Modern multi-tenant AI clusters are increasingly communication-bound, driven by high-volume and multi-round GPU-to-GPU collective communication. Consequently, the GPU dispatcher’s choice of a physical GPU subset for each tenant largely determines the job’s effective collective bandwidth and thus its performance ceiling...
<p> Our objective in the present work is to develop a fairly complete arithmetic theory of critical <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics>...
The existence and uniqueness of universal Boolean algebras are shown and the classes in which such algebras exist are determined, and the universal algebras up to isomorphism are classified.
Cryptographic evidence systems face fundamental trade-offs between confidentiality (Conf), reliability (Rel), and opposability (Opp), with Conf<inline-formula> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula>Rel<inline-formula> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula>Opp products...
<jats:p> The thermal partition function, <jats:inline-formula> <jats:alternatives> <jats:tex-math>Z</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">...
A set <inline-formula> <tex-math notation="LaTeX">$S\subseteq V(G)$ </tex-math></inline-formula> is called a <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-total dominating set of a graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> if every vertex of <inlin...
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