IA Scholar Query: Translating between the representations of a ranked convex geometry.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 30 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440A–E
https://scholar.archive.org/work/enoy33f5ejdntgmhbnitknxxlu
He gained a national reputation with the Viipuri Municipal Library , destroyed in World War II, and an international one with his Finnish pavilions at the World's Fairs at Paris (1937) and New York (1939-40). He made imaginative use of wood with brickwork, glass, copper and cement and also developed functional plywood furniture, mass-produced in his own factory. His range of commissions, including the Maison Carré in Paris, Baker House in Cambridge, Mass., and the Finlandia Concert Hall, Helsinki, was extensive: factories, museums, churches, theatres, department stores, private houses and public housing. He was professor of architecture at the Massachusetts Institute of Technology 1945-49. Aaron (c.14th-13th centuries BCE). Hebrew High Priest. In the Bible story, with his brother *Moses, he led the Israelites from Egypt to Canaan (Palestine) and became their first high priest, but while Moses was receiving the Ten Commandments on Mount Sinai he made a golden calf for the people to worship (Exodus xxiii).work_enoy33f5ejdntgmhbnitknxxluWed, 30 Nov 2022 00:00:00 GMTGeometry and analysis of contact instantons and entanglement of Legendrian links I
https://scholar.archive.org/work/uebt2r7sovh6ppe4k37pjuon5m
The purposes of the present paper are two-fold. Firstly we further develop the interplay between the contact Hamiltonian geometry and the geometric analysis of Hamiltonian-perturbed contact instantons with the Legendrian boundary condition, which is initiated by the present author in . We introduce the class of tame contact manifolds (M,λ), which includes compact ones but not necessarily compact, and establish uniform a priori C^0-estimates for the contact instantons. Then we study the problem of estimating the Reeb-untangling energy of one Legendrian submanifold from another, and formulate a particularly designed parameterized moduli space for the study of the problem. We establish the Gromov-Floer-Hofer type convergence result for contact instantons of finite energy and construct its compactification of the moduli space, first by defining the correct energy and then by proving uniform a priori energy bounds in terms of the oscillation of the relevant contact Hamiltonian. Secondly, as an application of this geometry and analysis of contact instantons, we prove that the self Reeb-untangling energy of a compact Legendrian submanifold R in any tame contact manifold (M,λ) is greater than that of the period gap T_λ(M,R) of the Reeb chords of R. This is an optimal result in general.Yong-Geun Ohwork_uebt2r7sovh6ppe4k37pjuon5mWed, 30 Nov 2022 00:00:00 GMTOn Scaling Properties for Two-State Problems and for a Singularly Perturbed T_3 Structure
https://scholar.archive.org/work/sltbrxhiyjftnlekkyv2dz7p4i
In this article we study quantitative rigidity properties for the compatible and incompatible two-state problems for suitable classes of 𝒜-free operators and for a singularly perturbed T_3-structure for the divergence operator. In particular, in the compatible setting of the two-state problem we prove that all homogeneous, first order, linear operators with affine boundary data which enforce oscillations yield the typical ϵ^2/3-lower scaling bounds. As observed in for higher order operators this may no longer be the case. Revisiting the example from , we show that this is reflected in the structure of the associated symbols and that this can be exploited for a new Fourier based proof of the lower scaling bound. Moreover, building on , we discuss the scaling behaviour of a T_3 structure for the divergence operator. We prove that as in this yields a non-algebraic scaling law.Bodgan Raiţă and Angkana Rüland and Camillo Tissotwork_sltbrxhiyjftnlekkyv2dz7p4iWed, 30 Nov 2022 00:00:00 GMTF–J
https://scholar.archive.org/work/cn4pwk4efnaa3ba27vpt6ux6ca
