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math/2710_db9c0f2f4b6f960d_1909.txt
When an expanding uniform-density dust ball's radius doesn't sufficiently exceed the Schwarzschild value, its expansion rate will actually be increasing because the dominant gravitational time dilation effect diminishes as the dust ball expands. But such acceleration of expansion is absent in "comoving coordinates" bec...
math/729033_48155ebf7a3ccceb_27265.txt
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agricultural Revolution, Albert Einstein, Alvin Toffler, anti-communist, bread and circuses, British Empire, David Attenborough, Dr. Strangelove, European colonialism, Future Shock, George Santayana, ghettoisation, Great Leap Forward, Gregor Mendel, Herbert Marcuse, hiring and firing, Joan Didion, laissez-faire capital...
math/4209381_a6a9c08d3029d935_31.txt
Reinout-g and I like Serena have been investigating possible LaTex editors. ILS has said that 'mathjax' is probably the best because it is usually used in other forums. Reinout seemed to think that the Latex could probably be delivered via a [tex][/tex] box. Do you think that this is how it would be ILS? Also, do you k...
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In Part II of the *Ethics* in IIP40S2*,* Spinoza differentiates three kinds of knowledge, which he calls imagination, reason, and intuitive knowledge. The first kind, imagination, mentioned above, has its sources in bodies affecting the human body and the ideas of these affections, or perception and sensation. It also ...
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Traditionally, research on Craig interpolation is concerned with (a) establishing the Craig interpolation property (CIP) of a logic saying that every valid implication in the logic has a Craig interpolant and (b) designing algorithms that extract Craig interpolants from proofs. Logics that lack the CIP are regarded as ...
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Notice that 2 × 2 = 4, and so it is appropriate to write – – √ 4 = 2. We also have that √ 4 equals 4, 8, and 10, since 4 × 4 = 4, 8 × 8 = 4, and 10 × 10 = 4 in clock math. In – – the same way, √ 1 equals 1, 5, 7, or 11, and √ 9 equals 3 – or 9. There is no number equivalent to √ 2, for instance, in this system. It is p...
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math/2710_db9c0f2f4b6f960d_2888.txt
In this paper, we propose a new test of uniformity on the circle based on the Gini mean difference of the sample arc-lengths. These sample arc-lengths, which are the gaps between successive observations on the circumference of the circle, are analogous to sample spacings on the real line. The Gini mean difference, whic...
math/2853639_9fec40bb5cdedcbd_49.txt
Circuli et Hyperbolae Quadratura, in which he had used exhaustion to compute areas under the rectangular hyperbola, which resulted in infinite series summing to logarithms. An article entitled “The Squaring of the Hyperbola, by an Infinite Series of Rational Numbers, Together with Its Demonstration, by that Eminent Mat...
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humidity line, P%. The adiabatic saturation line through a [these are a series of almost parallel lines as shown in Figure 10.6(a)] is ac . The adiabatic saturation temperature T as is obtained by drawing the vertical line through c. For the air-water system, the wet-bulb temperature T w is practically the same as /*. ...
math/5dd959b1_7403.txt
In harmony, one of the first operations will be to assemble a congress of grammarians and naturalists to compose a unified language, whose system will be regulated based on analogy, with the cries of animals and other natural documents. This work will barely be completed after a century; to finish it, they will have a ...
math/735679_8faa9997ae6fbdd7_516.txt
71. In addition to Jacques Tits, two other mathematicians also stake claim, at various stages, to introducing Bourbaki to Coxeter’s work. John Coleman suggested he may have provided the first point of contact. Coleman completed his master’s under Bourbaki member Claude Chevalley at Princeton. In 1949, he met with his t...
math/4922055_dcd4406d5f48241d_575.txt
And as I observed that in the words “I think, therefore I am”, there is nothing at all which gives me assurance of their truth beyond this, that I see very clearly that in order to think it is necessary to exist, I concluded that I might take, as a general rule, the principle, that all the things which we very clearly ...
math/2825922_fdb7b48aaf6e43d3_683.txt
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Another point. The title of the course Computation, Complexity, and Algorithms. Low and behold, other courses offered at Georgia Tech, but not yet to OMSCS students include Computational Complexity Theory, Design and Analysis of Algorithms, Graph Algorithms, Approximation Algorithms, and Randomized Algorithms. CCA incl...
