IA Scholar Query: A Second-Order Theory for NL.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgSat, 31 Dec 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Introduction: Things We Do Not Talk About
https://scholar.archive.org/work/6h23kk5b5nb7lewmahdh6go3q4
Jeffrey J Kripal, Wouter J. Hanegraaffwork_6h23kk5b5nb7lewmahdh6go3q4Sat, 31 Dec 2022 00:00:00 GMTUniqueness of Solutions to Nonlinear Schrödinger Equations from their Zeros
https://scholar.archive.org/work/xtomildlsngfvgylit7gshojgu
We show novel types of uniqueness and rigidity results for Schrödinger equations in either the nonlinear case or in the presence of a complex-valued potential. As our main result we obtain that the trivial solution u = 0 is the only solution for which the assumptions u(t = 0)| D = 0, u(t = T )| D = 0 hold, where D ⊂ R d are certain subsets of codimension one. In particular, D is discrete for dimension d = 1. Our main theorem can be seen as a nonlinear analogue of discrete Fourier uniqueness pairs such as the celebrated Radchenko-Viazovska formula in [21] , and the uniqueness result of the second author and M. Sousa for powers of integers [22] . As an additional application, we deduce rigidity results for solutions to some semilinear elliptic equations from their zeros.Christoph Kehle, João P.G. Ramoswork_xtomildlsngfvgylit7gshojguThu, 01 Dec 2022 00:00:00 GMTSimulating hyperbolic space on a circuit board
https://scholar.archive.org/work/l3szjt56tnclffwqvd7eazmkwa
The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space. Here we discuss and experimentally demonstrate that the spectral ordering of Laplacian eigenstates for hyperbolic (negatively curved) and flat two-dimensional spaces has a universally different structure. We use a lattice regularization of hyperbolic space in an electric-circuit network to measure the eigenstates of a 'hyperbolic drum', and in a time-resolved experiment we verify signal propagation along the curved geodesics. Our experiments showcase both a versatile platform to emulate hyperbolic lattices in tabletop experiments, and a set of methods to verify the effective hyperbolic metric in this and other platforms. The presented techniques can be utilized to explore novel aspects of both classical and quantum dynamics in negatively curved spaces, and to realise the emerging models of topological hyperbolic matter.Patrick M Lenggenhager, Alexander Stegmaier, Lavi K Upreti, Tobias Hofmann, Tobias Helbig, Achim Vollhardt, Martin Greiter, Ching Hua Lee, Stefan Imhof, Hauke Brand, Tobias Kießling, Igor Boettcher, Titus Neupert, Ronny Thomale, Tomáš Bzdušekwork_l3szjt56tnclffwqvd7eazmkwaThu, 01 Dec 2022 00:00:00 GMTTechnical Terms Used in General English Textbooks Across Disciplines
https://scholar.archive.org/work/fseuvec35natfowxscsbdq3af4
The study aimed to analyze lexical items underpinned in the textbooks used in the current teaching of ESP and GE. Using content analysis, a systematic evaluation of texts to examine nuances to bridge the gap between quantitative and qualitative data. This was such of importance, however, difficult to study due to issues of interest like in the study, frequency of lexical items in ESP, and GE textbooks. Results found 13,713 lexical items in Hospitality Management, 17,561 in Criminology, 4576 in Tourism, 7167 in Marine Engineering, and 512 in Information Technology. Furthermore, the overall percentage of ESP lexical items fell in Tier 2 (with multiple-meaning while the least was in Tier 3, specifically on context-specific vocabulary. It is the core of vocabulary learning to ensure English language teaching. It is its goal to help learners better understand language, allowing them to understand others as they want to express themselves as well. This applies not only in speaking but also in writing and reading. Wilkins (1972, p. 111-112) stated that without grammar very little understanding can be acquired and without vocabulary there can be no learning at all. Thus, even without good grammar, so long as you equipped with useful words and expression, one can still manage to communicate. Lewis (1993) argued that "lexis is the heart of language" and that it develops a better fluency and expression in English. He also added the significance to the learners of acquiring a more productive vocabulary knowledge, also, their eagerness to develop their own personal vocabulary strategies. Thus, a proposed bridge model program was recommended to highlight the study findings using the lexicons found from the different respective courses.Sammy Q. Dolbawork_fseuvec35natfowxscsbdq3af4Fri, 30 Sep 2022 00:00:00 GMTIntroduction ot Asteroseismology
https://scholar.archive.org/work/6k5o6g2urremhoi4y5lnqcu5bm
