In a companion paper, we introduced a notion of multi-Dirac structures, a graded version of Dirac structures, and we discussed their relevance for classical field theories. In the current paper we focus on the geometry of multi-Dirac structures. After recalling the basic definitions, we introduce a gradedmultiplication and amulti-Courant bracket on the space of sections of a multi-Dirac structu...

We interpret the physical B-field renormalization group flow in the language of Courant algebroids, clarifying the sense in which this flow is the natural “Ricci flow” for generalized geometry. Next we show that the B-field renormalization group flow preserves T-duality in a natural sense. As corollaries we obtain new long time existence results for the B-field renormalization group flow.

We consider several natural classes of committee scoring rules, namely, weakly separable, representation-focused, top-k-counting, OWAbased, and decomposable rules. We study some of their axiomatic properties, especially properties of monotonicity, and concentrate on containment relations between them. We characterize SNTV, Bloc, and k-approval Chamberlin–Courant, as the only rules in certain in...

Kuznetsov’s condition says that variables X and Y are independent when any product of bounded functions f X and g Y behaves in a certain way: the interval of expected values f X g Y must be equal to the interval product f X g Y . The main result of this paper shows how to compute lower expectations using Kuznetsov’s condition. We also generalize Kuznetsov’s condition to conditional expectation ...

Committee scoring voting rules are multiwinner analogues of positional scoring rules which constitute an important subclass of single-winner voting rules. We identify several natural subclasses of committee scoring rules, namely, weakly separable, representation-focused, top-$k$-counting, OWA-based, and decomposable rules. We characterize SNTV, Bloc, and $k$-Approval Chamberlin--Courant as the ...

Chromium (VI) (Cr(VI)) contamination of soil and groundwater is considered a major environmental concern. Bioreduction of Cr(VI) to chromium (III) (Cr(III)) can be considered an effective technology in remediating Cr(VI) contaminated sites. Among the Cr(VI) reducing bacteria, Shewanella oneidensis MR-1 (MR-1) is relatively effective. Reduction of Cr(VI) by MR-1 is defined by the dual-enzyme kin...

A computationally efficient, yet relatively simple Eulerian-Lagrangian method is proposed for solving the one-dimensional convection-dispersion solute transport equation assuming a steady or transient velocity field. The method uses a modified single-step reverse particle tracking (MSRPT) technique to handle steep concentration fronts. The scheme utilizes two weighting factors to control the mo...

We show that the Manin triple characterization of Lie bialgebras in terms of the Drinfel’d double may be extended to arbitrary Poisson manifolds and indeed Lie bialgebroids by using double cotangent bundles, rather than the direct sum structures (Courant algebroids) utilized for similar purposes by Liu, Weinstein and Xu. This is achieved in terms of an abstract notion of double Lie algebroid (w...