90, 110, and 130 °C) and moisture contents (15%, 25%, and 35%). The effects of the treatment on the pasting, thermal, rheological, structural, and morphological properties of the native and HMT HB flour were evaluated. The results showed that HMT at 90 °C and 25% moisture content induced the highest pasting viscosity (3626–5147 cPa) and final viscosity (3734–5384 cPa). In all conditions HMT increased gelatinization temperature (To, 55.77–73.72 °C; Tp, 60.47–80.69 °C; Tc, 66.16–91.71 °C) but decreased gelatinization enthalpy (6.41–0.43 J/g) in the HMT HB flour compared with that in the native HB flour. The HB flour treated at 15% moisture content had a higher storage modulus and loss modulus than native HB flour, indicating that HMT (moisture content, 15%, 25%, and 35%) favored the strengthening of the HB flour gels. X-ray diffraction and Fourier-transform infrared spectroscopy results showed that HMT HB flour retained the characteristics of an A-type crystal structure with an increased orderly structure of starch, while the relative crystallinity could be increased from 28.52% to 41.32%. The aggregation of starch granules and the denaturation of proteins were observed after HMT, with additional breakage of the starch granule surface as the moisture content increased. HMT could increase the resistant starch content from 24.77% to 33.40%, but it also led to an increase in the rapidly digestible starch content to 85.30% with the increase in moisture content and heating temperature. These results might promote the application of HMT technology in modifying HB flour.