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math/729033_088416c6542a36aa_2520.txt
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“it is easy for philosophers to be rich if they choose, but this is not what they care about.”9 Money is a numerical concept. When we want to see how much money we have, we count it. Over time, people naturally developed new forms of mathematics to keep track of money. As mathematics grew more sophisticated, investors ...
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There has been a recent wave of interest in intermediate trust models for differential privacy that eliminate the need for a fully trusted central data collector, but overcome the limitations of local differential privacy. This interest has led to the introduction of the shuffle model (Cheu et al., EUROCRYPT 2019; Erli...
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Depending on who you talked to, Lewis Dodgson was famous as the most aggressive geneticist of his generation, or the most reckless. Thirty-four, balding, hawk-faced, and intense, he had been dismissed by Johns Hopkins as a graduate student, for planning gene therapy on human patients without obtaining the proper FDA pr...
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solutions Eq. (2) are necessarily holomorphic (or anti-holomorphic) functions in the variables z j , z¯ j [29]. In this work, we shall examine the analogous question for meta-conformal invariance. Known physical examples of confirmed meta-conformal invariance are of two types. First, there exist spatially non-local rep...
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This paper introduces the Double Conformal / Darboux Cyclide Geometric Algebra (DCGA), based in the G8,2 Clifford geometric algebra. DCGA is an extension of CGA and has entities representing points and general Darboux cyclide surfaces in Euclidean 3D space. The general Darboux cyclide is a quartic surface. Darboux cycl...
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A tremendous amount of mathematics concerns groups acting on sets and the primitive permutation groups are the building blocks of all group actions. A primitive permutation group (X,G) is a group G together with an action of G on X such that there are no nontrivial equivalence relations on X preserved by G. An importan...
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In this article, we characterize monomials in de facto values.Carlitz-Goss rielle defined on the complement of Fq (T) in a finite place which arealgebraic on Fq (T ). In particular, this confirms Wen-Yao's conjecturestated in 2003. This gives a necessary and sufficient condition on an en-p-adic tier so that the value o...
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the notable CHARLES BABBAGE (1791–1871) in his design and planned construction of an “analytic engine,” Lovelace outlined the principles needed in performing mathematics on a machine and, in effect, was the first person to ever write a computer program. Daughter of the famous poet George Gordon, Lord Byron, Lovelace wa...
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pizza. If the pizza happens to be a perfect circle, then every line passing through its center exactly bisects the crust. To see that there is always a line that bisects both crust and sausage simultaneously, start with the potential cutting line in any fixed direction and rotate it about the center slowly, say, clockw...
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Patheos.com — December 15, 2015: Once upon a time, a priest, in full clericals, was sitting in a train carriage, reading. A young university student entered the carriage and was excited to see that the priest was engrossed in a philosophy book. The young man said, *“Father, I’m sorry to interrupt you but I see you ...
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KS: Yeah. So just to sort of fetishize circles is bizarre. But I guess, like, what are your other options? Well, there are lots of other options. But the Polsby-Popper is the most common. There's a handful of states that require specific compactness measures in their process, and many other states that require compactn...
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Complementary Reading (1) General References on ODE: There are dozens of excellent monographs on the theory of ordinary differential equations. For a comprehensive review on the most fundamental concepts (existence and uniqueness theorems, linear stability, etc.), Boyce, DiPrima, and Meade’s Elementary Differential Equat...
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Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. Unlike binary matrix factorization based on standard arithmetic, BMF employs the Boolean OR and AND operations for the matrix product, which improves interpretability and reduces the approximation e...
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International Political Theory (IPT) focuses on the point where two fields of study meet - International Relations and P 2,964 187 3MB Read more
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As mentioned earlier, local illumination is an incomplete method, from the physics point of view, but simplification produces acceptable results for real-time interaction. The model considers that the light intensity (I ) at one point on a surface has three components: ambient, diffuse, and specular reflections: I = Ia...
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How to deal with conflict is a significant issue in Dempster-Shafer evidence theory (DST). In the Dempster combination rule, conflicts will produce counter-intuitive phenomena. Therefore, many effective conflict handling methods have been presented. This paper proposes a new framework for reducing conflict based on pri...
