Computational Complexity of Synchronization under Regular Commutative Constraints

Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint languages, we give a full classification of the computational complexity of the constraint synchronization problem. Depending on the constraint language, our problem becomes PSPACE-complete, NP-complete or polynomial time solvable. In addition, we derive a polynomial time decision procedure for the complexity of the constraint synchronization problem, given some constraint automaton accepting a commutative language as input.Comment: Published in COCOON 2020 (The 26th International Computing and Combinatorics Conference); 2nd version is update of the published version and 1st version; both contain a minor error, the assumption of maximality in the NP-c and PSPACE-c results (propositions 5 & 6) is missing, and of incomparability of the vectors in main theorem; fixed in this version. See (new) discussion after main theore

Faster Exploration of Some Temporal Graphs

A temporal graph G = (G1, G2,..., GT ) is a graph represented by a sequence of T graphs over a common set of vertices, such that at the ith time step only the edge set Ei is active. The temporal graph exploration problem asks for a shortest temporal walk on some temporal graph visiting every vertex. We show that temporal graphs with n vertices can be explored in O(kn1.5 log n) days if the underlying graph has treewidth k and in O(n1.75 log n) days if the underlying graph is planar. Furthermore, we show that any temporal graph whose underlying graph is a cycle with k chords can be explored in at most 6kn days. Finally, we demonstrate that there are temporal realisations of sub cubic planar graphs that cannot be explored faster than in Ω(n log n) days. All these improve best known results in the literature

On the Number of Synchronizing Colorings of Digraphs

We deal with $k$-out-regular directed multigraphs with loops (called simply \emph{digraphs}). The edges of such a digraph can be colored by elements of some fixed $k$-element set in such a way that outgoing edges of every vertex have different colors. Such a coloring corresponds naturally to an automaton. The road coloring theorem states that every primitive digraph has a synchronizing coloring. In the present paper we study how many synchronizing colorings can exist for a digraph with $n$ vertices. We performed an extensive experimental investigation of digraphs with small number of vertices. This was done by using our dedicated algorithm exhaustively enumerating all small digraphs. We also present a series of digraphs whose fraction of synchronizing colorings is equal to $1-1/k^d$, for every $d \ge 1$ and the number of vertices large enough. On the basis of our results we state several conjectures and open problems. In particular, we conjecture that $1-1/k$ is the smallest possible fraction of synchronizing colorings, except for a single exceptional example on 6 vertices for $k=2$.Comment: CIAA 2015. The final publication is available at http://link.springer.com/chapter/10.1007/978-3-319-22360-5_1

Somatic Integration of Single Ion Channel Responses of α7 Nicotinic Acetylcholine Receptors Enhanced by PNU-120596

Positive allosteric modulators of highly Ca2+-permeable α7 nicotinic acetylcholine receptors, such as PNU-120596, may become useful therapeutic tools supporting neuronal survival and function. However, despite promising results, the initial optimism has been tempered by the concerns for cytotoxicity. The same concentration of a given nicotinic agent can be neuroprotective, ineffective or neurotoxic due to differences in the expression of α7 receptors and susceptibility to Ca2+ influx among various subtypes of neurons. Resolution of these concerns may require an ability to reliably detect, evaluate and optimize the extent of α7 somatic ionic influx, a key determinant of the likelihood of neuronal survival and function. In the presence of PNU-120596 and physiological choline (∼10 µM), the activity of individual α7 channels can be detected in whole-cell recordings as step-like current/voltage deviations. However, the extent of α7 somatic influx remains elusive because the activity of individual α7 channels may not be integrated across the entire soma, instead affecting only specific subdomains located in the channel vicinity. Such a compartmentalization may obstruct detection and integration of α7 currents, causing an underestimation of α7 activity. By contrast, if step-like α7 currents are integrated across the soma, then a reliable quantification of α7 influx in whole-cell recordings is possible and could provide a rational basis for optimization of conditions that support survival of α7-expressing neurons. This approach can be used to directly correlate α7 single-channel activity to neuronal function. In this study, somatic dual-patch recordings were conducted using large hypothalamic and hippocampal neurons in acute coronal rat brain slices. The results demonstrate that the membrane electrotonic properties do not impede somatic signaling, allowing reliable estimates of somatic ionic and Ca2+ influx through α7 channels, while the somatic space-clamp error is minimal (∼0.01 mV/µm). These research efforts could benefit optimization of potential α7-PAM-based therapies

