# Death Chain ##HOT##

Deathchain (originally named Winterwolf) is a Finnish extreme metal band from Kuopio.[2] The band is signed to Dynamic Arts Records and toured Europe with Candlemass and Destruction in late 2005.[citation needed]

## Death Chain

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The Hyper-cube queuing model was developed 45 years ago to solve spatial queuing problems and has been widely applied to emergency service and other service systems. We devise a novel alternative, a birth and death chain formulation of the spatial queuing problem, and show that it yields the same probability distribution of system states as the high dimensional hyper-cube queuing model. We prove our new algorithm always converges at a geometric rate to an exact solution. In several constructed examples, we show this formulation is, on average, more than 60% faster than solving the hyper-cube model. With the introduction of a parallel and distributed computing framework, the algorithm would be asynchronous and have a linear computation complexity.

According to Humboldt County Sheriff Department, Chain was struck by a falling tree while trying to stop logging.[5] He was killed instantly and died of massive head trauma. In response to his death, a Pacific Lumber Co. spokesperson said their logging crew did not see anybody in the area and were unaware of Chain's presence.[6] Earth First! said that the loggers had been deliberately felling huge trees, in a perpendicular manner rather than downhill,[7] in the protesters' direction.[8] One of the protesters also noted that the tree fellers were fully aware that they were there, as the activists had been "yelling at them, walking towards them, telling them 'Don't fall this tree'".[7] On a videotape supplied by Earth First!, Arlington Earl Ammons, the 52-year-old logger responsible for falling the tree that caused Chain's death can be heard shouting expletives and threatening the protesters.[1][7][9]

Based on the local sheriff's probe, Humboldt County district attorney Terry Farmer decided not to press charges, concluding Ammons had not knowingly aimed a tree at any of the protesters.[1] Farmer concluded Chain's death was an accident, and went further to say that he had considered charging Earth First! with involuntary manslaughter charges instead.[citation needed]

Following the reticence of the district attorney to file criminal charges, Chain's mother started a civil suit against Ammons, Pacific Lumber and its parent company, Maxxam, alleging they were reckless and responsible for the death of her son.[1]

A wrongful death settlement was reached three days before trial was scheduled to commence. Its financial terms remain undisclosed but other parts were made public, as a reminder of the tragedy, the 135-foot tree that struck Chain will remain where it fell, and a 100-foot buffer zone prevented any nearby logging. A memorial was also erected.[10]

Soon after Chain's death, it was revealed that the California Department of Forestry & Fire Protection had charged Pacific Lumber with at least 250 violations of the California Forest Practice Act between 1995 and 1997. These violations continued to accumulate in 1998, and in November of that year, Pacific Lumber became the first company ever to lose its logging license in California.[11]

Formation of the death-inducing signaling complex (DISC) is a critical step in death receptor-mediated apoptosis, yet the mechanisms underlying assembly of this key multiprotein complex remain unclear. Using quantitative mass spectrometry, we have delineated the stoichiometry of the native TRAIL DISC. While current models suggest that core DISC components are present at a ratio of 1:1, our data indicate that FADD is substoichiometric relative to TRAIL-Rs or DED-only proteins; strikingly, there is up to 9-fold more caspase-8 than FADD in the DISC. Using structural modeling, we propose an alternative DISC model in which procaspase-8 molecules interact sequentially, via their DED domains, to form a caspase-activating chain. Mutating key interacting residues in procaspase-8 DED2 abrogates DED chain formation in cells and disrupts TRAIL/CD95 DISC-mediated procaspase-8 activation in a functional DISC reconstitution model. This provides direct experimental evidence for a DISC model in which DED chain assembly drives caspase-8 dimerization/activation, thereby triggering cell death.

Among 378,048 death certificates from 2020 listing COVID-19, 5.5% listed COVID-19 without codes for any other conditions. Among 357,133 death certificates with at least one other condition, 97% had a co-occurring diagnosis of a plausible chain-of-event condition (e.g., pneumonia or respiratory failure), or a significant contributing condition (e.g., hypertension or diabetes), or both.

These findings support the accuracy of COVID-19 mortality surveillance in the United States using official death certificates. High-quality documentation of death certificate diagnoses is essential for an authoritative public record.

A small proportion (2.5%) of death certificates documented conditions that have not currently been described to be associated with COVID-19 critical illness or death. This was noted more often among those who died at home, declared dead on arrival, and whose manner of death was not natural. In particular, a higher percentage of decedents aged

These findings support the accuracy of COVID-19 mortality surveillance in the United States using official death certificates. High-quality documentation of co-occurring diagnoses on the death certificate is essential for a comprehensive and authoritative public record. Continued messaging to and training of professionals who complete death certificates (3) remains important as the pandemic progresses. Accurate mortality surveillance is critical for understanding the impact of SARS-CoV-2 variants and of COVID-19 vaccinations and for guiding public health action.

