Unstructured Randomness, Small Gaps and Localization

We study the Hamiltonian associated with the quantum adiabatic algorithm with a random cost function. Because the cost function lacks structure we can prove results about the ground state. We find the ground state energy as the number of bits goes to infinity, show that the minimum gap goes to zero exponentially quickly, and we see a localization transition. We prove that there are no levels approaching the ground state near the end of the evolution. We do not know which features of this model are shared by a quantum adiabatic algorithm applied to random instances of satisfiability since despite being random they do have bit structure

No-gaps delocalization for general random matrices

We prove that with high probability, every eigenvector of a random matrix is delocalized in the sense that any subset of its coordinates carries a non-negligible portion of its $\ell_2$ norm. Our results pertain to a wide class of random matrices, including matrices with independent entries, symmetric and skew-symmetric matrices, as well as some other naturally arising ensembles. The matrices can be real and complex; in the latter case we assume that the real and imaginary parts of the entries are independent.Comment: 45 page

Evidence for DNA-mediated nuclear compartmentalization distinct from phase separation.

RNA Polymerase II (Pol II) and transcription factors form concentrated hubs in cells via multivalent protein-protein interactions, often mediated by proteins with intrinsically disordered regions. During Herpes Simplex Virus infection, viral replication compartments (RCs) efficiently enrich host Pol II into membraneless domains, reminiscent of liquid-liquid phase separation. Despite sharing several properties with phase-separated condensates, we show that RCs operate via a distinct mechanism wherein unrestricted nonspecific protein-DNA interactions efficiently outcompete host chromatin, profoundly influencing the way DNA-binding proteins explore RCs. We find that the viral genome remains largely nucleosome-free, and this increase in accessibility allows Pol II and other DNA-binding proteins to repeatedly visit nearby DNA binding sites. This anisotropic behavior creates local accumulations of protein factors despite their unrestricted diffusion across RC boundaries. Our results reveal underappreciated consequences of nonspecific DNA binding in shaping gene activity, and suggest additional roles for chromatin in modulating nuclear function and organization

Ising formulations of many NP problems

We provide Ising formulations for many NP-complete and NP-hard problems, including all of Karp's 21 NP-complete problems. This collects and extends mappings to the Ising model from partitioning, covering and satisfiability. In each case, the required number of spins is at most cubic in the size of the problem. This work may be useful in designing adiabatic quantum optimization algorithms.Comment: 27 pages; v2: substantial revision to intro/conclusion, many more references; v3: substantial revision and extension, to-be-published versio

Incubators, accelerators and urban economic development

We combine theory and evidence on incubator and accelerator programmes, and their effects on urban economic development. These structured co-working programmes have grown rapidly. However, a rich descriptive literature reveals little about their impact on participants or surrounding urban areas. We situate programmes in a conceptual framework of co-location tools, theorise objectives and benefits, and report findings from systematic, OECD-wide reviews of the evaluation literature. These evaluations provide evidence that accelerators and incubators raise participant employment, with accelerators also aiding access to finance. Ecosystem features such as university involvement and urban economic conditions also influence programme outcomes. However, evaluation evidence is less clear on detailed intervention design. We consider wider lessons and lay out an agenda for future research

Semantically Derived Geometric Constraints for {MVS} Reconstruction of Textureless Areas

Conventional multi-view stereo (MVS) approaches based on photo-consistency measures are generally robust, yet often fail in calculating valid depth pixel estimates in low textured areas of the scene. In this study, a novel approach is proposed to tackle this challenge by leveraging semantic priors into a PatchMatch-based MVS in order to increase confidence and support depth and normal map estimation. Semantic class labels on image pixels are used to impose class-specific geometric constraints during multiview stereo, optimising the depth estimation on weakly supported, textureless areas, commonly present in urban scenarios of building facades, indoor scenes, or aerial datasets. Detecting dominant shapes, e.g., planes, with RANSAC, an adjusted cost function is introduced that combines and weighs both photometric and semantic scores propagating, thus, more accurate depth estimates. Being adaptive, it fills in apparent information gaps and smoothing local roughness in problematic regions while at the same time preserves important details. Experiments on benchmark and custom datasets demonstrate the effectiveness of the presented approach