math/729033_48155ebf7a3ccceb_30688.txt
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1. The use of ICT for data transfer, remote control of other systems, and clock synchronisation. Pant et al. (2016) show that ICT is crucial for the successful operation of the UK’s rail infrastructure. The study shows that flooding of the ICT assets in the1-in-200 year floodplain would disrupt 46% of passenger journey...
math/4922055_3a58688b356c39be_76.txt
At this point I’m convinced you’re deliberately uncharitable (and therefore won’t engage further), but if you want you can convince me that you’re not, these words would do it: “I honestly cannot find any meaningful distinction between the statement ‘A exists therefore, by logic, B can not exist’ and ‘People think B is...
math/729033_3907eeff353c9d52_93.txt
Like most who were there, my overiding memories are of the cruelty and abuse of some of the staff and the ritualised humiliation that they seemed to think was a vital part of the process of education. However, I don't recall being particularly concerned about "Square" who seemed to be hopelessly lost during our era. Bu...
math/729033_48155ebf7a3ccceb_16521.txt
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Polyvector-valued gauge field theories in Clifford spaces are used to construct a novel Cl(3, 2) gauge theory of gravity that furnishes modified curvature and torsion tensors leading to important modifications of the standard gravitational action with a cosmological constant. Vacuum solutions exist which allow a cancel...
math/2710_db9c0f2f4b6f960d_325.txt
In the context of QFT and Gauge Theory, the introduction of Natural Units, as a quantization in disguise'' combined with Buckingham's Pi-Theorem, provides a direct connection with de Rham Periods, as also hinted by Feynman amplitudes, Dessins d'Enfant and Belyi maps models of baryon modes etc.A program emerges: Physics...
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math/107483_db9c0f2f4b6f960d_2827.txt
One is reminded in this paper of the often overlooked fact that the geometric straight line, or GSL, of Euclidean geometry is not necessarily identical with its usual Cartesian coordinatisation given by the real numbers in R. Indeed, the GSL is an abstract idea, while the Cartesian, or for that matter, any other specif...
math/1866757_bb0f8b9cd73ec091_609.txt
Condensed matter physics (2) The ergodic time is the time needed for a particle to explore the available phase space in a d system. In a disordered metal grain of size L and diffusion constant D, one has τerg ≃ L2/D. If the motion is ballistic (with velocity vF) rather than diffusive, one has in­ stead τerg ≃ L/vF. (3)...
math/353276_5aa5448a9477b0bf_348.txt
Bayesian optimization (BO) is a powerful framework to optimize black-box expensive-to-evaluate functions via sequential interactions. In several important problems (e.g. drug discovery, circuit design, neural architecture search, etc.), though, such functions are defined over large $\textit{combinatorial and unstructur...
math/735679_8faa9997ae6fbdd7_432.txt
The golden ratio is derived from a celebrated sequence of numbers discovered in 1202 by Leonardo of Pisa, also known as Fibonacci (his father was nicknamed Bo Nacci, or “the good natured guy,” so he was “the son of good nature”). Fibonacci noticed this special sequence of numbers by watching rabbits reproduce. “He assu...
math/4209381_c048c6987c9c5a0c_227.txt
EL: Yeah, and I just can't recommend — I haven't looked, I think I've looked at Experiencing Geometry, but not spent as much time with it as the crocheting one because around the time I, you know, a friend gave me a little crochet kit (not because of math at all, just because like, Oh, you like crafty things, you might...
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Where do you get the facts you’ve been vomiting? Most of the Trump supporters I know are highly educated. They’re not out stealing, looting, and vandalizing to promote “peace and equality”. How educated were the looters, thieves, and vandals that destroyed cities all over the country and took over city blocks to have d...
math/729033_48155ebf7a3ccceb_31631.txt
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***“Courage is rightly esteemed the first of human qualities . . . because it is the quality which guarantees all others.” – Winston Churchill*** ‘Veer Gatha’ CBSE activity was organized for grades 3 to 5 in the month of November to honour the acts of bravery and sacrifice of the officers/personnel of the armed forces ...
math/3742825_f4fb2ea9339839a1_240.txt
We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fixed angle away from the point of tethering. Using the kernel method, we derive the full generating function for this model in two and three di...
math/729033_088416c6542a36aa_14287.txt
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math/59738_e26caa74eb27f4da_69.txt
The data mixture for large language model pre-training significantly impacts performance, yet how to determine an effective mixture remains unclear. We propose RegMix to automatically identify a high-performing data mixture by formulating it as a regression task. RegMix trains many small models on diverse data mixtures...
math/1475_fd3fb90f22416ce7_1.txt
ACKNOWLEDGMENT The effort of many people went into producing this second volume in the Indexes to Mathematical Problems series. Their help is greatly appreciated. Data entry and proofreading were done by Selma Burrows, Mark Buxbaum, Michael Clarke, Anne R. Costa, Joan Duprey, Kathi Duprey, Cheryl Hoffman, Helen Metcalf...
