Super-resolution provided by the arbitrarily strong superlinearity of the blackbody radiation

Blackbody radiation is a fundamental phenomenon in nature, and its explanation by Planck marks a cornerstone in the history of Physics. In this theoretical work, we show that the spectral radiance given by Planck's law is strongly superlinear with temperature, with an arbitrarily large local exponent for decreasing wavelengths. From that scaling analysis, we propose a new concept of super-resolved detection and imaging: if a focused beam of energy is scanned over an object that absorbs and linearly converts that energy into heat, a highly nonlinear thermal radiation response is generated, and its point spread function can be made arbitrarily smaller than the excitation beam focus. Based on a few practical scenarios, we propose to extend the notion of super-resolution beyond its current niche in microscopy to various kinds of excitation beams, a wide range of spatial scales, and a broader diversity of target objects

Bis-rhodamines bridged with a diazoketone linker: synthesis, structure, and photolysis

Two fluorophores bound with a short photoreactive bridge are fascinating structures and remained unexplored. To investigate the synthesis and photolysis of such dyes, we linked two rhodamine dyes via a diazoketone bridge (−COCN2−) attached to position 5′ or 6′ of the pendant phenyl rings. For that, the mixture of 5′- or 6′-bromo derivatives of the parent dye was prepared, transformed into 1,2-diarylacetylenes, hydrated to 1,2-diarylethanones, and converted to diazoketones Ar1COCN2Ar2. The high performance liquid chromatography (HPLC) separation gave four individual regioisomers of Ar1COCN2Ar2. Photolysis of the model compound─C6H5COCN2C6H5─in aqueous acetonitrile at pH 7.3 and under irradiation with 365 nm light provided diphenylacetic acid amide (Wolff rearrangement). However, under the same conditions, Ar1COCN2Ar2 gave mainly α-diketones Ar1COCOAr2. The migration ability of the very bulky dye residues was low, and the Wolff rearrangement did not occur. We observed only moderate fluorescence increase, which may be explained by the insufficient quenching ability of diazoketone bridge (−COCN2−) and its transformation into another (weaker) quencher, 1,2-diarylethane-1,2-dione

Relating Structure and Power: Comonadic Semantics for Computational Resources

Combinatorial games are widely used in finite model theory, constraint satisfaction, modal logic and concurrency theory to characterize logical equivalences between structures. In particular, Ehrenfeucht-Fraisse games, pebble games, and bisimulation games play a central role. We show how each of these types of games can be described in terms of an indexed family of comonads on the category of relational structures and homomorphisms. The index k is a resource parameter which bounds the degree of access to the underlying structure. The coKleisli categories for these comonads can be used to give syntax-free characterizations of a wide range of important logical equivalences. Moreover, the coalgebras for these indexed comonads can be used to characterize key combinatorial parameters: tree-depth for the Ehrenfeucht-Fraisse comonad, tree-width for the pebbling comonad, and synchronization-tree depth for the modal unfolding comonad. These results pave the way for systematic connections between two major branches of the field of logic in computer science which hitherto have been almost disjoint: categorical semantics, and finite and algorithmic model theory.Comment: To appear in Proceedings of Computer Science Logic 201

Constraint Satisfaction with Counting Quantifiers

We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly between exists^1:=exists and exists^n:=forall (the domain being of size n) already affords the maximal possible complexity of QCSPs (which have both exists and forall), being Pspace-complete for a suitably chosen template. Next, we focus on the complexity of subsets of counting quantifiers on clique and cycle templates. For cycles we give a full trichotomy -- all such problems are in L, NP-complete or Pspace-complete. For cliques we come close to a similar trichotomy, but one case remains outstanding. Afterwards, we consider the generalisation of CSPs in which we augment the extant quantifier exists^1:=exists with the quantifier exists^j (j not 1). Such a CSP is already NP-hard on non-bipartite graph templates. We explore the situation of this generalised CSP on bipartite templates, giving various conditions for both tractability and hardness -- culminating in a classification theorem for general graphs. Finally, we use counting quantifiers to solve the complexity of a concrete QCSP whose complexity was previously open

Deep Brain Stimulation Programming 2.0: Future Perspectives for Target Identification and Adaptive Closed Loop Stimulation

Deep brain stimulation has developed into an established treatment for movement disorders and is being actively investigated for numerous other neurological as well as psychiatric disorders. An accurate electrode placement in the target area and the effective programming of DBS devices are considered the most important factors for the individual outcome. Recent research in humans highlights the relevance of widespread networks connected to specific DBS targets. Improving the targeting of anatomical and functional networks involved in the generation of pathological neural activity will improve the clinical DBS effect and limit side-effects. Here, we offer a comprehensive overview over the latest research on target structures and targeting strategies in DBS. In addition, we provide a detailed synopsis of novel technologies that will support DBS programming and parameter selection in the future, with a particular focus on closed-loop stimulation and associated biofeedback signals