Miracle-dz/UniFAR-FTUs huggingface dataset:
Goal oriented adaptivity in the IRGNM for parameter identification in PDEs: II. all-at-once formulations

In this paper we investigate adaptive discretization of the iteratively regularized Gauss–Newton method IRGNM. All-at-once formulations considering the PDE and the measurement equation simultaneously allow to avoid (approximate) solution of a potentially nonlinear PDE in each Newton step as compared to the reduced form Kaltenbacher et al (2014 Inverse Problems 30 045001). We analyze a least squares and a generalized Gauss–Newton formulation and in both cases prove convergence and convergence rates with a posteriori choice of the regularization parameters in each Newton step and of the stopping index under certain accuracy requirements on four quantities of interest. Estimation of the error in these quantities by means of a weighted dual residual method is discussed, which leads to an algorithm for adaptive mesh refinement. Numerical experiments with an implementation of this algorithm show the numerical efficiency of this approach, which especially for strongly nonlinear PDEs outperforms the nonlinear Tikhonov regularization considered in Kaltenbacher et al (2011 Inverse Problems 27 125008).
Application of the white rot fungus Phanerochaete chrysosporium in biotreatment of craft pulping effluent.

One of the major problems of pollution control is scientific research, especially in the paper industry. The type of contamination resulting from industrial wastewater unsuitable and its very important for scientific background for researchers. Paper industries consume large volume of water, which usually contains a number of contaminants such as halogenated organic substances, lignin, etc. Biotechnology approach in the treatment of pollution sources is effective economically and environmentally. White fungus is one of the organisms that is given much attention. In the recent decades due to the inherent ability of the degradation of lignin in woody plants polymeric structures. This has received a good option for treatment of wastewater of paper industry. Fungus Phanerochaete Chrysosporium is a model of the lignin biodegradation studies and other biological materials for the development of enzyme production lignetic because it can produce a large collection of lignetic enzymes (manganese peroxides, lignin peroxides, lignin peroxides, laccase) can generate more than other species of fungi. This study aimed to investigate the impact of these fungi in the biological treatment of wastewater from paper and pulp industries; including waste reduction parameters: biochemical oxygen demand (BOD), chemical oxygen demand (COD), total suspended solids (TSS), total dissolved solids (TDS), turbidity and tree different pHs (pH 5, 6 and 7) at a temperature of 30°C. Results indicate 50% reduction of BOD, COD in the first three days of the test. Maximum reduction of wastewater parameters on the sixth day and occurred at pH6 and then fell on the ninth day of the test. This could be due to a lack of nutrients in the culture medium. Result in a temperature of 30° in pH6 after six days in 400 mg/l weight you can achieve optimal conditions for the purification. The results were 93%, 94%, 88%, 70%, and 83% respectively for BOD, COD, TSS, TDS and Turbidity. This method of wastewater treatment for pulp and paper industry is advisable. You can improve results and increase the efficiency of wastewater treatment fungi culture conditions by adding nutrients also examine the best conditions for growing white rot fungi upgraded.
Dextrous hand grasping force optimization

A key goal in dextrous robotic hand grasping is to balance external forces and at the same time achieve grasp stability and minimum grasping energy by choosing an appropriate set of internal grasping forces. Since it appears that there is no direct algebraic optimization approach, a recursive optimization, which is adaptive for application in a dynamic environment, is required. One key observation in this paper is that friction force limit constraints and force balancing constraints are equivalent to the positive definiteness of a certain matrix subject to linear constraints. Based on this observation, we formulate the task of grasping force optimization as an optimization problem on the smooth manifold of linearly constrained positive definite matrices for which there are known globally exponentially convergent solutions via gradient flows. There are a number of versions depending on the Riemannian metric chosen, each with its advantages, Schemes involving second derivative information for quadratic convergence are also studied. Several forms of constrained gradient flows are developed for point contact and soft-finger contact friction models. The physical meaning of the cost index used for the gradient flows is discussed in the context of grasping force optimization. A discretized version for real-time applicability is presented. Numerical examples demonstrate the simplicity, the good numerical properties, and optimality of the approach.
Geometric Baum-Connes assembly map for twisted Differentiable Stacks