Fabergé, Peter Carl (1846Carl ( -1920)) . Russian jeweller, of French descent. He achieved fame by the ingenuity and extravagance of the jewelled objects (especially Easter eggs) he devised for the Russian nobility and the tsar in an age of ostentatious extravagance which ended on the outbreak of World War I. He died in Switzerland.work_cn4pwk4efnaa3ba27vpt6ux6caWed, 30 Nov 2022 00:00:00 GMTBracket Polynomial Expression of Discriminant-Resultants as SL2-invariant
https://scholar.archive.org/work/k3jqy66llndefohi3lmri46wyu
We give a bracket polynomial expression for intermediate terms between discriminant and resultant for pair of binary forms. As an application of the bracket polynomial expression, we give an algebraic proof of the algebraic independence of intermediate terms, which was shown in the theory of dynamical systems.Rin Gotouwork_k3jqy66llndefohi3lmri46wyuTue, 29 Nov 2022 00:00:00 GMTQuantum entanglement: an overview of the separability problem in two quantum bits
https://scholar.archive.org/work/e633yl3et5aurhuzlglanrvxea
The separability problem is one of the basic and emergent problems in the present and future quantum information processing. The latter focuses on information and computing based on quantum mechanics and uses quantum bits as its basic information units. In this paper, we present an overview of the progress in the separability problem in bipartite systems, more specifically in two quantum bits systems from the criterion based on the inequalities of Bell in 1964 to the recent criteria of separability in 2018.Honorine Gnonfin, Laure Goubawork_e633yl3et5aurhuzlglanrvxeaTue, 29 Nov 2022 00:00:00 GMTThe Poisson boundary of hyperbolic groups without moment conditions
https://scholar.archive.org/work/ucfn4qjtavfntpgineijdocn7m
We prove that the Poisson boundary of a random walk with finite entropy on a non-elementary hyperbolic group can be identified with its hyperbolic boundary, without assuming any moment condition on the measure. We also extend our method to groups with an action by isometries on a hyperbolic metric space containing a WPD element; this applies to a large class of non-hyperbolic groups such as relatively hyperbolic groups, mapping class groups, and groups acting on CAT(0) spaces.Kunal Chawla, Behrang Forghani, Joshua Frisch, Giulio Tiozzowork_ucfn4qjtavfntpgineijdocn7mTue, 29 Nov 2022 00:00:00 GMT2017
https://scholar.archive.org/work/uowfgqp7hzh2lltvflrcjwdtsm
Fresnel and Fraunhoffer diffraction-Polarization methods for the production of polarized light. Einstein's coefficients (expression for energy density). Requisites of a Laser system. Condition for laser action. Principle, Construction and working of He-Ne laser Holography-Principle of Recording and reconstruction of images. Propagation mechanism in optical fibers. Angle of acceptance. Numerical aperture. Types of optical fibers and modes of propagation. Attenuation, Block diagram discussion of point to point communication, applications. Module -4 10 hours Crystal Structure: Space lattice, Bravais lattice-Unit cell, primitive cell. Lattice parameters. Crystal systems. Direction and planes in a crystal. Miller indices. Expression for interplanar spacing. Coordination number. Atomic packing factors (SC, FCC, BCC). Bragg's law, Determination of crystal structure using Bragg's X-ray diffractometer. Polymorphism and Allotropy. Crystal Structure of Diamond. Module -5 10 hours ELEMENTS OF ELECTRONICS ENGINEERING Subject Code 17SEC13/23 IA Marks 50 Number of lecture hours/week 04 Exam Marks 50 Total number of lecture hours 50 Credits 04 Course Objectives: 1. To provide basic concepts D.C circuits and circuit analysis techniques 2. To provide knowledge on A.C circuit fundamental techniques 3. To understand construction and operation of BJT and Junction FET 4. Explain the different modes of communications from wired to wireless and the computing involved. 5. To provide fundamental knowledge of Digital Logic. Course Outcomes: CO1: Understand concepts of electrical circuits and elements. CO2: Apply basic electric laws in solving circuit problems. CO3: Analyse simple circuits containing transistors CO4: Understand concept of cellular wireless networks. CO5: Understand Number systems and design basic digital circuits.BTECH.MECHwork_uowfgqp7hzh2lltvflrcjwdtsmMon, 28 Nov 2022 00:00:00 GMTCluster scattering diagrams and theta functions for reciprocal generalized cluster algebras
https://scholar.archive.org/work/c7edmn6dqreyjcoxextszcccsq
