Invariance and Necessity

Properties and relations in general have a certain degree of invariance, and some types of properties/relations have a stronger degree of invariance than others. In this paper I will show how the degrees of invariance of different types of properties are associated with, and explain, the modal force of the laws governing them. This explains differences in the modal force of laws/principles of different disciplines, starting with logic and mathematics and proceeding to physics and biology

Descriptional complexity of cellular automata and decidability questions

We study the descriptional complexity of cellular automata (CA), a parallel model of computation. We show that between one of the simplest cellular models, the realtime-OCA. and "classical" models like deterministic finite automata (DFA) or pushdown automata (PDA), there will be savings concerning the size of description not bounded by any recursive function, a so-called nonrecursive trade-off. Furthermore, nonrecursive trade-offs are shown between some restricted classes of cellular automata. The set of valid computations of a Turing machine can be recognized by a realtime-OCA. This implies that many decidability questions are not even semi decidable for cellular automata. There is no pumping lemma and no minimization algorithm for cellular automata

On the descriptional complexity of iterative arrays

The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable

A novel mutation in isoform 3 of the plasma membrane Ca2+ pump impairs cellular Ca2+ homeostasis in a patient with cerebellar ataxia and laminin subunit 1\u3b1 mutations.

The particular importance of Ca2+ signaling to neurons demands its precise regulation within their cytoplasm. Isoform 3 of the plasma membrane Ca2+ ATPase (the PMCA3 pump), which is highly expressed in brain and cerebellum, plays an important role in the regulation of neuronal Ca2+. A genetic defect of the function of the PMCA3 pump has been described in one family with X-linked congenital cerebellar ataxia. Here we describe a novel mutation of the PMCA3 pump (ATP2B3) in a patient with global developmental delay, generalized hypotonia and cerebellar ataxia. The mutation (a R482H replacement) impairs the Ca2+ ejection function of the pump. It reduces the ability of the pump expressed in model cells to control Ca2+ transients generated by cell stimulation and impairs its Ca2+ extrusion function under conditions of low resting cytosolic Ca2+ as well. In silico analysis of the structural effect of the mutation suggests a reduced stabilization of the portion of the pump surrounding the mutated residue in the Ca2+-bound state. The patient also carries two missense mutations in LAMA1, encoding for laminin subunit 1\u3b1. On the basis of the family pedigree of the patient, the presence of both PMCA3 and LAMA1 mutations appears to be necessary for the development of the disease. Considering the observed defect in cellular Ca2+ homeostasis and the previous finding that PMCAs act as digenic modulators in Ca2+-linked pathologies, the PMCA3 dysfunction along with LAMA1 mutations could act synergistically to cause the neurological phenotype

Simplicity-Expressiveness Tradeoffs in Mechanism Design

A fundamental result in mechanism design theory, the so-called revelation principle, asserts that for many questions concerning the existence of mechanisms with a given outcome one can restrict attention to truthful direct revelation-mechanisms. In practice, however, many mechanism use a restricted message space. This motivates the study of the tradeoffs involved in choosing simplified mechanisms, which can sometimes bring benefits in precluding bad or promoting good equilibria, and other times impose costs on welfare and revenue. We study the simplicity-expressiveness tradeoff in two representative settings, sponsored search auctions and combinatorial auctions, each being a canonical example for complete information and incomplete information analysis, respectively. We observe that the amount of information available to the agents plays an important role for the tradeoff between simplicity and expressiveness