We construct the geometric Baum-Connes assembly map for twisted Lie groupoids, that means for Lie groupoids together with a given groupoid equivariant $PU(H)-$principle bundle. The construction is based on the use of geometric deformation groupoids, these objects allow in particular to give a geometric construction of the associated pushforward maps and to establish the functoriality. The main results in this paper are to define the geometric twisted K-homology groups and to construct the assembly map. Even in the untwisted case the fact that the geometric twisted K-homology groups and the geometric assembly map are well defined for Lie groupoids is new, as it was only sketched by Connes in his book for general Lie groupoids without any restrictive hypothesis, in particular for non Hausdorff Lie groupoids. We also prove the Morita invariance of the assembly map, giving thus a precise meaning to the geometric assembly map for twisted differentiable stacks. We discuss the relation of the assembly map with the associated assembly map of the $S^1$-central extension. The relation with the analytic assembly map is treated, as well as some cases in which we have an isomorphism. One important tool is the twisted Thom isomorphism in the groupoid equivariant case which we establish in the appendix.
The internal magnetic field structures and current density profiles in the Helicity Injected Spherical Torus plasma driven by coaxial helicity injection

In the Helicity Injected Spherical Torus device [Nagata et al., Proceedings of the 17th International Atomic Energy Agency Fusion Energy Conference, Yokohama, 1998 (International Atomic Energy Agency, Vienna, 1998) CD-ROM, EXP4/10], internal magnetic field and current density structures of spherical torus (ST) plasmas sustained by coaxial helicity injection (CHI) have been revealed via intensive internal magnetic measurements. The internal magnetic configuration of the ST plasma formed by CHI is in good agreement with the results of numerical equilibrium fitting calculations. The generation of closed poloidal flux of ST has been verified by varying the external toroidal field strength in the same device. Interestingly, the transition of the current profile from hollow to peaked has been observed during the sustainment phase, which could be explained by inductive effects of currents on open field lines winding the central conductor.
Infinitely many positive solutions of nonlinear Schr\"{o}dinger equations with non-symmetric potentials

We consider the standing-wave problem for a nonlinear Schr\"{o}dinger equation, corresponding to the semilinear elliptic problem \begin{equation*} -\Delta u+V(x)u=|u|^{p-1}u,\ u\in H^1(\mathbb{R}^2), \end{equation*} where $V(x)$ is a uniformly positive potential and $p>1$. Assuming that \begin{equation*} V(x)=V_\infty+\frac{a}{|x|^m}+O\Big(\frac{1}{|x|^{m+\sigma}}\Big),\ \text{as}\ |x|\rightarrow+\infty, %\tag{$V2$} \end{equation*} for instance if $p>2$, $m>2$ and $\sigma>1$ we prove the existence of infinitely many positive solutions. If $V(x)$ is radially symmetric, this result was proved in \cite{WY-10}. The proof without symmetries is much more difficult, and for that we develop a new {\em intermediate Lyapunov-Schmidt reduction method}, which is a compromise between the finite and infinite dimensional versions of it.
Asymptotic Distributions of Impulse Response Functions and Forecast Error Variance Decompositions of Vector Autoregressive Models

In recent years, vector autoregressive models have become standard tools for economic analyses. Impulse response functions and forecast error variance decompositions are usually computed from these models in order to investigate the interrelationships within the system. However, sometimes no measures of estimation uncertainty are provided by authors. One reason may be that the relevant asymptotic distribution theory is distributed over various publications. In this article, the available results are summarized and the missing links are provided in order to facilitate the computation of standard errors and test statistics. Copyright 1990 by MIT Press.
Wedge Operations and Torus Symmetries II