We give a construction of generalized cluster varieties and generalized cluster scattering diagrams for reciprocal generalized cluster algebras, the latter of which were defined by Chekhov and Shapiro. These constructions are analogous to the structures given for ordinary cluster algebras in the work of Gross, Hacking, Keel, and Kontsevich. As a consequence of these constructions, we are also able to construct theta functions for generalized cluster algebras, again in the reciprocal case, and demonstrate a number of their structural properties.Man-Wai Mandy Cheung, Elizabeth Kelley, Gregg Musikerwork_c7edmn6dqreyjcoxextszcccsqMon, 28 Nov 2022 00:00:00 GMTRegularisation of Lie algebroids and Applications
https://scholar.archive.org/work/eiecssxiwza4xdcqkoz7rndgja
We describe a procedure, called regularisation, that allows us to study geometric structures on Lie algebroids via foliated geometric structures on a manifold of higher dimension. This procedure applies to various classes of Lie algebroids; namely, those whose singularities are of b^k, complex-log, or elliptic type, possibly with self-crossings. One of our main applications is a proof of the Weinstein conjecture for overtwisted b^k-contact structures. This was proven by Miranda-Oms using a certain technical hypothesis. Our approach avoids this assumption by reducing the proof to the foliated setting. As a by-product, we also prove the Weinstein conjecture for other Lie algebroids. Along the way we also introduce tangent distributions, i.e. subbundles of Lie algebroids, as interesting objects of study and present a number of constructions for them.Álvaro del Pino, Aldo Wittework_eiecssxiwza4xdcqkoz7rndgjaSun, 27 Nov 2022 00:00:00 GMTMulti-task Learning for Camera Calibration
https://scholar.archive.org/work/5otz5vbrsjfxxgwnechuwdggze
For a number of tasks, such as 3D reconstruction, robotic interface, autonomous driving, etc., camera calibration is essential. In this study, we present a unique method for predicting intrinsic (principal point offset and focal length) and extrinsic (baseline, pitch, and translation) properties from a pair of images. We suggested a novel method where camera model equations are represented as a neural network in a multi-task learning framework, in contrast to existing methods, which build a comprehensive solution. By reconstructing the 3D points using a camera model neural network and then using the loss in reconstruction to obtain the camera specifications, this innovative camera projection loss (CPL) method allows us that the desired parameters should be estimated. As far as we are aware, our approach is the first one that uses an approach to multi-task learning that includes mathematical formulas in a framework for learning to estimate camera parameters to predict both the extrinsic and intrinsic parameters jointly. Additionally, we provided a new dataset named as CVGL Camera Calibration Dataset [1] which has been collected using the CARLA Simulator [2]. Actually, we show that our suggested strategy out performs both conventional methods and methods based on deep learning on 8 out of 10 parameters that were assessed using both real and synthetic data. Our code and generated dataset are available at https://github.com/thanif/Camera-Calibration-through-Camera-Projection-Loss.Talha Hanif Butt, Murtaza Tajwork_5otz5vbrsjfxxgwnechuwdggzeSun, 27 Nov 2022 00:00:00 GMTLinear Classification of Neural Manifolds with Correlated Variability
https://scholar.archive.org/work/3mnuuaowkzaa7e4z2mtkdxa2yq
Understanding how the statistical and geometric properties of neural activations relate to network performance is a key problem in theoretical neuroscience and deep learning. In this letter, we calculate how correlations between object representations affect the capacity, a measure of linear separability. We show that for spherical object manifolds, introducing correlations between centroids effectively pushes the spheres closer together, while introducing correlations between the spheres' axes effectively shrinks their radii, revealing a duality between neural correlations and geometry. We then show that our results can be used to accurately estimate the capacity with real neural data.Albert J. Wakhloo, Tamara J. Sussman, SueYeon Chungwork_3mnuuaowkzaa7e4z2mtkdxa2yqSun, 27 Nov 2022 00:00:00 GMTCylindrical contact homology of links of simple singularities (V2)