This lecture gives an introduction to theoretical asteroseismology. It is neither a review nor is exhaustive. It attends to give to Master and PhD students an idea on why we are able to interpret asteroseismic observations in terms of internal structure and evolutionary stages of the stars. The fundation and basic understanding of asteroseismology rely on well-known physical principles and mathematical tools. Nervetheless there are many issues that still ought to be elucidated. This resquires data of higher and higher quality for an increasing number of stars. This is the goal of future space missions to provide with such data sets.Mjo Goupilwork_6k5o6g2urremhoi4y5lnqcu5bmThu, 29 Sep 2022 00:00:00 GMTPhotoexcitation of planar Wannier excitons by twisted photons
https://scholar.archive.org/work/mt3mgy3srzdzfkyrpgxflpnsi4
Photoexcitation of planar Wannier excitons by twisted photons in thin semiconductor films is investigated. The explicit general formulas for transition probabilities between exciton states are derived. The selection rules for the projection of the total angular momentum are obtained. As examples, the Coulomb and Rytova-Keldysh electron-hole interaction potentials are considered. The use of planar excitons as a pure on-chip source of twisted photons is discussed. The formulas obtained also describe photoexcitation of states of electrons and holes bound to charged impurities in planar semiconductors.P.O. Kazinski, V.A. Ryakinwork_mt3mgy3srzdzfkyrpgxflpnsi4Wed, 28 Sep 2022 00:00:00 GMTImproved asteroseismic inversions for red-giant surface rotation rates
https://scholar.archive.org/work/zwuuq2254ve3lcw5hgjeaaxzo4
Asteroseismic observations of internal stellar rotation have indicated a substantial lack of angular momentum transport in theoretical models of subgiant and red-giant stars. Accurate core and surface rotation rate measurements are therefore needed to constrain internal transport processes included in the models. We eliminate substantial systematic errors of asteroseismic surface rotation rates found in previous studies. We propose a new objective function for the Optimally Localized Averages method of rotational inversions for red-giant stars, which results in more accurate envelope rotation rate estimates obtained from the same data. We use synthetic observations from stellar models across a range of evolutionary stages and masses to demonstrate the improvement. We find that our new inversion technique allows us to obtain estimates of the surface rotation rate that are independent of the core rotation. For a star at the base of the red-giant branch, we reduce the systematic error from about 20% to a value close to 0, assuming constant envelope rotation. We also show the equivalence between this method and the method of linearised rotational splittings. Our new rotational inversion method substantially reduces the systematic errors of red-giant surface rotation rates. In combination with independent measures of the surface rotation rate, this will allow better constraints to be set on the internal rotation profile. This will be a very important probe to further constrain the internal angular momentum transport along the lower part of the red-giant branch.F. Ahlborn, E. P. Bellinger, S. Hekker, S. Basu, D. Mokrytskawork_zwuuq2254ve3lcw5hgjeaaxzo4Wed, 28 Sep 2022 00:00:00 GMTA Tutorial Introduction to Lattice-based Cryptography and Homomorphic Encryption
https://scholar.archive.org/work/vlqa6rnsa5d3vnpa3qeaizot6a
Why study Lattice-based Cryptography? There are a few ways to answer this question. 1. It is useful to have cryptosystems that are based on a variety of hard computational problems so the different cryptosystems are not all vulnerable in the same way. 2. The computational aspects of lattice-based cryptosystem are usually simple to understand and fairly easy to implement in practice. 3. Lattice-based cryptosystems have lower encryption/decryption computational complexities compared to popular cryptosystems that are based on the integer factorisation or the discrete logarithm problems. 4. Lattice-based cryptosystems enjoy strong worst-case hardness security proofs based on approximate versions of known NP-hard lattice problems. 5. Lattice-based cryptosystems are believed to be good candidates for post-quantum cryptography, since there are currently no known quantum algorithms for solving lattice problems that perform significantly better than the best-known classical (non-quantum) algorithms, unlike for integer factorisation and (elliptic curve) discrete logarithm problems. 6. Last but not least, interesting structures in lattice problems have led to significant advances in Homomorphic Encryption, a new research area with wide-ranging applications.Yang Li, Kee Siong Ng, Michael Purcellwork_vlqa6rnsa5d3vnpa3qeaizot6aWed, 28 Sep 2022 00:00:00 GMTNonparametric augmented probability weighting with sparsity
https://scholar.archive.org/work/laghyuyicvhbnpxws32hp6opia