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secant A line that intersects a curve, usually at more than one point, is called a secant of the curve. If the secant cuts the curve at two points, the segment of the line between the two points of intersection is called a CHORD of the curve. In planar geometry, the secant theorem refers to the property that the length...
math/3742825_d4655b6808b69bdd_2104.txt
Explicit deep generative models (DGMs), e.g., VAEs and Normalizing Flows, have shown to offer an effective data modelling alternative for lossless compression. However, DGMs themselves normally require large storage space and thus contaminate the advantage brought by accurate data density estimation. To eliminate the r...
math/ff5e2920_3926.txt
Feng Qian, Lingfeng Zhang, Tao Luo, Shiqi Xu, Zhijun Yu, and Wei Wang, Ant Group Today, cameras are everywhere, generating vast video evidence essential for justice, security, and legal matters. However, advanced video manipulation and creation techniques threaten their authenticity, casting doubt on their reliability....
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"The Dead Zone" would be hard to beat. Derived from the Stephen King novel about a man cursed with the ability to see the future with every handshake (and featuring Christopher Walken at his icy peak) converse all star, get ed out first. You might not be aware you've lost feeling in your feetMckenzie said: am aware of ...
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We construct nontrivial deformations of the standard map which preserve the symplectic actions, respectively the Lyapunov exponents, of infinitely many periodic orbits accumulating to an invariant curve. The proof uses a resonant normal-form construction to obtain a sequence of periodic orbits accumulating on an invari...
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In this paper we contribute to the frequently studied question of how to decompose a continuous piecewise linear (CPWL) function into a difference of two convex CPWL functions. Every CPWL function has infinitely many such decompositions, but for applications in optimization and neural network theory, it is crucial to f...
math/392d7b1a_0895.txt
Andrew S. Cassidy , Guillaume Garreau , Jay Sivagnaname , Mike Grassi , Bernard Brezzo , John V. Arthur , Dharmendra S. Modha We show for invertible problems that transform data from a source domain (for example, Logic Condition Tables (LCTs)) to a destination domain (for example, Hardware Description Language (HDL) co...
math/4922055_dcd4406d5f48241d_378.txt
CASTLES IN THE AIR 23 3. HOW TO BUILD FINANCIAL WEAPONS OF MASS DESTRUCTION 45 4. HURRICANE SEASON 69 5. MADLY IN ALL DIRECTIONS 99 6. TOMORROW CAPITALISM? 129 MY DEBTS 157 NOTES 159 REFERENCES 167 INDEX 179 I can calculate the motions of the heavenly bodies, but not the madness of people. -Isaac Newton, after losing a...
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Just gotta say, Rev Joe’s is the most sensible comment I’ve read here. Instead of spouting hate and describing liberalism as all the Venezuelan and Stalinist things it ain’t, why not just harvest whatever good stuff you can find in it and add to the list of best practices for improving our nation. We should pass on a b...
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Another mathematical “possible” to which Weyl gave a great deal of thought is the continuum. During the period 1918–1921 he wrestled with the problem of providing the mathematical continuum—the real number line—with a logically sound formulation. Weyl had become increasingly critical of the principles underlying the se...
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and other large galaxies can have as many as a trillion. Dwarf galaxies such as the aforementioned Large Magellanic Cloud have about 10 billion stars. Je n'ai rien contre car le gnosticisme s'est proccup des "archontes" en tant que "parasites extra terrestres" et tout semble converge pour faire de Yaldabatoh alias Jhov...
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The Department does not believe that it is either appropriate or consistent with the ADA to defer to local laws that prohibit certain breeds of dogs based on local concerns that these breeds may have a history of unprovoked aggression or attacks. Such deference would have the effect of limiting the rights of persons wi...
