Knowledge about complex events is usually incomplete in practice. Zeros can be utilized to capture such events within probability models. In this article, Geiger and Pearl’s conditional probabilistic independence statements are investigated in the presence of zeros. Random variables can be specified to be zero-free, i.e., to disallow zeros in their domains. Zero-free random variables provide an...

This paper presents the duality hypothesis of search and tagging, two important behaviors of web users. The hypothesis states that if a user views a document D in the search results for query Q, the user would tend to assign document D a tag identical to or similar to Q; similarly, if a user tags a document D with a tag T , the user would tend to view document D if it is in the search results o...

Bianchi type IX, ’Mixmaster’ universes are investigated in low-energyeffective-action string cosmology. We show that, unlike in general relativity, there is no chaos in these string cosmologies for the case of the tree-level action. The characteristic Mixmaster evolution through a series of Kasner epochs is studied in detail. In the Einstein frame an infinite sequence of chaotic oscillations of...

W introduce the pathwise optimization (PO) method, a new convex optimization procedure to produce upper and lower bounds on the optimal value (the “price”) of a high-dimensional optimal stopping problem. The PO method builds on a dual characterization of optimal stopping problems as optimization problems over the space of martingales, which we dub the martingale duality approach. We demonstrate...

We introduce the Quantum Dissipative Villain (QDV) model as a prototype model to study tunneling in dissipative quantum mechanics. Dissipation is provided by a coupled linear environment. In the QDV model, the discrete character of a tunneling degree of freedom coupled to an environment is explicit, leading to a rich dual structure. We derive general exact mappings of the QDV model on several d...

We present a combinatorial method for the min-cost flow problem and prove that its expected running time is bounded by Õ(m3/2). This matches the best known bounds, which previously have only been achieved by numerical algorithms or for special cases. Our contribution contains three parts that might be interesting in their own right: (1) We provide a construction of an equivalent auxiliary netwo...

In a nutshell, a duality for a constraint satisfaction problem equates the existence of one homomorphism to the non-existence of other homomorphisms. In this survey paper, we give an overview of logical, combinatorial, and algebraic aspects of the following forms of duality for constraint satisfaction problems: finite duality, bounded pathwidth duality, and bounded treewidth duality.

in this paper, using clarke’s generalized directional derivative and di-invexity we introduce new concepts of nonsmooth k-α-di-invex and generalized type i univex functions over cones for a nonsmooth vector optimization problem with cone constraints. we obtain some sufficient optimality conditions and mond-weir type duality results under the foresaid generalized invexity and type i cone-univexi...

In a first contribution, we revisit two certificates of positivity on (possibly non-compact) basic semialgebraic sets due to Putinar and Vasilescu (C R Acad Sci Ser I Math 328(6):495–499, 1999). We use Jacobi’s technique from (Math Z 237(2):259–273, 2001) provide an alternative proof with effective degree bound the sums squares weights in such certificates. As consequence, it allows one define ...

We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. propose data-driven approach to stabilize systems when only sample trajectories dynamics accessible. Our method is built on density-function-based stability certificate that dual Lyapunov function for dynamic systems. Unlike Lyapunov-based methods, density functions lea...