Ernst Cassirer's transcendental account of mathematical reasoning

Cassirer's philosophical agenda revolved around what appears to be a paradoxical goal, that is, to reconcile the Kantian explanation of the possibility of knowledge with the conceptual changes of nineteenth and early twentieth-century science. This paper offers a new discussion of one way in which this paradox manifests itself in Cassirer's philosophy of mathematics. Cassirer articulated a unitary perspective on mathematics as an investigation of structures independently of the nature of individual objects making up those structures. However, this posed the problem of how to account for the applicability of abstract mathematical concepts to empirical reality. My suggestion is that Cassirer was able to address this problem by giving a transcendental account of mathematical reasoning, according to which the very formation of mathematical concepts provides an explanation of the extensibility of mathematical knowledge. In order to spell out what this argument entails, the first part of the paper considers how Cassirer positioned himself within the Marburg neo-Kantian debate over intellectual and sensible conditions of knowledge in 1902–1910. The second part compares what Cassirer says about mathematics in 1910 with some relevant examples of how structural procedures developed in nineteenth-century mathematics.     

A recurrent 15q13.3 microdeletion syndrome associated with mental retardation and seizures

We report a recurrent microdeletion syndrome causing mental retardation, epilepsy and variable facial and digital dysmorphisms. We describe nine affected individuals, including six probands: two with de novo deletions, two who inherited the deletion from an affected parent and two with unknown inheritance. The proximal breakpoint of the largest deletion is contiguous with breakpoint 3 (BP3) of the Prader-Willi and Angelman syndrome region, extending 3.95 Mb distally to BP5. A smaller 1.5-Mb deletion has a proximal breakpoint within the larger deletion (BP4) and shares the same distal BP5. This recurrent 1.5-Mb deletion contains six genes, including a candidate gene for epilepsy (CHRNA7) that is probably responsible for the observed seizure phenotype. The BP4-BP5 region undergoes frequent inversion, suggesting a possible link between this inversion polymorphism and recurrent deletion. The frequency of these microdeletions in mental retardation cases is approximately 0.3% (6/2,082 tested), a prevalence comparable to that of Williams, Angelman and Prader-Willi syndromes.     

A degradation-sensitive anionic trypsinogen (PRSS2) variant protects against chronic pancreatitis

Chronic pancreatitis is a common inflammatory disease of the pancreas. Mutations in the genes encoding cationic trypsinogen (PRSS1) and the pancreatic secretory trypsin inhibitor (SPINK1) are associated with chronic pancreatitis. Because increased proteolytic activity owing to mutated PRSS1 enhances the risk for chronic pancreatitis, mutations in the gene encoding anionic trypsinogen (PRSS2) may also predispose to disease. Here we analyzed PRSS2 in individuals with chronic pancreatitis and controls and found, to our surprise, that a variant of codon 191 (G191R) is overrepresented in control subjects: G191R was present in 220/6,459 (3.4%) controls but in only 32/2,466 (1.3%) affected individuals (odds ratio 0.37; P = 1.1 x 10(-8)). Upon activation by enterokinase or trypsin, purified recombinant G191R protein showed a complete loss of trypsin activity owing to the introduction of a new tryptic cleavage site that renders the enzyme hypersensitive to autocatalytic proteolysis. In conclusion, the G191R variant of PRSS2 mitigates intrapancreatic trypsin activity and thereby protects against chronic pancreatitis.     

The Recent Uses of Sol-Gel Doped Catalysts in Fine Chemistry

A variety of sol-gel entrapped catalysts is available on the chemical market due to the unique advantages offered by these highly porous oxides doped with transition metal catalyst, enzymes or even living cells. Catalytic sol-gel lipase immobilizates were rapidly commercialized by Fluka after their invention by Reetz and coworkers in 1995 and have now reached a 2^nd generation level of performance. Besides esterification reactions these materials are also excellent catalysts in the kinetic resolution of chiral alcohols and amines, and are recyclable without any substantial loss in enantioselectivity （residual activity of 70 % even after 20 reaction cycles）.     

A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor

Silicon has long been the optimal material for electronics, but it is only relatively recently that it has been considered as a material option for photonics. One of the key limitations for using silicon as a photonic material has been the relatively low speed of silicon optical modulators compared to those fabricated from III-V semiconductor compounds and/or electro-optic materials such as lithium niobate. To date, the fastest silicon-waveguide-based optical modulator that has been demonstrated experimentally has a modulation frequency of only approximately 20 MHz (refs 10, 11), although it has been predicted theoretically that a approximately 1-GHz modulation frequency might be achievable in some device structures. Here we describe an approach based on a metal-oxide-semiconductor (MOS) capacitor structure embedded in a silicon waveguide that can produce high-speed optical phase modulation: we demonstrate an all-silicon optical modulator with a modulation bandwidth exceeding 1 GHz. As this technology is compatible with conventional complementary MOS (CMOS) processing, monolithic integration of the silicon modulator with advanced electronics on a single silicon substrate becomes possible.     

238U束流发射度的测量

为实现236U的高灵敏测量,对意大利那不勒斯第二大学的同位素研究环境与文化遗产中心的加速器质谱装置进行了升级改造。采用单缝单丝法测量了238U的束流发射度,并与13C和H的束流发射度进行了比较。测量结果表明,238U在X方向和Y方向的边界发射度分别为(9.5±1.0)、(2.7±0.3)mm.m rad。根据测量的发射度数值,确定了拟安装的飞行时间探测器在束流线上的位置。