https://scholar.archive.org/work/63c5tzufcbb33pora64o5hm46q
We compute the cylindrical contact homology of the links of the simple singularities. These manifolds are contactomorphic to S^3/G for finite subgroups G⊂SU(2). We perturb the degenerate contact form on S^3/G with a Morse function, invariant under the corresponding H⊂SO(3) action on S^2, to achieve nondegeneracy up to an action threshold. The cylindrical contact homology is recovered by taking a direct limit of the action filtered homology groups. The ranks of this homology are given in terms of |Conj(G)|, demonstrating a form of the McKay correspondence.Leo Digiosiawork_63c5tzufcbb33pora64o5hm46qSun, 27 Nov 2022 00:00:00 GMTPairs in discrete lattice orbits with applications to Veech surfaces
https://scholar.archive.org/work/5vkg7seacjh2nmglovncljqoei
Let Λ_1, Λ_2 be two discrete orbits under the linear action of a lattice Γ<SL_2(ℝ) on the Euclidean plane. We prove a Siegel-Veech-type integral formula for the averages ∑_𝐱∈Λ_1∑_𝐲∈Λ_2 f(𝐱, 𝐲) from which we derive new results for the set S_M of holonomy vectors of saddle connections of a Veech surface M. This includes an effective count for generic Borel sets with respect to linear transformations, and upper bounds on the number of pairs in S_M with bounded determinant and on the number of pairs in S_M with bounded distance. This last estimate is used in the appendix to prove that for almost every (θ,ψ)∈ S^1× S^1 the translations flows F_θ^t and F_ψ^t on any Veech surface M are disjoint.Claire Burrin, Samantha Fairchild, Jon Chaikawork_5vkg7seacjh2nmglovncljqoeiSat, 26 Nov 2022 00:00:00 GMTExtractors for Images of Varieties
https://scholar.archive.org/work/apfsslxulvatvfsurup6p7gqui
We construct explicit deterministic extractors for polynomial images of varieties, that is, distributions sampled by applying a low-degree polynomial map f : 𝔽_q^r →𝔽_q^n to an element sampled uniformly at random from a k-dimensional variety V ⊆𝔽_q^r. This class of sources generalizes both polynomial sources, studied by Dvir, Gabizon and Wigderson (FOCS 2007, Comput. Complex. 2009), and variety sources, studied by Dvir (CCC 2009, Comput. Complex. 2012). Assuming certain natural non-degeneracy conditions on the map f and the variety V, which in particular ensure that the source has enough min-entropy, we extract almost all the min-entropy of the distribution. Unlike the Dvir-Gabizon-Wigderson and Dvir results, our construction works over large enough finite fields of arbitrary characteristic. One key part of our construction is an improved deterministic rank extractor for varieties. As a by-product, we obtain explicit Noether normalization lemmas for affine varieties and affine algebras. Additionally, we generalize a construction of affine extractors with exponentially small error due to Bourgain, Dvir and Leeman (Comput. Complex. 2016) by extending it to all finite prime fields of quasipolynomial size.Zeyu Guo, Ben Lee Volk, Akhil Jalan, David Zuckermanwork_apfsslxulvatvfsurup6p7gquiSat, 26 Nov 2022 00:00:00 GMTConditional Gradient Methods
https://scholar.archive.org/work/b2imrksvmfclhaik7ghfh6bcte
The purpose of this survey is to serve both as a gentle introduction and a coherent overview of state-of-the-art Frank--Wolfe algorithms, also called conditional gradient algorithms, for function minimization. These algorithms are especially useful in convex optimization when linear optimization is cheaper than projections. The selection of the material has been guided by the principle of highlighting crucial ideas as well as presenting new approaches that we believe might become important in the future, with ample citations even of old works imperative in the development of newer methods. Yet, our selection is sometimes biased, and need not reflect consensus of the research community, and we have certainly missed recent important contributions. After all the research area of Frank--Wolfe is very active, making it a moving target. We apologize sincerely in advance for any such distortions and we fully acknowledge: We stand on the shoulder of giants.Gábor Braun, Alejandro Carderera, Cyrille W. Combettes, Hamed Hassani, Amin Karbasi, Aryan Mokhtari, Sebastian Pokuttawork_b2imrksvmfclhaik7ghfh6bcteFri, 25 Nov 2022 00:00:00 GMTThe algebraic dynamics of the pentagram map
