Cover pebbling numbers and bounds for certain families of graphs

Given a configuration of pebbles on the vertices of a graph, a pebbling move is defined by removing two pebbles from some vertex and placing one pebble on an adjacent vertex. The cover pebbling number of a graph, gamma(G), is the smallest number of pebbles such that through a sequence of pebbling moves, a pebble can eventually be placed on every vertex simultaneously, no matter how the pebbles are initially distributed. The cover pebbling number for complete multipartite graphs and wheel graphs is determined. We also prove a sharp bound for gamma(G) given the diameter and number of vertices of G.Comment: 10 pages, 1 figure, submitted to Discrete Mathematic

Domination Cover Pebbling: Structural Results

This paper continues the results of "Domination Cover Pebbling: Graph Families." An almost sharp bound for the domination cover pebbling (DCP) number for graphs G with specified diameter has been computed. For graphs of diameter two, a bound for the ratio between the cover pebbling number of G and the DCP number of G has been computed. A variant of domination cover pebbling, called subversion DCP is introducted, and preliminary results are discussed.Comment: 15 page

Reverse Shock Emission Revealed in Early Photometry in the Candidate Short GRB 180418A

We present observations of the possible short GRB 180418A in $\gamma$-rays, X-rays, and in the optical. Early optical photometry with the TAROT and RATIR instruments show a bright peak ($\approx$ 14.2 AB mag) between $T+28$ and $T+90$ seconds that we interpret as the signature of a reversal shock. Later observations can be modeled by a standard forward shock model and show no evidence of jet break, allowing us to constrain the jet collimation to $\theta_j> 7^\circ$. Using deep late-time optical observations we place an upper limit of $r>24$ AB mag on any underlying host galaxy. The detection of the afterglow in the \textit{Swift} UV filters constrains the GRB redshift to $z<1.3$ and places an upper bound on the $\gamma$-ray isotropic equivalent energy $E_{\rm{\gamma,iso}} < 3 \times 10^{51}$ erg. The properties of this GRB (e.g. duration, hardness ratio, energetic, and environment) lie at the intersection between short and long bursts, and we can not conclusively identify its type. We estimate that the probability that it is drawn from the population of short GRBs is 10\%-30\%.Comment: Accepted por publication in Ap

Formal modelling as a component of user centred design

User centred design approaches typically focus understanding on context and producing sketch designs. These sketches are often non functional (e.g., paper) prototypes. They provide a means of exploring candidate design possibilities using techniques such as cooperative evaluation. This paper describes a further step in the process using formal analysis techniques. The sketch design of a device is enhanced into a specification that is then analysed using formal techniques, thus providing a systematic approach to checking plausibility and consistency during early design stages. Once analysed, a further prototype is constructed using an executable form of the specification, providing the next candidate for evaluation with potential users. The technique is illustrated through an example based on a pill dispenser.We are grateful to Nuno Rodrigues, João Vilaça and Nuno Dias from IPCA (Polytechnic Institute of Cavado and Ave) who developed the first prototypeof the pill dispenser. José C. Campos, Paolo Masci and Michael Harrison werefunded by project NORTE-01-0145-FEDER-000016, financed by the North Por-tugal Regional Operational Programme (NORTE 2020), under the PORTUGAL2020 Partnership Agreement, and through the European Regional DevelopmentFund (ERDF)

CHERI Concentrate: Practical Compressed Capabilities

We present CHERI Concentrate, a new fat-pointer compression scheme applied to CHERI, the most developed capability-pointer system at present. Capability fat-pointers are a primary candidate for enforcing fine-grained and non-bypassable security properties in future computer systems, although increased pointer size can severely affect performance. Thus, several proposals for capability compression have been suggested but these did not support legacy instruction sets, ignored features critical to the existing software base, and also introduced design inefficiencies to RISC-style processor pipelines. CHERI Concentrate improves on the state-of-the-art region-encoding efficiency, solves important pipeline problems, and eases semantic restrictions of compressed encoding, allowing it to protect a full legacy software stack. We analyze and extend logic from the open-source CHERI prototype processor design on FPGA to demonstrate encoding efficiency, minimize delay of pointer arithmetic, and eliminate additional load-to-use delay. To verify correctness of our proposed high-performance logic, we present a HOL4 machine-checked proof of the decode and pointer-modify operations. Finally, we measure a 50%-75% reduction in L2 misses for many compiled C-language benchmarks running under a commodity operating system using compressed 128-bit and 64-bit formats, demonstrating both compatibility with and increased performance over the uncompressed, 256-bit format