Characterization of inverted coaxial 76 Ge detectors in GERDA for future double- β decay experiments

Neutrinoless double-β decay of 76Ge is searched for with germanium detectors where source and detector of the decay are identical. For the success of future experiments it is important to increase the mass of the detectors. We report here on the characterization and testing of five prototype detectors manufactured in inverted coaxial (IC) geometry from material enriched to 88% in 76Ge. IC detectors combine the large mass of the traditional semi-coaxial Ge detectors with the superior resolution and pulse shape discrimination power of point contact detectors which exhibited so far much lower mass. Their performance has been found to be satisfactory both when operated in vacuum cryostat and bare in liquid argon within the Gerda setup. The measured resolutions at the Q-value for double-β decay of 76Ge (Qββ = 2039 keV) are about 2.1 keV full width at half maximum in vacuum cryostat. After 18 months of operation within the ultra-low background environment of the GERmanium Detector Array (Gerda) experiment and an accumulated exposure of 8.5 kg⋅year, the background index after analysis cuts is measured to be 4.9+7.3−3.4×10−4 counts/(keV⋅kg⋅year) around Qββ. This work confirms the feasibility of IC detectors for the next-generation experiment Legend

Search for tri-nucleon decays of ^{76}Ge in GERDA

We search for tri-nucleon decays of 76Ge in the dataset from the GERmanium Detector Array (GERDA) experiment. Decays that populate excited levels of the daughter nucleus above the threshold for particle emission lead to disintegration and are not considered. The ppp-, ppn-, and pnn-decays lead to 73Cu, 73Zn, and 73Ga nuclei, respectively. These nuclei are unstable and eventually proceed by the beta decay of 73Ga to 73Ge (stable). We search for the 73Ga decay exploiting the fact that it dominantly populates the 66.7 keV 73mGa state with half-life of 0.5 s. The nnn-decays of 76Ge that proceed via 73mGe are also included in our analysis. We find no signal candidate and place a limit on the sum of the decay widths of the inclusive tri-nucleon decays that corresponds to a lower lifetime limit of 1.2×1026 yr  (90% credible interval). This result improves previous limits for tri-nucleon decays by one to three orders of magnitude

Pulse shape analysis in GERDA Phase II

The GERmanium Detector Array (GERDA) collaboration searched for neutrinoless double-\beta decay in ^{76}Ge using isotopically enriched high purity germanium detectors at the Laboratori Nazionali del Gran Sasso of INFN. After Phase I (2011–2013), the experiment benefited from several upgrades, including an additional active veto based on LAr instrumentation and a significant increase of mass by point-contact germanium detectors that improved the half-life sensitivity of Phase II (2015–2019) by an order of magnitude. At the core of the background mitigation strategy, the analysis of the time profile of individual pulses provides a powerful topological discrimination of signal-like and background-like events. Data from regular ^{228}Th calibrations and physics data were both considered in the evaluation of the pulse shape discrimination performance. In this work, we describe the various methods applied to the data collected in GERDA Phase II corresponding to an exposure of 103.7 kg year. These methods suppress the background by a factor of about 5 in the region of interest around Q_{\beta \beta }= 2039 keV, while preserving (81\pm 3)% of the signal. In addition, an exhaustive list of parameters is provided which were used in the final data analysis

Liquid argon light collection and veto modeling in GERDA Phase II

The ability to detect liquid argon scintillation light from within a densely packed high-purity germanium detector array allowed the Gerda experiment to reach an exceptionally low background rate in the search for neutrinoless double beta decay of 76 Ge. Proper modeling of the light propagation throughout the experimental setup, from any origin in the liquid argon volume to its eventual detection by the novel light read-out system, provides insight into the rejection capability and is a necessary ingredient to obtain robust background predictions. In this paper, we present a model of the Gerda liquid argon veto, as obtained by Monte Carlo simulations and constrained by calibration data, and highlight its application for background decomposition