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Since 2018, the potential for a high-energy neutrino telescope, named the Pacific Ocean Neutrino Experiment (P-ONE), has been thoroughly examined by two pathfinder missions, STRAW and STRAW-b, short for short for Strings for Absorption Length in Water. The P-ONE project seeks to install a neutrino detector with a one cubic kilometer volume in the Cascadia Basin's deep marine surroundings, situated near the western shores of Vancouver Island, Canada. To assess the environmental conditions and feasibility of constructing a neutrino detector of that scale, the pathfinder missions, STRAW and STRAW-b, have been deployed at a depth of 2.7 km within the designated site for P-ONE and were connected to the NEPTUNE observatory, operated by Ocean Networks Canada (ONC). While STRAW focused on analyzing the optical properties of water in the Cascadia Basin, \ac{strawb} employed cameras and spectrometers to investigate the characteristics of bioluminescence in the deep-sea environment. This report introduces the STRAW-b concept, covering its scientific objectives and the instrumentation used. Furthermore, it discusses the design considerations implemented to guarantee a secure and dependable deployment process of STRAW-b. Additionally, it showcases the data collected by battery-powered loggers, which monitored the mechanical stress on the equipment throughout the deployment. The report also offers an overview of STRAW-b's operation, with a specific emphasis on the notable advancements achieved in the data acquisition (DAQ) system and its successful integration with the server infrastructure of ONC., Comment: 20 pages, 11 figures, 2 tables

Consider a distribution of pebbles on a graph. A pebbling move removes two pebbles from a vertex and place one at an adjacent vertex. A vertex is reachable under a pebble distribution if it has a pebble after the application of a sequence of pebbling moves. A pebble distribution is solvable if each vertex is reachable under it. The size of a pebble distribution is the total number of pebbles. The optimal pebbling number $\pi^*(G)$ is the size of the smallest solvable distribution. A $t$-restricted pebble distribution places at most $t$ pebbles at each vertex. The $t$-restricted optimal pebbling number $\pi_t^*(G)$ is the size of the smallest solvable $t$-restricted pebble distribution. We show that deciding whether $\pi^*_2(G)\leq k$ is NP-complete. We prove that $\pi_t^*(G)=\pi^*(G)$ if $\delta(G)\geq \frac{2|V(G)|}{3}-1$ and we show infinitely many graphs which satisfies $\delta(H)\approx \frac{1}{2}|V(H)|$ but $\pi_t^*(H)\neq\pi^*(H)$, where $\delta$ denotes the minimum degree.

Kernel methods are the basis of most classical machine learning algorithms such as Gaussian Process (GP) and Support Vector Machine (SVM). Computing kernels using noisy intermediate scale quantum (NISQ) devices has attracted considerable attention due to recent progress in the design of NISQ devices. However noise and errors on current NISQ devices can negatively affect the predicted kernels. In this paper we utilize two quantum kernel machine learning (ML) algorithms to predict the labels of a Breast Cancer dataset on two different NISQ devices: quantum kernel Gaussian Process (qkGP) and quantum kernel Support Vector Machine (qkSVM). We estimate the quantum kernels on the 11 qubit IonQ and the 5 qubit IBMQ Belem quantum devices. Our results demonstrate that the predictive performances of the error mitigated quantum kernel machine learning algorithms improve significantly compared to their non-error mitigated counterparts. On both NISQ devices the predictive performances became comparable to those of noiseless quantum simulators and their classical counterparts, Comment: The result of paper is for IBMQ Belem Computer with old technology

The STRings for Absorption length in Water (STRAW) are the first in a series of pathfinders for the Pacific Ocean Neutrino Experiment (P-ONE), a future large-scale neutrino telescope in the north-eastern Pacific Ocean. STRAW consists of two 150 m long mooring lines instrumented with optical emitters and detectors. The pathfinder is designed to measure the attenuation length of the water and perform a long-term assessment of the optical background at the future P-ONE site. After two years of continuous operation, measurements from STRAW show an optical attenuation length of about 28 metres at 450 nm. Additionally, the data allow a study of the ambient undersea background. The overall optical environment reported here is comparable to other deep-water neutrino telescopes and qualifies the site for the deployment of P-ONE., Comment: 11 pages, 13 figures