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Bazându-mă pe proprietatea remarcabilă a vectorului lui Darboux de a fi perpendicular pe normală, definesc un nou triedru asociat curbelor din spațiu și demonstrez că și acest triedru satisface formulele lui Frenet. Spre deosebire de lucrarea anterioară, unde am folosit pentru simplitate forma trigonometrică a formulel...
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All participants in Exp. 1–3 played 34 rounds of an investment game (3 blocks of 10 rounds and 1 ‘bonus’ block of 4 rounds). On each round, each player was allocated an endowment of 2, 4, 6, 8 or 10 coins (2, 4 or 10 coins in Exp. 1) depending on the endowment condition to which they were allocated, and whether they we...
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An important practical example is the 3 3 case. In rotation group SO(3)) , it is shown that one can identify every A so (3) with an Euler vector ω θ u , where u ( x , y , z ) is a unit magnitude vector.
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Automated driving systems rely on 3D object detectors to recognize possible obstacles from LiDAR point clouds. However, recent works show the adversary can forge non-existent cars in the prediction results with a few fake points (i.e., *appearing attack*). By removing statistical outliers, existing defenses are however...
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Glide Reflection A reflection in a line followed by a translation in a direction parallel to that line is called a glide reflection. Reflection in a Point A reflection in a point O in the plane is the isometry that takes a point P in the plane to the corresponding point P′ such that O lies at the MIDPOINT of the line s...
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Biographical Sketch Dedication Acknowledgements Table of Contents List of Figures Background Introduction Structure of t 142 21 1MB Read more
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3.7 Word Embedding Vectors GloVe is capable of procuring vector representations for a given textual data input. The importance and usage of word embeddings are that they can be utilized for grouping words that are synonyms to each other in context and meaning in a similar representation. Each word is mapped to one word...
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When a deep learning model is deployed in the wild, it can encounter test data drawn from distributions different from the training data distribution and suffer drop in performance. For safe deployment, it is essential to estimate the accuracy of the pre-trained model on the test data. However, the labels for the test ...
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Understanding the spatio-temporal evolution of epidemics with multiple pathogens requires not only new theoretical models but also careful analysis of their practical consequences. Building on the Multiplex Bi-Virus Reaction-Diffusion framework (MBRD) introduced in our companion paper, we investigate how the super-infe...
math/353276_d0fe46e444a903da_6.txt
Thus far we have discussed bounds for the normalised Steklov eigenvalues. Do there exist Riemannian metrics on a given underlying surface that realise these bounds? This is the subject of Sect. 5. Fraser and Schoen [98, 823–890 (2016)")] first discovered and studied a deep connection between such extremal metrics on su...
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Doyle, Peter G., and J. Laurie Snell. Random Walks and Electric Networks. Washington, D.C.: Mathematical Association of America, 1984. Dunham, William. Journey through Genius. New York: John Wiley & Sons, 1990. ———. The Mathematical Universe: An Alphabetical Journey through Great Proofs, Problems, and Personalities. Ne...
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The rapid advancement of artificial intelligence (AI) and deep learning (DL) has catalyzed the emergence of several optimization-driven subfields, notably neuromorphic computing and quantum machine learning. Leveraging the differentiable nature of hybrid models, researchers have explored their potential to address comp...
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We consider ensembles of trajectories associated with large deviations of time-integrated quantities in stochastic models. Motivated by proposals that these ensembles are relevant for physical processes such as shearing and glassy relaxation, we show how they can be generated directly using auxiliary stochastic process...
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Exercises Exercise 29.6. Verify that the cup product renders H ∗ (X) a commutative graded ring. Exercise 29.7. (a) Let n, k > 0. Compute H ∗ ((S k )n ; R) as an R-algebra. When k is odd, this is an “exterior algebra.” (b) Rn is the universal cover of (S 1 )n = Rn /Zn . Let M be an n × n matrix with entries in Z. It def...
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The rational Bézier curve adds adjustable weights to provide closer approximations to arbitrary shapes. The numerator is a weighted Bernstein-form Bézier curve and the denominator is a weighted sum of Bernstein polynomials. Rational Bézier curves can, among other uses, be used to represent segments of conic sections ex...