If the interval \( S \) has a minimum value \( a \in \Z \) then of course we must have \( q(a) = 0 \). If \( r(a) = 1 \), the boundary point \( a \) is absorbing and if \( p(a) = 1 \), then \( a \) is reflecting. Similarly, if the interval \( S \) has a maximum value \( b \in \Z \) then of course we must have \( p(b) = 0 \). If \( r(b) = 1 \), the boundary point \( b \) is absorbing and if \( p(b) = 1 \), then \( b \) is reflecting. Several other special models that we have studied are birth-death chains; these are explored in .

If \( S \) is finite, classification of the states of a birth-death chain as recurrent or transient is simple, and depends only on the state graph. In particular, if the chain is irreducible, then the chain is positive recurrent. So we will study the classification of birth-death chains when \( S = \N \). We assume that \( p(x) \gt 0 \) for all \( x \in \N \) and that \( q(x) \gt 0 \) for all \( x \in \N_+ \) (but of course we must have \( q(0) = 0 \)). Thus, the chain is irreducible.

We will use the test for recurrence derived earlier with \( A = \N_+ \), the set of positive states. That is, we will compute the probability that the chain never hits 0, starting in a positive state.

Let \( P_+ \) denote the restriction of \( P \) to \( \N_+ \times \N_+ \), and define \( u_+: \N_+ \to [0, 1] \) by\[ u_+(x) = \P(X_1 \gt 0, X_2 \gt 0, \ldots \mid X_0 = x), \quad x \in \N_+ \]So \( u_+(x) \) is the probability that chain never reaches 0, starting in \( x \in \N_+ \). From our general theory, we know that \( u_+ \) satisfies \( u_+ = P_+ u_+ \) and is the largest such function with values in \( [0, 1] \). Furthermore, we know that either \( u_+(x) = 0 \) for all \( x \in \N_+ \) or that \( \sup\u_+(x): x \in [0, 1]\ = 1 \). In the first case the chain is recurrent, and in the second case the chain is transient.

Note that \( r \), the function that assigns to each state \( x \in \N \) the probability of an immediate return to \( x \), plays no direct role in whether the chain is transient or recurrent. Indeed all that matters are the ratios \( q(x) / p(x) \) for \( x \in \N_+ \).

Note again that \( r \), the function that assigns to each state \( x \in \N \) the probability of an immediate return to \( x \), plays no direct role in whether the chain is transient, null recurrent, or positive recurrent. Also, we know that an irreducible, recurrent chain has a positive invariant function that is unique up to multiplication by positive constants, but the birth-death chain gives an example where this is also true in the transient case.

Suppose now that \( n \in \N_+ \) and that \( \bs X = (X_0, X_1, X_2, \ldots) \) is a birth-death chain on the integer interval \( \N_n = \0, 1, \ldots, n\ \). We assume that \( p(x) \gt 0 \) for \( x \in \0, 1, \ldots, n - 1\ \) while \( q(x) \gt 0 \) for \( x \in \1, 2, \ldots n\ \). Of course, we must have \( q(0) = p(n) = 0 \). With these assumptions, \( \bs X \) is irreducible, and since the state space is finite, positive recurrent. So all that remains is to find the invariant distribution. The result is essentially the same as when the state space is \( \N \).

Note that \( B_n \to B \) as \( n \to \infty \), and if \( B \lt \infty \), \( f_n(x) \to f(x) \) as \( n \to \infty \) for \( x \in \N \). We will see this type of behavior again. Results for the birth-death chain on \( \N_n \) often converge to the corresponding results for the birth-death chain on \( \N \) as \( n \to \infty \).

Often when the state space \( S = \N \), the state of a birth-death chain represents a population of individuals of some sort (and so the terms birth and death have their usual meanings). In this case state 0 is absorbing and means that the population is extinct. Specifically, suppose that \( \bs X = (X_0, X_1, X_2, \ldots) \) is a birth-death chain on \( \N \) with \( r(0) = 1 \) and with \( p(x), \, q(x) \gt 0 \) for \( x \in \N_+ \). Thus, state 0 is absorbing and all positive states lead to each other and to 0. Let \( N = \min\n \in \N: X_n = 0\ \) denote the time until absorption, where as usual, \( \min \emptyset = \infty \).