Nonresponse frequently arises in practice, and simply ignoring it may lead to erroneous inference. Besides, the number of collected covariates may increase as the sample size in modern statistics, so parametric imputation or propensity score weighting usually leads to inefficiency without consideration of sparsity. In this paper, we propose a nonparametric imputation method with sparse learning by employing an efficient kernel-based learning gradient algorithm to identify truly informative covariates. Moreover, an augmented probability weighting framework is adopted to improve the estimation efficiency of the nonparametric imputation method and establish the limiting distribution of the corresponding estimator under regularity assumptions. The performance of the proposed method is also supported by several simulated examples and one real-life analysis.Xin He, Xiaojun Mao, Zhonglei Wangwork_laghyuyicvhbnpxws32hp6opiaWed, 28 Sep 2022 00:00:00 GMTExtending linear growth functionals to functions of bounded fractional variation
https://scholar.archive.org/work/lflayccwjnffvfyqc5hyznsvni
In this paper we consider the minimization of a novel class of fractional linear growth functionals involving the Riesz fractional gradient. These functionals lack the coercivity properties in the fractional Sobolev spaces needed to apply the direct method. We therefore utilize the recently introduced spaces of bounded fractional variation and study the extension of the linear growth functional to these spaces through relaxation with respect to the weak* convergence. Our main result establishes an explicit representation for this relaxation, which includes an integral term accounting for the singular part of the fractional variation and features the quasiconvex envelope of the integrand. The role of quasiconvexity in this fractional framework is explained by a technique to switch between the fractional and classical settings. We complement the relaxation result with an existence theory for minimizers of the extended functional.Hidde Schönbergerwork_lflayccwjnffvfyqc5hyznsvniWed, 28 Sep 2022 00:00:00 GMTFinite temperature equilibrium density profiles of integrable systems in confining potentials
https://scholar.archive.org/work/g2x6wzo4hvg7pbauzxna5ed33i
We study the equilibrium density profile of particles in two one-dimensional classical integrable models, namely hard rods and the hyperbolic Calogero model, placed in confining potentials. For both of these models the inter-particle repulsion is strong enough to prevent particle trajectories from intersecting. We use field theoretic techniques to compute the density profile and their scaling with system size and temperature, and compare them with results from Monte-Carlo simulations. In both cases we find good agreement between the field theory and simulations. We also consider the case of the Toda model in which inter-particle repulsion is weak and particle trajectories can cross. In this case, we find that a field theoretic description is ill-suited due to the lack of a thermodynamic length scale. The density profiles for the Toda model obtained from Monte-Carlo simulations can be understood by studying the analytically tractable harmonic chain model (Hessian approximation of the Toda model). For the harmonic chain model one can derive an exact expression for the density that shines light on some of the qualitative features of the Toda model in a quadratic trap. Our work provides an analytical approach towards understanding the equilibrium properties for interacting integrable systems in confining traps.Jitendra Kethepalli, Debarshee Bagchi, Abhishek Dhar, Manas Kulkarni, Anupam Kunduwork_g2x6wzo4hvg7pbauzxna5ed33iWed, 28 Sep 2022 00:00:00 GMTUtilising Neutrosophic Logic in the Design of a Smart Air-Conditioning System
https://scholar.archive.org/work/wfmlnfc5fzhzbbor46exyqaq5q
Air conditioners, which have become the most widely used cooling system, have already been employed in both household and commercial environments. Automation in air conditioning is a very complex and demanding task today. When a sensor in an automatic human detection air conditioner detects the motion and activity of people, it will automatically turn on and set the temperature accordingly. However, in situations in which there are no humans around or in which human presence is unstable for an extended period, energy and power are wasted. In this regard, a control system was created utilising a Neutrosophic logic controller to regulate the AC temperature to a specific level by reducing the compressor and fan speeds without considering other parameters. Since neutrosophic logic handles the truth, ambiguity, and untruth of people in a closed environment, a more intelligent air-conditioning system is created by the suggested approach. As a result, massive quantities of energy savings are achieved. To accomplish the desired outcome, a MATLAB simulation is applied.Hemalatha Karunakaran, Venkateswarlu Bhumireddywork_wfmlnfc5fzhzbbor46exyqaq5qWed, 28 Sep 2022 00:00:00 GMTHeintze-Karcher inequality and capillary hypersurfaces in a wedge
