P\'olya number of continuous-time quantum walks

We propose a definition for the P\'olya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of measurements on the system, each carried out on a different member from an ensemble in order to minimize the disturbance caused by it. We examine various graphs, including the ring, the line, higher dimensional integer lattices and a number of other graphs and calculate their P\'olya number. For the timing of the measurements a Poisson process as well as regular timing are discussed. We find that the speed of decay for the probability at the origin is the key for recurrence.Comment: 8 pages, no figures. Accepted for publication in Physical Review

Poor sleep quality predicts psychotic‐like symptoms: an experience sampling study in young adults with schizotypal traits

Objective: Psychotic-like experiences (PLEs) are unusual experiences such as perceptual abnormalities and delusional-like thoughts that resemble the symptoms of psychosis at the sub-clinical level. PLEs are associated with sleep complaints in healthy and clinical samples; however, evidence for day-to-day associations between poor sleep and subsequent PLEs under naturalistic conditions is scarce. We hypothesized that poor sleep quality would predict next days’ PLEs, and vice versa, daytime PLEs would be associated with worse subsequent sleep quality. Method: Seventy-three university students with moderate to high levels of positive schizotypy participated in an experience sampling study. Participants rated their sleep each morning, as well as PLEs and affective states during the day over 3 weeks. Results: Multilevel regression models indicated that poor sleep quality predicted increased PLEs the following day. Poor sleep was linked to negative daytime mood that partially mediated the associations between sleep quality and next days’ PLEs. Furthermore, PLEs were enhanced in the evening as compared to daytime reports. The prediction of poor sleep quality by previous days’ PLEs was negligible. Conclusions: The results are consistent with the position that sleep related interventions might reduce the risk of psychosis, especially in individuals that tend to experience psychotic-like phenomena and negative affect

Syntactic Markovian Bisimulation for Chemical Reaction Networks

In chemical reaction networks (CRNs) with stochastic semantics based on continuous-time Markov chains (CTMCs), the typically large populations of species cause combinatorially large state spaces. This makes the analysis very difficult in practice and represents the major bottleneck for the applicability of minimization techniques based, for instance, on lumpability. In this paper we present syntactic Markovian bisimulation (SMB), a notion of bisimulation developed in the Larsen-Skou style of probabilistic bisimulation, defined over the structure of a CRN rather than over its underlying CTMC. SMB identifies a lumpable partition of the CTMC state space a priori, in the sense that it is an equivalence relation over species implying that two CTMC states are lumpable when they are invariant with respect to the total population of species within the same equivalence class. We develop an efficient partition-refinement algorithm which computes the largest SMB of a CRN in polynomial time in the number of species and reactions. We also provide an algorithm for obtaining a quotient network from an SMB that induces the lumped CTMC directly, thus avoiding the generation of the state space of the original CRN altogether. In practice, we show that SMB allows significant reductions in a number of models from the literature. Finally, we study SMB with respect to the deterministic semantics of CRNs based on ordinary differential equations (ODEs), where each equation gives the time-course evolution of the concentration of a species. SMB implies forward CRN bisimulation, a recently developed behavioral notion of equivalence for the ODE semantics, in an analogous sense: it yields a smaller ODE system that keeps track of the sums of the solutions for equivalent species.Comment: Extended version (with proofs), of the corresponding paper published at KimFest 2017 (http://kimfest.cs.aau.dk/

Parentage testing and looking for single nucleotide markers associated with antler quality in deer (<i>Cervus elaphus</i>)

To provide a cost-efficient parentage testing kit for red deer (Cervus elaphus), a 63 SNP set has been developed from a high-density Illumina BovineHD BeadChip containing 777 962 SNPs after filtering of genotypes of 50 stags. The successful genotyping rate was 38.6 % on the chip. The ratio of polymorphic loci among effectively genotyped loci was 6.5 %. The selected 63 SNPs have been applied to 960 animals to perform parentage control. Thirty SNPs out of the 63 had worked on the OpenArray platform. Their combined value of the probability of identity and exclusion probability was 4.9×10-11 and 0.99803, respectively. A search for loci linked with antler quality was also performed on the genotypes of the above-mentioned stags. Association studies revealed 14 SNPs associated with antler quality, where low-quality antlers with short and thin main beam antlers had values from 1 to 2, while high-quality antlers with long and strong main beams had values between 4 and 5. The chance for a stag to be correctly identified as having high-value antlers is expected to be over 88 %.</p

Spine neck plasticity regulates compartmentalization of synapses

Dendritic spines have been proposed to transform synaptic signals through chemical and electrical compartmentalization. However, the quantitative contribution of spine morphology to synapse compartmentalization and its dynamic regulation are still poorly understood. We used time-lapse super-resolution stimulated emission depletion (STED) imaging in combination with fluorescence recovery after photobleaching (FRAP) measurements, two-photon glutamate uncaging, electrophysiology and simulations to investigate the dynamic link between nanoscale anatomy and compartmentalization in live spines of CA1 neurons in mouse brain slices. We report a diversity of spine morphologies that argues against common categorization schemes and establish a close link between compartmentalization and spine morphology, wherein spine neck width is the most critical morphological parameter. We demonstrate that spine necks are plastic structures that become wider and shorter after long-term potentiation. These morphological changes are predicted to lead to a substantial drop in spine head excitatory postsynaptic potential (EPSP) while preserving overall biochemical compartmentalization