A pebbling move on a graph removes two pebbles from a vertex and adds one pebble to an adjacent vertex. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using pebbling moves. The optimal pebbling number $\pi_{opt}$ is the smallest number m needed to guarantee a pebble distribution of m pebbles from which any vertex is reachable. The optimal pebbling number of the square grid graph $P_n\square P_m$ was investigated in several papers. In this paper, we present a new method using some recent ideas to give a lower bound on $\pi_{opt}$. We apply this technique to prove that $\pi_{opt}(P_n\square P_m)\geq \frac{2}{13}nm$. Our method also gives a new proof for $\pi_{opt}(P_n)=\pi_{opt}(C_n)=\left\lceil\frac{2n}{3}\right\rceil$.

Consider a distribution of pebbles on a connected graph $G$. A pebbling move removes two pebbles from a vertex and places one to an adjacent vertex. A vertex is reachable under a pebbling distribution if it has a pebble after the application of a sequence of pebbling moves. The optimal pebbling number $\pi^*(G)$ is the smallest number of pebbles which we can distribute in such a way that each vertex is reachable. It was known that the optimal pebbling number of any connected graph is at most $\frac{4n}{\delta+1}$, where $\delta$ is the minimum degree of the graph. We strengthen this bound by showing that equality cannot be attained and that the bound is sharp. If $\operatorname{diam}(G)\geq 3$ then we further improve the bound to $\pi^*(G)\leq\frac{3.75n}{\delta+1}$. On the other hand, we show that for arbitrary large diameter and any $\epsilon>0$ there are infinitely many graphs whose optimal pebbling number is bigger than $\left(\frac{8}{3}-\epsilon\right)\frac{n}{(\delta+1)}$.

A pebbling move on a graph removes two pebbles from a vertex and adds one pebble to an adjacent vertex. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using pebbling moves. The optimal pebbling number $\pi_{opt}$ is the smallest number $m$ needed to guarantee a pebble distribution of $m$ pebbles from which any vertex is reachable. A rubbling move is similar to a pebbling move, but it can remove the two pebbles from two different vertex. The optimal rubbling number $\rho_{opt}$ is defined analogously to the optimal pebbling number. In this paper we give lower bounds on both the optimal pebbling and rubbling numbers by the distance $k$ domination number. With this bound we prove that for each $k$ there is a graph $G$ with diameter $k$ such that $\rho_{opt}(G)=\pi_{opt}(G)=2^k$.

Let G be a graph with a distribution of pebbles on its vertices. A pebbling move consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The optimal pebbling number of G is the smallest number of pebbles which can placed on the vertices of G such that, for any vertex v of G, there is a sequence of pebbling moves resulting in at least one pebble on v. We determine the optimal pebbling number for several classes of induced subgraphs of the square grid, which we call staircase graphs.

In [C. Xue, C. Yerger: Optimal Pebbling on Grids, Graphs and Combinatorics] the authors conjecture that if every vertex of an infinite square grid is reachable from a pebble distribution, then the covering ratio of this distribution is at most $3.25$. First we present such a distribution with covering ratio $3.5$, disproving the conjecture. The authors in the above paper also claim to prove that the covering ratio of any pebble distribution is at most $6.75$. The proof contains some errors. We present a few interesting pebble distributions that this proof does not seem to cover and highlight some other difficulties of this topic.

A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this new move, one pebble each is removed at vertices $v$ and $w$ adjacent to a vertex $u$, and an extra pebble is added at vertex $u$. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using rubbling moves. The optimal rubbling number is the smallest number $m$ needed to guarantee a pebble distribution of $m$ pebbles from which any vertex is reachable. We determine the optimal rubbling number of ladders ($P_n\square P_2$), prisms ($C_n\square P_2$) and M\"oblus-ladders.