https://scholar.archive.org/work/wuarto6w35c5zkjaf2bei7ey7u
In this paper, we utilize the method of Heintze-Karcher to prove a "best" version of Heintze-Karcher-type inequality for capillary hypersurfaces in the half-space or in a wedge. One of new crucial ingredients in the proof is modified parallel hypersurfaces which are very natural to be used to study capillary hypersurfaces. A more technical part is a subtle analysis along the edge of a wedge. As an application, we classify completely embedded capillary constant mean curvature hypersurfaces that hit the edge in a wedge, which is a subtler case.Xiaohan Jia, Guofang Wang, Chao Xia, Xuwen Zhangwork_wuarto6w35c5zkjaf2bei7ey7uWed, 28 Sep 2022 00:00:00 GMTRefined probabilistic local well-posedness for a cubic Schrödinger half-wave equation
https://scholar.archive.org/work/gmxvyvkjrbgjte3erusp2j2h5q
We obtain probabilistic local well-posedness in quasilinear regimes for the Schr\"odinger half-wave equation with a cubic nonlinearity. We need to use a refined ansatz because of the lack of probabilistic smoothing in the Picard's iterations, which is due to the high-low-low frequency interactions. The proof is an adaptation of the method of Bringmann on the derivative nonlinear wave equation to Schr\"odinger-type equations. In addition, we discuss ill-posedness results for this equation.Nicolas Camps, Louise Gassot, Slim Ibrahimwork_gmxvyvkjrbgjte3erusp2j2h5qWed, 28 Sep 2022 00:00:00 GMTSimplicity of right-angled Hecke C^∗-algebras
https://scholar.archive.org/work/hctkiwwzxzhzlcsjfz2uaxwpqu
By exploiting properties of boundaries associated with Coxeter groups we obtain a complete characterization of simple right-angled multi-parameter Hecke C^∗-algebras. This extends previous results by Caspers, Larsen and the author. Based on work by Raum and Skalski, we further describe the center and the character space of right-angled Hecke C^∗-algebras.Mario Klissework_hctkiwwzxzhzlcsjfz2uaxwpquWed, 28 Sep 2022 00:00:00 GMTLinearised Perturbation of Constant Mass Aspect Function Foliation in Schwarzschild Black Hole Spacetime
https://scholar.archive.org/work/rah7qd5nkndw5i32u4posplaeu
We study the linearised perturbation of the constant mass aspect function foliation in a Schwarzschild black hole spacetime. In particular, we investigate the linearised perturbation of the asymptotic geometry of the foliation at null infinity. We show that there is a 4-dimensional linear space for the linearised perturbation of the initial leaf inside the event horizon, corresponding to which the linearised perturbation of the asymptotic geometry of the foliation at null infinity is preserved to be round. For such a linearised perturbation of the initial leaf in this 4-dimensional linear space, we calculate the corresponding linearised perturbation of the energy-momentum vector and the Bondi mass at null infinity. We show that the linearised perturbations of the Bondi energy and the Bondi mass both vanish, and every possible linearised perturbation of the linear momentum can be achieved by a linearised perturbation of the initial leaf in the 4-dimensional linear space.Pengyu Lework_rah7qd5nkndw5i32u4posplaeuWed, 28 Sep 2022 00:00:00 GMTRandomized K-FACs: Speeding up K-FAC with Randomized Numerical Linear Algebra
https://scholar.archive.org/work/zlogl4av2nckhokq4ws332oqia
K-FAC is a successful tractable implementation of Natural Gradient for Deep Learning, which nevertheless suffers from the requirement to compute the inverse of the Kronecker factors (through an eigen-decomposition). This can be very time-consuming (or even prohibitive) when these factors are large. In this paper, we theoretically show that, owing to the exponential-average construction paradigm of the Kronecker factors that is typically used, their eigen-spectrum must decay. We show numerically that in practice this decay is very rapid, leading to the idea that we could save substantial computation by only focusing on the first few eigen-modes when inverting the Kronecker-factors. Randomized Numerical Linear Algebra provides us with the necessary tools to do so. Numerical results show we obtain ≈2.5× reduction in per-epoch time and ≈3.3× reduction in time to target accuracy. We compare our proposed K-FAC sped-up versions with a more computationally efficient NG implementation, SENG, and observe we perform on par with it.Constantin Octavian Puiuwork_zlogl4av2nckhokq4ws332oqiaWed, 28 Sep 2022 00:00:00 GMTPrimordial black holes and gravitational waves induced by exponential-tailed perturbations
https://scholar.archive.org/work/wymvubhpjrgo5bmasmv56gpzgi
