On Lower Bounds for Parity Branching Programs

Diese Arbeit beschaeftigt sich mit der Komplexität von parity Branching Programmen. Es werden superpolynomiale untere Schranken für verschiedene Varianten bewiesen, nämlich für well-structured graph-driven parity branching programs, general graph-driven parity branching programs und Summen von graph-driven parity branching programs

Treatment with the C5a receptor antagonist ADC-1004 reduces myocardial infarction in a porcine ischemia-reperfusion model

<p>Abstract</p> <p>Background</p> <p>Polymorphonuclear neutrophils, stimulated by the activated complement factor C5a, have been implicated in cardiac ischemia/reperfusion injury. ADC-1004 is a competitive C5a receptor antagonist that has been shown to inhibit complement related neutrophil activation. ADC-1004 shields the neutrophils from C5a activation before they enter the reperfused area, which could be a mechanistic advantage compared to previous C5a directed reperfusion therapies. We investigated if treatment with ADC-1004, according to a clinically applicable protocol, would reduce infarct size and microvascular obstruction in a large animal myocardial infarct model.</p> <p>Methods</p> <p>In anesthetized pigs (42-53 kg), a percutaneous coronary intervention balloon was inflated in the left anterior descending artery for 40 minutes, followed by 4 hours of reperfusion. Twenty minutes after balloon inflation the pigs were randomized to an intravenous bolus administration of ADC-1004 (175 mg, n = 8) or saline (9 mg/ml, n = 8). Area at risk (AAR) was evaluated by ex vivo SPECT. Infarct size and microvascular obstruction were evaluated by ex vivo MRI. The observers were blinded to the treatment at randomization and analysis.</p> <p>Results</p> <p>ADC-1004 treatment reduced infarct size by 21% (ADC-1004: 58.3 ± 3.4 vs control: 74.1 ± 2.9%AAR, p = 0.007). Microvascular obstruction was similar between the groups (ADC-1004: 2.2 ± 1.2 vs control: 5.3 ± 2.5%AAR, p = 0.23). The mean plasma concentration of ADC-1004 was 83 ± 8 nM at sacrifice. There were no significant differences between the groups with respect to heart rate, mean arterial pressure, cardiac output and blood-gas data.</p> <p>Conclusions</p> <p>ADC-1004 treatment reduces myocardial ischemia-reperfusion injury and represents a novel treatment strategy of myocardial infarct with potential clinical applicability.</p

Lower Bounds for the Sum of Graph–driven Read–Once Parity Branching Programs

We prove the first lower bound for restricted read–once parity branching programs with unlimited parity nondeterminism where for each input the variables may be tested according to several orderings. Proving a superpolynomial lower bound for read–once parity branching programs is still a challenging open problem. The following variant of read–once parity branching programs is well–motivated. Let k be a fixed integer. For each input a there are k orderings σ1(a),..., σk(a) of the variables such that for each computation path activated by a the bits are queried according to σi(a) for some i, 1 ≤ i ≤ k. This model that we call k–⊕BP1s for convenience strictly generalizes all restricted variants of read–once parity branching programs for that lower bounds are known. We consider a slightly more restricted version, i.e. the sum of k graph–driven ⊕BP1s with polynomial size graph– orderings. We prove lower bounds for linear codes and show that the considered variant strictly generalizes well–structured graph–driven ⊕BP1s as well as (⊕, k)-BPs examined by Savick´y and Sieling in [24]

Characterizing the Complexity of Boolean Functions represented by Well-Structured Graph-Driven Parity-FBDDs

We investigate well-structured graph-driven parity-FBDDs, which strictly generalize the two well-known models parity OBDDs and well-structured graph-driven FBDDs. The first main result is a characterization of the complexity of Boolean functions represented by well-structured graph-driven parity-FBDDs in terms of invariants of the function represented and the graph-ordering used. As a consequence, we derive a lower bound criterion and prove an exponential lower bound for certain linear code functions. The second main result of this paper is a polynomial time algorithm that minimizes the number of nodes in a graph-driven parity-FBDD

On approximation by ⊕OBDDs

The usual OBDD-data structure can easily be equipped with nondeterminism by allowing several edges with the same label leaving a node. Depending on how acceptance is defined we distinguish between ∨OBDDs (accept if the number of source-to-sink-path is positive) and ⊕OBDDs (accept if the number of source-to-sink-path is odd). It is known that both models are incomparable: Some functions with small OBDDs of one type require exponential size OBDDs of the other type. We show, that nevertheless ⊕OBDDs might be stronger with respect to approximation: For every function computable by an ∨OBDD of quasiplynomial size there is a ⊕OBDD of quasipolynomial size that computes the same function on all but a small fraction of the inputs. Further we prove that the final step in approximation — the simulation by ⊕OBDDs — cannot be improved and we argue, that proving a non-approximability result or a significant lower bound on the quality of approximations of specific functions requires a major breakthrough in Boolean complexity theory.