Abstract A fundamental idea in toric topology is that classes of manifolds with well-behaved torus actions (simply, toric spaces) are classified by pairs of simplicial complexes and (non-singular) characteristic maps. In a previous paper, the authors provided a new way to find all characteristic maps on a simplicial complex $K(J)$ obtainable by a sequence of wedgings from $K$ . The main idea was that characteristic maps on $K$ theoretically determine all possible characteristic maps on a wedge of $K$ . We further develop our previous work for classification of toric spaces. For a star-shaped simplicial sphere $K$ of dimension $n-1$ with $m$ vertices, the Picard number Pic $(K)$ of $K$ is $m-n$ . We call $K$ a seed if $K$ cannot be obtained by wedgings. First, we show that for a fixed positive integer $\ell $ , there are at most finitely many seeds of Picard number $\ell $ supporting characteristic maps. As a corollary, the conjecture proposed by V. V. Batyrev in is solved affirmatively. Secondly, we investigate a systematicmethod to find all characteristic maps on $K(J)$ using combinatorial objects called (realizable) puzzles that only depend on a seed $K$ . These two facts lead to a practical way to classify the toric spaces of fixed Picard number.
ADAMANT: A Query Executor with Plug-In Interfaces for Easy Co-processor Integration

Today’s processor landscape is increasingly heterogeneous with the availability of co-processors. This landscape impacts query engines, as they need to be reworked to keep competitive performance by leveraging the underlying architectures. Such a rework might be costly if, for each external processor or SDK, peripheral components needed to be developed as well; resulting in redundant effort and adoption difficulties. In this paper, we propose an approach to overcome these shortcomings through ADAMANT – a query executor equipped with interfaces to plug-in new co-processors without reworking other components of a query engine. ADAMANT consists of 1) pluggable interfaces that allow interaction with co-processors, encapsulating operator implementations, and 2) a unified runtime that handles the execution on arbitrary co-processors, with a chunked execution model for scalable query processing. To evaluate ADAMANT’s versatility, we plug different implementations of a CPU/GPU-based system (using OpenCL, OpenMP, & CUDA) and analyze their performance on TPC-H queries. We identify a 4x performance difference between an arbitrary chunked execution vs. a more architecturally conscious pipelined execution. Furthermore, our comparisons with HeavyDB show complex performance variations from speed-ups up to a factor of 2x from our hardware-conscious execution. We envision initiatives like ADAMANT to ease the study of complex optimizations required in co-processor systems, paving the way for efficient and portable data management tools without cutbacks.
Wild Lorenz like attractors

We give the first examples of flows which exhibit robust singular attractors containing a wild hyperbolic set (in the sense of Newhouse). A hyperbolic set is said to be wild, if it has tangencies between its stable and unstable manifolds, in a robust way. The only restriction on the ambient manifold is that its dimension should be at least 5.
Wright-Fisher diffusions for evolutionary games with death-birth updating

We investigate spatial evolutionary games with death-birth updating in large finite populations. Within growing spatial structures subject to appropriate conditions, the density processes of a fixed type are proven to converge to the Wright-Fisher diffusions with drift. In addition, convergence in the Wasserstein distance of the laws of their occupation measures holds. The proofs of these results develop along an equivalence between the laws of the evolutionary games and certain voter models and rely on the analogous results of voter models on large finite sets by convergences of the Radon-Nikodym derivative processes. As another application of this equivalence of laws, we show that in a general, large population of size $N$, for which the stationary probabilities of the corresponding voting kernel are comparable to uniform probabilities, a first-derivative test among the major methods for these evolutionary games is applicable at least up to weak selection strengths in the usual biological sense (that is, selection strengths of the order $\mathcal O(1/N)$).
Interaction between separate spatial soliton pairs in a biased serial photovoltaic photorefractive crystal circuit and its application

Theoretical model of two laser beams propagating in a biased serial photovoltaic photorefractive crystal circuit is first developed and the forming conditions of three different kinds of separate spatial soliton pairs are discussed. Studies on the interaction between two solitons in one soliton pair show that only the dark soliton can affect the other, whereas the bright one cannot. The asymmetry comes from our results determined under the limit of the spatial extent of the optical beam being much less than the width of the crystal. Finally, potential application of this unilateral effect is discussed.
Porosity of the branch set of discrete open mappings with controlled linear dilatation