Primordial black holes (PBHs) whose masses are in ∼[10^-15M_⊙,10^-11M_⊙] have been extensively studied as a candidate of whole dark matter (DM). One of the probes to test such a PBH-DM scenario is scalar-induced stochastic gravitational waves (GWs) accompanied with the enhanced primordial fluctuations to form the PBHs with frequency peaked in the mHz band being targeted by the LISA mission. In order to utilize the stochastic GWs for checking the PBH-DM scenario, it needs to exactly relate the PBH abundance and the amplitude of the GWs spectrum. Recently in Kitajima et al., the impact of the non-Gaussianity of the enhanced primordial curvature perturbations on the PBH abundance has been investigated based on the peak theory, and they found that a specific non-Gaussian feature called the exponential tail significantly increases the PBH abundance compared with the Gaussian case. In this work, we investigate the spectrum of the induced stochastic GWs associated with PBH DM in the exponential-tail case. In order to take into account the non-Gaussianity properly, we employ the diagrammatic approach for the calculation of the spectrum. We find that the amplitude of the stochastic GW spectrum is slightly lower than the one for the Gaussian case, but it can still be detectable with the LISA sensitivity. We also find that the non-Gaussian contribution can appear on the high-frequency side through their complicated momentum configurations. Although this feature emerges under the LISA sensitivity, it might be possible to obtain information about the non-Gaussianity from GW observation with a deeper sensitivity such as the DECIGO mission.Katsuya T. Abe, Ryoto Inui, Yuichiro Tada, Shuichiro Yokoyamawork_wymvubhpjrgo5bmasmv56gpzgiWed, 28 Sep 2022 00:00:00 GMTAn Extension of Heron's Formula to Tetrahedra, and the Projective Nature of Its Zeros
https://scholar.archive.org/work/wq4vgu5fmfdtrmsnbtmke6m3kq
A natural extension of Heron's 2000 year old formula for the area of a triangle to the volume of a tetrahedron is presented. This gives the fourth power of the volume as a polynomial in six simple rational functions of the areas of its four faces and three medial parallelograms, which will be referred to herein as "interior faces." Geometrically, these rational functions are the areas of the triangles into which the exterior faces are divided by the points at which the tetrahedron's in-sphere touches those faces. This leads to a conjecture as to how the formula extends to n-dimensional simplices for all n > 3. Remarkably, for n = 3 the zeros of the polynomial constitute a five-dimensional semi-algebraic variety consisting almost entirely of collinear tetrahedra with vertices separated by infinite distances, but with generically well-defined distance ratios. These unconventional Euclidean configurations can be identified with a quotient of the Klein quadric by an action of a group of reflections isomorphic to ℤ_2^4, wherein four-point configurations in the affine plane constitute a distinguished three-dimensional subset. The paper closes by noting that the algebraic structure of the zeros in the affine plane naturally defines the associated 4-element, rank-3 chirotope, aka affine oriented matroid.Timothy F. Havelwork_wq4vgu5fmfdtrmsnbtmke6m3kqWed, 28 Sep 2022 00:00:00 GMTHigh Dimensional Portfolio Selection with Cardinality Constraints
https://scholar.archive.org/work/am25e4pc5vc3pdb6kegw2sgeqq
The expanding number of assets offers more opportunities for investors but poses new challenges for modern portfolio management (PM). As a central plank of PM, portfolio selection by expected utility maximization (EUM) faces uncontrollable estimation and optimization errors in ultrahigh-dimensional scenarios. Past strategies for high-dimensional PM mainly concern only large-cap companies and select many stocks, making PM impractical. We propose a sample-average approximation-based portfolio strategy to tackle the difficulties above with cardinality constraints. Our strategy bypasses the estimation of mean and covariance, the Chinese walls in high-dimensional scenarios. Empirical results on S&P 500 and Russell 2000 show that an appropriate number of carefully chosen assets leads to better out-of-sample mean-variance efficiency. On Russell 2000, our best portfolio profits as much as the equally-weighted portfolio but reduces the maximum drawdown and the average number of assets by 10% and 90%, respectively. The flexibility and the stability of incorporating factor signals for augmenting out-of-sample performances are also demonstrated. Our strategy balances the trade-off among the return, the risk, and the number of assets with cardinality constraints. Therefore, we provide a theoretically sound and computationally efficient strategy to make PM practical in the growing global financial market.Jin-Hong Du, Yifeng Guo, Xueqin Wangwork_am25e4pc5vc3pdb6kegw2sgeqqWed, 28 Sep 2022 00:00:00 GMT