https://scholar.archive.org/work/wpg2nhsanzbshf5efsektxkz4a
The pentagram map, introduced by Schwartz [The pentagram map. Exp. Math.1(1) (1992), 71–81], is a dynamical system on the moduli space of polygons in the projective plane. Its real and complex dynamics have been explored in detail. We study the pentagram map over an arbitrary algebraically closed field of characteristic not equal to 2. We prove that the pentagram map on twisted polygons is a discrete integrable system, in the sense of algebraic complete integrability: the pentagram map is birational to a self-map of a family of abelian varieties. This generalizes Soloviev's proof of complex integrability [F. Soloviev. Integrability of the pentagram map. Duke Math. J.162(15) (2013), 2815–2853]. In the course of the proof, we construct the moduli space of twisted n-gons, derive formulas for the pentagram map, and calculate the Lax representation by characteristic-independent methods.MAX H. WEINREICHwork_wpg2nhsanzbshf5efsektxkz4aFri, 25 Nov 2022 00:00:00 GMTA dichotomy theory for height functions
https://scholar.archive.org/work/je55i7cxxzb43ar7oh4hsaktmu
Height functions are random functions on a given graph, in our case integer-valued functions on the two-dimensional square lattice. We consider gradient potentials which (informally) lie between the discrete Gaussian and solid-on-solid model (inclusive). The phase transition in this model, known as the roughening transition, Berezinskii-Kosterlitz-Thouless transition, or localisation-delocalisation transition, was established rigorously in the 1981 breakthrough work of Fröhlich and Spencer. It was not until 2005 that Sheffield derived continuity of the phase transition. First, we establish sharpness, in the sense that covariances decay exponentially in the localised phase. Second, we show that the model is delocalised at criticality, in the sense that the set of potentials inducing localisation is open in a natural topology. Third, we prove that the pointwise variance of the height function is at least clog n in the delocalised regime, where n is the distance to the boundary, and where c>0 denotes a universal constant. This implies that the effective temperature of any potential cannot lie in the interval (0,c) (whenever it is well-defined), and jumps from 0 to at least c at the critical point. We call this range of forbidden values the effective temperature gap.Piet Lammerswork_je55i7cxxzb43ar7oh4hsaktmuFri, 25 Nov 2022 00:00:00 GMTFrom equivariant volumes to equivariant periods
https://scholar.archive.org/work/d6m3xtmefnbqfgvci4pqh72424
We consider generalizations of equivariant volumes of abelian GIT quotients obtained as partition functions of 1d, 2d, and 3d supersymmetric GLSM on S^1, D^2 and D^2 × S^1, respectively. We define these objects and study their dependence on equivariant parameters for non-compact toric Kahler quotients. We generalize the finite-difference equations (shift equations) obeyed by equivariant volumes to these partition functions. The partition functions are annihilated by differential/difference operators that represent equivariant quantum cohomology/K-theory relations of the target and the appearence of compact divisors in these relations plays a crucial role in the analysis of the non-equivariant limit. We show that the expansion in equivariant parameters contains information about genus-zero Gromov–Witten invariants of the target.Luca Cassia, Nicolo Piazzalunga, Maxim Zabzinework_d6m3xtmefnbqfgvci4pqh72424Wed, 23 Nov 2022 00:00:00 GMTOn the elliptical range theorems for the Davis-Wielandt shell, the numerical range, and the conformal range
https://scholar.archive.org/work/btroc55e2nattpee6quuklr62a
The conformal range, which is a horizontal projection of the Davis-Wielandt shell, can be considered as the hyperbolic version of the numerical range. Here we explain (the analogue of) the elliptical range theorem of 2×2 complex matrices for the conformal range. In that course, comparison to the Davis-Wielandt shell and the numerical range is made.Gyula Lakoswork_btroc55e2nattpee6quuklr62aWed, 23 Nov 2022 00:00:00 GMT