Assume that $X$ and $Y$ are locally compact and locally doubling metric spaces, which are also generalized $n$-manifolds, that $X$ is locally linearly locally $n$-connected, and that $Y$ has bounded turning. In this paper, addressing Heinonen's ICM 02 talk, we study the geometry of the branch set $\mathcal{B}_f$ of a quasiregular mapping between metric $n$-manifolds. In particular, we show that $\mathcal{B}_f\cap \{x\in X:H_f(x)<\infty\}$ is countably porous, as is its image $f\big(\mathcal{B}_f\cap \{x\in X:H_f(x)<\infty\}\big)$. As a corollary, $\mathcal{B}_f\cap \{x\in X:H_f(x)<\infty\}$ and its image are null sets with respect to any locally doubling measures on $X$ and Y, respectively. Moreover, if either $H_f(x)\leq H$ or $H_f^*(x)\leq H^*$ for all $x\in X$, then both $\mathcal{B}_f$ and $f\big(\mathcal{B}_f\big)$ are countably $\delta$-porous, quantitatively, with a computable porosity constant. When further metric and analytic assumptions are placed on $X$, $Y$, and $f$, our theorems generalize the well-known Bonk--Heinonen theorem and Sarvas' theorem to a large class of metric spaces. Moreover, our results are optimal in terms of the underlying geometric structures. As a direct application, we obtain the important V\"ais\"al\"a's inequality in greatest generality. Applying our main results to special cases, we solve an open problem of Heinonen--Rickman and an open question of Heinonen--Semmes.
Integrated glass lenses fabrication for parallel interferometric inspection systems of MEMS and MOEMS

We present the application of glass microlenses for the fabrication of inspection systems based on interferometric measurements. The microlenses are molded from wet etched silicon by using microfabrication techniques. The concerned system requires lenses to be used in a Mirau interferometer configuration. The principle of the system is presented, as well as different choices of lenses to be integrated. The use of glass microlenses monolithically molded on a substrate is proven as the proper technology to be used in the system.
Transport phenomena in kaolinite clay: Molecular simulation, homogenization analysis and similitude law

Kaolinite is a common clay mineral. It is a nanomaterial with a platelet crystalline structure. In order to analyze the behavior of kaolinite, its microscopic structure and material properties must be specified correctly. A molecular dynamics (MD) simulation is used for determining the microscale properties of hydrated kaolinite, and these properties are introduced into a multiscale homogenization analysis (HA). We previously developed such an MD/HA technique to investigate seepage, diffusion, sorption and consolidation in bentonite clay (Proceedings of the Science Basis for Nuclear Waste Management, Davos, Switzerland, vol. XXI. Material Research Society: Warrendale, PA, 1997; 359–366; Eng. Geol. 1999; 54:21–31; Eng. Geol. 2001; 60:127–138; Coupled Thermo‐Hydro‐Mechanical‐Chemical Processes in Geo‐systems. Elsevier: Amsterdam, 2005; 457–464). We here apply the method to kaolinite clay to investigate the permeability, diffusion and related similitude law. The obtained results are supported by existing experimental data. Copyright © 2008 John Wiley & Sons, Ltd.
Corks, exotic 4-manifolds and knot concordance

We show that, for each integer n, there exist infinitely many pairs of n-framed knots representing homeomorphic but non-diffeomorphic (Stein) 4-manifolds, which are the simplest possible exotic 4-manifolds regarding handlebody structures. To produce these examples, we introduce a new description of cork twists and utilize satellite maps. As an application, we produce knots with the same 0-surgery which are not concordant for any orientations, disproving the Akbulut-Kirby conjecture given in 1978.
Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces

In this paper, the problem of the order of approximation for the multivariate sampling Kantorovich operators is studied. The cases of the uniform approximation for uniformly continuous and bounded functions/signals belonging to Lipschitz classes and the case of the modular approximation for functions in Orlicz spaces are considered. In the latter context, Lipschitz classes of Zygmund-type which take into account of the modular functional involved are introduced. Applications to Lp(R^n), interpolation and exponential spaces can be deduced from the general theory formulated in the setting of Orlicz spaces. The special cases of multivariate sampling Kantorovich operators based on kernels of the product type and constructed by means of Fejer's and B-spline kernels have been studied in details.
Topological qubit design and leakage

