MVMO, a new weighted multi-objective attack, can inflate earnings and lower fraud scores in about 50 to 66 percent of firm-years, versus under 14 percent for standard attacks.
Casimir functions of free nilpotent Lie groups of steps three and four
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abstract
Any free nilpotent Lie algebra is determined by its rank and step. We consider free nilpotent Lie algebras of steps 3, 4 and corresponding connected and simply connected Lie groups. We construct Casimir functions of such groups, i.e., invariants of the coadjoint representation. For free 3-step nilpotent Lie groups we get a full description of coadjoint orbits. It turns out that general coadjoint orbits are affine subspaces, and special coadjoint orbits are affine subspaces or direct products of nonsingular quadrics. The knowledge of Casimir functions is useful for investigation of integration properties of dynamical systems and optimal control problems on Carnot groups. In particular, for some wide class of time-optimal problems on 3-step free Carnot groups we conclude that extremal controls corresponding to two-dimensional coadjoint orbits have the same behavior as in time-optimal problems on the Heisenberg group or on the Engel group.
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Adversarial Machine Learning Attacks on Financial Reporting via Maximum Violated Multi-Objective Attack
MVMO, a new weighted multi-objective attack, can inflate earnings and lower fraud scores in about 50 to 66 percent of firm-years, versus under 14 percent for standard attacks.