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At Microsoft our mission and values are to help people and businesses throughout the world realize their full potential.
We determined the Newtonian Constant of Gravitation G by interferometrically measuring the change in spacing between two free-hanging pendulum masses caused by the gravitational field from large tungsten source masses. We find a value for G of (6.672...
society engenders caring labor, theorists Sara Ruddick, Virginia Held, and Eva Feder Kittay suggest caring should be performed and care givers valued in
Beyond assigning the correct class, an activity recognition model should also be able to determine, how certain it is in its predictions. We present the first study of how welthe confidence values of modern action recognition architectures indeed ref...
We prove the finiteness of the Zsigmondy set associated to the critical orbit of f(z) = z^d+c for rational values of c by finding an effective bound on the size of the set. For non-recurrent critical orbits, the Zsigmondy set is explicitly computed b...
This paper presents a predictive framework for adversarial energy-depletion defense against a maneuverable inbound threat (IT). The IT solves a receding-horizon problem to minimize its own energy while reaching a high-value asset (HVA) and avoiding i...
Without strip (), bananas is present in the dictionary but with an empty string as value. With strip (), this code will throw an exception because it strips the tab of the banana line.
Excellent people, products and customer service are building blocks for success – and Ivans is building on all of these. The Ivans team works together with our customers to help them get the most value …
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Chinese literary classics hold significant cultural and educational value, offering deep insights into morality, history, and human nature. These works often include classical Chinese and complex narratives, making them difficult for children to read...
The demands for accurate and representative generative AI systems means there is an increased demand on participatory evaluation structures. While these participatory structures are paramount to to ensure non-dominant values, knowledge and material c...
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Threat analysts routinely rely on natural-language reports that describe attacker actions without enumerating the full kill chain or the dependencies between phases, making automated reconstruction of ATT&CK consistent intrusion paths a difficult ope...
We present here simple trace formulas for Hecke operators $T_k(p)$ for all $p>3$ on $S_k(Γ_0(3))$ and $S_k(Γ_0(9))$, the spaces of cusp forms of weight $k$ and levels 3 and 9. These formulas can be expressed in terms of special values of Gaussian h...
We present here a formula for expressing the trace of the Frobenius endomorphism of an elliptic curve $E$ over $\mathbb{F}_q$ satisfying $j(E)\neq 0,1728$ and $q\equiv 1 \pmod{12}$ in terms of special values of Gaussian hypergeometric series. This...
In his 1972 paper, John Lamperti characterized all positive self-similar Markov processes as time-changes of exponentials of Levy processes. In the past decade the problem of classifying all non-negative self-similar Markov processes that do not nece...