We examine how best to design qubits for use in topological quantum computation. These qubits are topological Hilbert spaces associated with small groups of anyons. Operations are performed on these by exchanging the anyons. One might argue that in order to have as many simple single-qubit operations as possible, the number of anyons per group should be maximized. However, we show that there is a maximal number of particles per qubit, namely 4, and more generally a maximal number of particles for qudits of dimension d. We also look at the possibility of having topological qubits for which one can perform two-qubit gates without leakage into non-computational states. It turns out that the requirement that all two-qubit gates are leakage free is very restrictive and this property can only be realized for two-qubit systems related to Ising-like anyon models, which do not allow for universal quantum computation by braiding. Our results follow directly from the representation theory of braid groups, which implies that they are valid for all anyon models. We also make some remarks about generalizations to other exchange groups.
Sheath structure around particles in low-pressure discharges

Collisionless orbit theory is used to model isolated particles in low‐pressure discharges with and without the presence of negative ions. The key results are as follows: (1) Debye–Huckel theory works well for approximating the potential profile around the particle, and (2) the size of the sheath around the particle is determined by a Debye length that results from linearizing the Poisson–Vlasov equation. These results are valid as long as the ratio of particle radius to Debye length is small and the ratio of Debye length to mean free path is small.
Inferring three-dimensional shapes from two-dimensional silhouettes

Although an infinity of three-dimensional (3-D) objects could generate any given silhouette, we usually infer only one 3-D object from its two-dimensional (2-D) projection. What are the constraints that restrict this infinity of choices? We identify three mathematical properties of smooth surfaces plus one simple viewing constraint that seem to drive our preferred interpretation of 3-D shape from 2-D contour. The constraint is an extension of the notion of general position. Taken together, our interpretation rules predict that “dents” in a 3-D surface should never be inferred from a smooth 2-D silhouette.
A convergence criterion for the solutions of nonlinear difference equations and dynamical systems

Abstract We show that the solutions of nonlinear higher order difference equations may have convergent subsequences, even when the solution as a whole does not converge, if the defining function sequence is suitably bounded near the origin. The delay size and pattern in the higher order equation play an essential role in determining which subsequences of its solutions converge. We then show that this method can be extended to planar systems and discuss applications to discrete dynamical systems that have been used in biological population models.
Equivariant Motivic Homotopy Theory

In this paper we study a model structure on a category of schemes with a group action and the resulting unstable and stable equivariant motivic homotopy theories. The new model structure introduced here samples a comparison to the one by Voevodsky and Hu-Kriz-Ormsby. We show that it allows to detect equivariant motivic weak equivalences on fixed points and how this property leads to a topologically convenient behavior of stable equivalences. We also prove a negative result concerning descent for equivariant algebraic K-theory.
$L^p(\Omega)$-Difference of One-Dimensional Stochastic Differential Equations with Discontinuous Drift

We consider a one-dimensional stochastic differential equations (SDE) with irregular coefficients. The purpose of this paper is to estimate the $L^p(\Omega)$-difference of SDEs using the norm of the difference of coefficients, where the discontinuous drift coefficient satisfies a one-sided Lipschitz condition and the diffusion coefficient is bounded, uniformly elliptic and H\"older continuous. As an application, we consider the stability problem.
On the effective cone of $\mathbb{P}^n$ blown-up at $n+3$ points

We compute the facets of the effective and movable cones of divisors on the blow-up of $\mathbb{P}^n$ at $n+3$ points in general position. Given any linear system of hypersurfaces of $\mathbb{P}^n$ based at $n+3$ multiple points in general position, we prove that the secant varieties to the rational normal curve of degree $n$ passing through the points, as well as their joins with linear subspaces spanned by some of the points, are cycles of the base locus and we compute their multiplicity. We conjecture that a linear system with $n+3$ points is linearly special only if it contains such subvarieties in the base locus and we give a new formula for the expected dimension.