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Really the first president in how long that wanted to put our country first keep illegals out crack down on people abusing welfare bring jobs back to America. He was his worst enemy not you idiots and that election like most was decided before it ever happened. Trump as a person maybe you don’t like especially a lot of...
math/107483_db9c0f2f4b6f960d_2257.txt
According to general relativity the geometry of space depends on the distribution of matter or energy fields. The relation between the locally defined geometry parameters and the volume elements depends on curvature. Thus integration of local properties like energy density, defined in the Euclidean tangent space, does ...
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Satellite data has the potential to inspire a seismic shift for machine learning---one in which we rethink existing practices designed for traditional data modalities. As machine learning for satellite data (SatML) gains traction for its real-world impact, our field is at a crossroads. We can either continue applying i...
math/2853639_cfec8cd96ffe694b_269.txt
Numerical analysis in Zurich – 50 years ago∗ Martin H. Gutknecht Surely, applied mathematics originated in ancient times and slowly matured through the centuries, but it started to blossom colorfully only when electronic computers became available in the late 1940s and early 1950s. This was the gold miners’ time of com...
math/353276_f467e2efefddb294_609.txt
Generative models for materials, especially inorganic crystals, hold potential to transform the theoretical prediction of novel compounds and structures. Advancement in this field depends on robust benchmarks and minimal, information-rich datasets that enable meaningful model evaluation. This paper critically examines ...
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hyperbolic geometry (Lobachevskian geometry) Independently discovered in 1823 by Hungarian mathematician JÁNOS BOLYAI (1802–60) and in 1829 by Russian mathematician NIKOLAI IVANOVICH LOBACHEVSKY (1792–1856), hyperbolic geometry is a NON-EUCLIDEAN GEOMETRY in which the famous PARALLEL POSTULATE fails in the following ma...
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- TinySpline: Open source C-library for NURBS, B-splines and Bézier curves with bindings for various languages - C library to generate Bézier functions at compile time - Simple Bézier curve implementation via recursive method in Python
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The main cardioid is the period 1 continent. 35 It is the region of parameters c displaystyle c for which the map f c ( z ) z 2 c displaystyle f _ c (z) z 2 c has an attracting fixed point . 36 It consists of all parameters of the form c ( μ ) : μ 2 ( 1 μ 2 ) displaystyle c( mu ): frac mu ...
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Selecting high-quality pre-training data is important for creating capable language models, but existing methods rely on simple heuristics. We introduce QuRating, a method for selecting pre-training data that can capture human intuitions about data quality. In this paper, we investigate four qualities - writing style, ...
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**Mycorrhizal symbioses and tree diversity in global forest communities** Jiang, F.; Jiang, F.; Pu, X.; Schmid, B.; Reich, P. B.; Liang, J.; Abbasi, A. O.; Aguirre-Gutiérrez, J.; Zambrano, A. M. A.; Altman, J.; Álvarez-González, J. G.; Alves, L. F.; Amani, B. H. K.; Ammer, C.; Aymard, G. A.; Babu Kanda, N.; Bastian, M....
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The command from numarray import dot instructs the interpreter to load the function dot (which computes the dot product of two vectors) from the module numarray. The colon (:) operator, known as the slicing operator in Python, works the same way it does in MATLAB and Fortran90—it defines a section of an array. The state...
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There’s a trick in Birrell and Davies 1], credited to Unruh, for deducing the linear combination of Minkowski modes that corresponds to a given Rindler mode that bypasses the need to work out the Bogolyubov coefficients explicitly (though the normalization must be inserted by hand, and the switch to a second, alternati...
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A regular hexagon has six rotational symmetries ( rotational symmetry of order six ) and six reflection symmetries ( six lines of symmetry ), making up the dihedral group D 6 . 4 There are 16 subgroups. There are 8 up to isomorphism: itself (D 6 ), 2 dihedral: (D 3, D 2 ), 4 cyclic : (Z 6 , Z 3 , Z 2 , Z 1 ) and th...
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This bound (2.34) tells us that linear interpolations (n = 1) lead to errors that are proportional to h2 , whereas quadratic interpolations (n = 2) lead to errors proportional to h3 , for example. That is, halving h reduces the error by a factor of 4 and a factor of 8 in linear and quadratic interpolations, respectivel...
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Tree ap­prox­im­a­tion is a new form of non­lin­ear ap­prox­im­a­tion which ap­pears nat­ur­ally in some ap­plic­a­tions such as im­age pro­cessing and ad­apt­ive nu­mer­ic­al meth­ods. It is some­what more re­strict­ive than the usu­al \( n \)-term ap­prox­im­a­tion. We show that the re­stric­tions of tree ap­prox­im­...
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