Computation in Non-Classical Foundations?

The Church-Turing Thesis is widely regarded as true, because of evidence that there is only one genuine notion of computation. By contrast, there are nowadays many different formal logics, and different corresponding foundational frameworks. Which ones can deliver a theory of computability? This question sets up a difficult challenge: the meanings of basic mathematical terms (like "set", "function", and "number") are not stable across frameworks. While it is easy to compare what different frameworks say, it is not so easy to compare what they mean. We argue for some minimal conditions that must be met if two frameworks are to be compared; if frameworks are radical enough, comparison becomes hopeless. Our aim is to clarify the dialectical situation in this bourgeoning area of research, shedding light on the nature of non-classical logic and the notion of computation alike.

On AGM for Non-Classical Logics

The AGM theory of belief revision provides a formal framework to represent the dynamics of epistemic states. In this framework, the beliefs of the agent are usually represented as logical formulas while the change operations are constrained by rationality postulates. In the original proposal, the logic underlying the reasoning was supposed to be supraclassical, among other properties. In this paper, we present some of the existing work in adapting the AGM theory for non-classical logics and discuss their interconnections and what is still missing for each approach.

Mechanistic Insights into a Non-Classical Diffusion Pathway for the Formation of Hollow Intermetallics: A Route to Multicomponent Hollow Structures

Hollow nanostructures are used for various applications including catalysis, sensing, and drug delivery. Methods based on the Kirkendall effect have been the most successful for obtaining hollow nanostructures of various multicomponent systems. The classical Kirkendall effect relies on the presence of a faster diffusing species in the core; the resultant imbalance in flux results in the formation of hollow structures. Here, an alternate non-Kirkendall mechanism that is operative for the formation of hollow single crystalline particles of intermetallic PtBi is demonstrated. The synthesis method involves sequential reduction of Pt and Bi salts in ethylene glycol under microwave irradiation. Detailed analysis of the reaction at various stages indicates that the formation of the intermetallic PtBi hollow nanoparticles occurs in steps. The mechanistic details are elucidated using control experiments. The use of microwave results in a very rapid synthesis of intermetallics PtBi that exhibits excellent electrocatalytic activity for formic acid oxidation reaction. The method presented can be extended to various multicomponent systems and is independent of the intrinsic diffusivities of the species involved.

Non Classical Design in MOSFETs for Improving OTA gain-bandwidth trade off

In this paper, gain-bandwidth (GB) trade-off associated with analog device/circuit design due to conflicting requirements for enhancing gain and cutoff frequency is examined. It is demonstrated that the use of a nonclassical source/drain (S/D) profile (also known as underlap channel) can alleviate the GB trade-off associated with analog design. Operational transconductance amplifier (OTA) with 60 nm underlap S/D MOSFETs achieve 15 dB higher open loop voltage gain along with three times higher cutoff frequency as compared to OTA with classical nonunderlap S/D regions. Underlap design provides a methodology for scaling analog devices into the sub-100 nm regime and is advantageous for high temperature applications with OTA, preserving functionality up to 540 K. Advantages of underlap architecture over graded channel (GC) or laterally asymmetric channel (LAC) design in terms of GB behavior are demonstrated. Impact of transistor structural parameters on the performance of OTA is also analyzed. Results show that underlap OTAs designed with spacer-to-straggle ratio of 3.2 and operated below a bias current of 80 microamps demonstrate optimum performance. The present work provides new opportunities for realizing future ultra wide band OTA design with underlap DG MOSFETs in silicon-on-insulator (SOI) technology. Index Terms—Analog/RF, double gate, gain-bandwidth product, .

Multi-Prover and parallel repetition in non-classical interactive games

Depuis l’introduction de la mécanique quantique, plusieurs mystères de la nature ont trouvé leurs explications. De plus en plus, les concepts de la mécanique quantique se sont entremêlés avec d’autres de la théorie de la complexité du calcul. De nouvelles idées et solutions ont été découvertes et élaborées dans le but de résoudre ces problèmes informatiques. En particulier, la mécanique quantique a secoué plusieurs preuves de sécurité de protocoles classiques. Dans ce m´emoire, nous faisons un étalage de résultats récents de l’implication de la mécanique quantique sur la complexité du calcul, et cela plus précisément dans le cas de classes avec interaction. Nous présentons ces travaux de recherches avec la nomenclature des jeux à information imparfaite avec coopération. Nous exposons les différences entre les théories classiques, quantiques et non-signalantes et les démontrons par l’exemple du jeu à cycle impair. Nous centralisons notre attention autour de deux grands thèmes : l’effet sur un jeu de l’ajout de joueurs et de la répétition parallèle. Nous observons que l’effet de ces modifications a des conséquences très différentes en fonction de la théorie physique considérée.

On the geometry of non-classical curves

In this paper we relate the numerical invariants attached to a projective curve, called the order sequence of the curve, to the geometry of the varieties of tangent linear spaces to the curve and to the Gauss maps of the curve. © 1992 Sociedade Brasileira de Matemática.

