Remarks on a Constrained Optimization Problem for the Ginibre Ensemble

We study the limiting distribution of the eigenvalues of the Ginibre ensemble conditioned on the event that a certain proportion lie in a given region of the complex plane. Using an equivalent formulation as an obstacle problem, we describe the optimal distribution and some of its monotonicity properties.     

A Light‐Activated Olefin Metathesis Catalyst Equipped with a Chromatic Orthogonal Self‐Destruct Function

A sulfur‐chelated photolatent ruthenium olefin metathesis catalyst has been equipped with supersilyl protecting groups on the N‐heterocyclic carbene ligand. The silyl groups function as an irreversible chromatic kill switch, thus decomposing the catalyst when it is irradiated with 254 nm UV light. Therefore, different types of olefin metathesis reactions may be started by irradiation with 350 nm UV light and prevented by irradiation with shorter wavelengths. The possibility to induce and impede catalysis just by using light of different frequencies opens the pathway for stereolithographic applications and novel light‐guided chemical sequences.     

A framework for reasoning under uncertainty based on non-deterministic distance semantics

In this paper, we introduce a general and modular framework for formalizing reasoning with incomplete and inconsistent information. Our framework is composed of non-deterministic semantic structures and distance-based considerations. This combination leads to a variety of entailment relations that can be used for reasoning about non-deterministic phenomena and are inconsistency-tolerant. We investigate the basic properties of these entailments, as well as some of their computational aspects, and demonstrate their usefulness in the context of model-based diagnostic systems.     

ℤ2-Graded Number Theory

Let ? be the set of pairs of integers, together with addition and multiplication as given in (1) and (2) below. The arithmetics of ? reflects a certain arithmetics of characters of symmetric groups, whose corresponding Young diagrams are supported on hooks. This arithmetics gives rise to a ?₂-graded (or super or hyperbolic) number theory. Many theorems from number theory have their ?₂-graded analogues in ?. Here we study a few basic aspects of that theory.     

Nonlocal surface-wave solitons

We demonstrate, experimentally and theoretically, surface-wave solitons occurring at the interface between a dielectric medium (air) and a nonlinear material with a very long-range nonlocal response. These surface solitons are always attracted toward the surface, and unlike their Kerr-like counterparts, they do not exhibit a power threshold.     

Quenched invariance principle for random walks in balanced random environment

We consider random walks in a balanced random environment in ${\mathbb{Z}^d}$ , d?≥ 2. We first prove an invariance principle (for d?≥ 2) and the transience of the random walks when d?≥ 3 (recurrence when d?=?2) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for random walks in i.i.d. balanced environments.     

Observation of random-phase gap solitons in photonic lattices

We report what is to our knowledge the first experimental observation of gap random-phase lattice solitons: self-trapped spatially incoherent entities whose modal constituents lie within a photonic bandgap.