Stochastic resonance on Newman-Watts networks of Hodgkin-Huxley neurons with local periodic driving

We study the phenomenon of stochastic resonance on Newman-Watts small-world networks consisting of biophysically realistic Hodgkin-Huxley neurons with a tunable intensity of intrinsic noise via voltage-gated ion channels embedded in neuronal membranes. Importantly thereby, the subthreshold periodic driving is introduced to a single neuron of the network, thus acting as a pacemaker trying to impose its rhythm on the whole ensemble. We show that there exists an optimal intensity of intrinsic ion channel noise by which the outreach of the pacemaker extends optimally across the whole network. This stochastic resonance phenomenon can be further amplified via fine-tuning of the small-world network structure, and depends significantly also on the coupling strength among neurons and the driving frequency of the pacemaker. In particular, we demonstrate that the noise-induced transmission of weak localized rhythmic activity peaks when the pacemaker frequency matches the intrinsic frequency of subthreshold oscillations. The implications of our findings for weak signal detection and information propagation across neural networks are discussed.     

Trace-preserving homomorphisms of semigroups

We consider those homomorphisms φ of semigroups of trace-class operators on a Hilbert space that preserve trace. If φ is a spatially induced isomorphism on a semigroup , that is φ(S)T=TS for an invertible operator T and for all S in , then φ clearly has this property. More generally, if T in the relation above is a densely defined, closed, injective operator with dense image, φ still preserves trace. We prove the converse of this statement under certain conditions. Using these results we prove simultaneous similarity theorems for semigroups of operators (on finite or infinite-dimensional spaces) whose members are individually similar to unitary or J-unitary operators.     

Cayley compositions,partitions, polytopes,and geometric bijections

In 1857, Cayley showed that certain sequences, now called Cayley compositions, are equinumerous with certain partitions into powers of 2. In this paper we give a simple bijective proof of this result and a geometric generalization to equality of Ehrhart polynomials between two convex polytopes. We then apply our results to give a new proof of Braun?s conjecture proved recently by the authors [15].     

Experimental investigation of integral and local flow field properties on rotating porous disc

Flow field through rotating porous disc was investigated with experimental fluid dynamics and compared with computational fluid dynamics. Open cell aluminum metal foam with 88% porosity was used. On rotating porous disc, integral measurements of static pressure difference in dependence of air volume flow rate were performed. Local measurements of velocity profiles close to disc circumference were performed with hot-wire anemometry. The airflow visualization method using smoke generator and digital camera was performed. Flow structures through porous disc were visualized at three different air volume flow rates. Numerical simulation of homogenous rotating porous disc was performed. Experimental and numerical results were compared. The results showed appropriate comparison of integral and local properties. The presented experimental approach can be used for the investigation and understanding of flow field phenomena on rotating porous materials. The proposed conclusions can be applied for variable applications on rotating porous materials.     

Toward characterizing locally common graphs

A graph $H$ is common if the number of monochromatic copies of $H$ in a 2-edge-coloring of the complete graph is asymptotically minimized by the random coloring. The classification of common graphs is one of the most intriguing problems in extremal graph theory. We study the notion of weakly locally common graphs considered by Csóka, Hubai, and Lovász [arXiv:1912.02926], where the graph is required to be the minimizer with respect to perturbations of the random 2-edge-coloring. We give a complete analysis of the 12 initial terms in the Taylor series determining the number of monochromatic copies of $H$ in such perturbations and classify graphs $H$ based on this analysis into three categories:

• Graphs of Class I are weakly locally common.
• Graphs of Class II are not weakly locally common.
• Graphs of Class III cannot be determined to be weakly locally common or not based on the initial 12 terms.

As a corollary, we obtain new necessary conditions on a graph to be common and new sufficient conditions on a graph to be not common.