Non-classical HLA-E gene variability in Brazilians: a nearly invariable locus surrounded by the most variable genes in the human genome

The non-classical human leukocyte antigen (HLA) class I genes present a very low rate of variation. So far, only 10 HLA-E alleles encoding three proteins have been described, but only two are frequently found in worldwide populations. Because of its historical background, Brazilians are very suitable for population genetic studies. Therefore, 104 bone marrow donors from Brazil were evaluated for HLA-E exons 14. Seven variation sites were found, including two known single nucleotide polymorphisms (SNPs) at positions +424 and +756 and five new SNPs at positions +170 (intron 1), +1294 (intron 3), +1625, +1645 and +1857 (exon 4). Haplotyping analysis did show eight haplotypes, three of them known as E*01:01:01, E*01:03:01 and E*01:03:02:01 and five HLA-E new alleles that carry the new variation sites. The HLA-E*01:01:01 allele was the predominant haplotype (62.50%), followed by E*01:03:02:01 (24.52%). Selective neutrality tests have disclosed an interesting pattern of selective pressures in which balancing selection is probably shaping allele frequency distributions at an SNP at exon 3 (codon 107), sequence diversity at exon 4 and the non-coding regions is facing significant purifying pressure. Even in an admixed population such as the Brazilian one, the HLA-E locus is very conserved, presenting few polymorphic SNPs in the coding region.

Cross-sectional observational study of 208 patients with non-classical urea cycle disorders

Urea cycle disorders (UCDs) are inherited disorders of ammonia detoxification often regarded as mainly of relevance to pediatricians. Based on an increasing number of case studies it has become obvious that a significant number of UCD patients are affected by their disease in a non-classical way: presenting outside the newborn period, following a mild course, presenting with unusual clinical features, or asymptomatic patients with only biochemical signs of a UCD. These patients are surviving into adolescence and adulthood, rendering this group of diseases clinically relevant to adult physicians as well as pediatricians. In preparation for an international workshop we collected data on all patients with non-classical UCDs treated by the participants in 20 European metabolic centres. Information was collected on a cohort of 208 patients 50% of which were ≥ 16 years old. The largest subgroup (121 patients) had X-linked ornithine transcarbamylase deficiency (OTCD) of whom 83 were female and 29% of these were asymptomatic. In index patients, there was a mean delay from first symptoms to diagnosis of 1.6 years. Cognitive impairment was present in 36% of all patients including female OTCD patients (in 31%) and those 41 patients identified presymptomatically following positive newborn screening (in 12%). In conclusion, UCD patients with non-classical clinical presentations require the interest and care of adult physicians and have a high risk of neurological complications. To improve the outcome of UCDs, a greater awareness by health professionals of the importance of hyperammonemia and UCDs, and ultimately avoidance of the still long delay to correctly diagnose the patients, is crucial.

Non-classical karyotypic features in relapsed childhood B-cell precursor acute lymphoblastic leukemia

Karyotype analysis of acute lymphoblastic leukemia (ALL) at diagnosis has provided valuable prognostic markers for treatment stratification. However, reports of cytogenetic studies of relapsed ALL samples are limited. We compared the karyotypes from 436 nonselected B-cell precursor ALL patients at initial diagnosis and of 76 patients at first relapse. We noticed a relative increase of karyotypes that did not fall into the classic ALL cytogenetic subgroups (high hyperdiploidy, t(12;21), t(9;22), 11q23, t(1;19), <45 chromosomes) in a group of 29 patients at relapse (38%) compared to 130 patients at presentation (30%). Non-classical cytogenetic aberrations in these 29 patients were mostly found on chromosomes 1, 2, 7, 9, 13, 14, and 17. We also describe six rare reciprocal translocations, three of which involved 14q32. The most frequent abnormalities were found in 9p (12/29 cases) and were associated with a marked decrease in the duration of the second remission, but not of the probability of 10-year event-free survival after relapse treatment. From 29 patients with non-classical cytogenetic aberrations, only 8 (28%) had been stratified to a high risk-arm on the first treatment protocol, suggesting that this subgroup might benefit from the identification of new prognostic markers in future studies.

Canonical proof nets for classical logic

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there should be a canonical function from sequent proofs to proof nets, (b) it should be possible to check the correctness of a net in polynomial time, (c) every correct net should be obtainable from a sequent calculus proof, and (d) there should be a cut-elimination procedure which preserves correctness. Previous attempts to give proof-net-like objects for propositional classical logic have failed at least one of the above conditions. In Richard McKinley (2010) [22], the author presented a calculus of proof nets (expansion nets) satisfying (a) and (b); the paper defined a sequent calculus corresponding to expansion nets but gave no explicit demonstration of (c). That sequent calculus, called LK∗ in this paper, is a novel one-sided sequent calculus with both additively and multiplicatively formulated disjunction rules. In this paper (a self-contained extended version of Richard McKinley (2010) [22]), we give a full proof of (c) for expansion nets with respect to LK∗, and in addition give a cut-elimination procedure internal to expansion nets – this makes expansion nets the first notion of proof-net for classical logic satisfying all four criteria.