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Venn diagram A simple way of representing sets and subsets, which makes use of overlapping circles. Venn diagrams are named after the Englishman John Venn (1834–1923), a fellow of Cambridge University. Venn was a cleric in the Anglican Church, an authority on what was then called “moral science,” the compiler of a mass...
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I propose three new curved spacetime versions of the Dirac Equation. These equations have been developed mainly to try and account in a natural way for the observed anomalous gyromagnetic ratio of Fermions. The derived equations suggest that particles including the Electron which is thought to be a point particle do ha...
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* Ian M. Chiswell: *Euler Characteristics of Groups*, S. 1 GDZ Göttingen * Rudolf Scharlau: *Paare alternierender Formen*, S. 13 GDZ Göttingen * Michael Wiegner: *Ein optimaler Reularitätssatz für schwache Lösungen gewisser elliptischer Systeme*, S. 21 GDZ Göttingen * Paul E. Ehrlich: *Zwei Bemerkungen über die Ricci-K...
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16:40 On Empirical Cumulant Generating Functions of Code Lengths for Individual Sequences Neri Merhav (Technion, Israel) We consider the problem of lossless compression of individual sequences using finite-state (FS) machines, from the perspective of the best achievable empirical cumulant generating function (CGF) of t...
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Modern computational science allows complex scientific processes to be described by mathematical models implemented in computer codes, or simulators. When these simulators are computationally expensive, it is common to approximate them using statistical emulators constructed from computer experiments. Often, the overar...
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This paper consists of three parts: Starting with the field $mathbb{C}$ of complex numbers,the Banach space $mathcal{C}(V)$ of continuous, $mathbb{C}$-valued functions on a simply connected compact region $Vsubsetmathbb{C}$ is shown to decompose the topological direct sum of two complementary subspaces: a subspace of i...
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gmsh/model/mesh/field/add Add a new mesh size field of type fieldType. If tag is positive, assign the tag explicitly; otherwise a new tag is assigned automatically. Return the field tag. Available field types are listed in the "Gmsh mesh size fields" chapter of the Gmsh reference manual. Input: fieldType (string), tag ...
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[Joint with Probability] This talk will be about the convergence problem in mean field control (MFC), i.e. the challenge of rigorously justifying the convergence of certain "symmetric" \(N\)-particle control problems towards their mean field counterparts. On the one hand, this convergence problem is already well-unders...
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Everywhere we turn these days, we find that networks can be used to describe relevant interactions. In the high tech world, we see the Internet, the World Wide Web, mobile phone networks, and a variety of online social networks. In economics, we are increasingly experiencing both the positive and negative effects of a ...
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Authors: Loïc Renaut, Laurent Bruneau Comments: 65 Pages. In French The aim of this thesis is to study the basic concepts and the mathematical formalism of quantum mechanics. To do so, we will first examine Newtonian mechanics. This was the prevailing theory until the early 20th century for describing the motion of obj...
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Exercises with Solutions: The exercises cover a range of topics including « Constructing a Stochastic Process Using Kolmogorov’s Extension, » which explores the foundational aspects of stochastic process construction. « Harmonic Stochastic Process » and « Continuity of the Autocovariance Function of WSS Processes » del...
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– Box costs X (X=12). – Handling , storage, distribution, etc costs 4X (48). – Final price is 5X (60). – Now box costs X+5 (17). – Why does it affect handling, storage and distribution? Why is it the default that they put markup on the tariff component? It should still cost 4\*12 (48) as previously and not 4\*17 = 68. ...
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This course focuses on the nursing care of acutely- and critically-ill adult patients with complex physical health needs in high acuity settings and also addresses management of adult patients with related chronic conditions. Students synthesize prior knowledge with new knowledge of nursing, pathophysiology, pharmacolo...
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included on one slide of a presentation given to the commission by Assistant Commissioner of Safety Richard Bailey. Spin Echo spectra of Gd(\_1 x)xYxAP(\_2) and Gd(\_1 x)La(\_x)AP(\_2) (0 x 0.4) were studied in the ferromagnetically ordered state at 42 K. The Al resonance line profiles were analysed under the assumptio...
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