The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning

Properties of L1210 cells resistant to α-difluoromethylornithine

L1210 cells were selected for resistance to the ornithine decarboxylase (ODC) inhibitor, α-difluromethylornithine. When grown in the absence of the inhibitor, these cells possessed very high ornithine decarboxylase levels. These represented about 1 part in 300 of the soluble protein, which is several hundred times greater than the maximal value found in the original L1210 cells. The resistant cells contained at least 100-fold higher levels of ODC mRNA but the half-life of ODC (about 45 min) was not altered significantly. The resistant cells had much higher putrescine and cadaverine levels than control cells, but there was no significant difference in cellular spermidine or spermine content or in production of 5'-methylthioadenosine, which is a measure of polyamine synthesis. Addition of putrescine to the control or resistant cells had no effect on their content of spermidine and spermine but addition of decarboxylated S-adenosylmethionine increased the content of spermidine and spermine. These results indicate that ornithine decarboxylase is not the rate-limiting step in polyamine synthesis in these L1210 cells. The growth of the α -difluoromethylornithine-resistant L1210 cells was inhibited when their ability to synthesize spermidine and spermine was blocked by the addition of the S-adenosylmethionine decarboxylase inhibitor, 5'-deoxy-5'-[N-methyl-N-(3-hydrazinopropyl)]aminoadenosine. Treatment with this compound produced a reduction of more than 85% in the production of 5'-methylthioadenosine and led to a large increase in the content of putrescine and a substantial decline in the content of spermidine and spermine. These results indicate the potential value of S-adenosylmethionine decarboxylase inhibitors as therapeutic agents in conditions where ODC inhibitors are ineffective

Creation of macroscopic quantum superposition states by a measurement

We propose a novel protocol for the creation of macroscopic quantum superposition (MQS) states based on a measurement of a non-monotonous function of a quantum collective variable. The main advantage of this protocol is that it does not require switching on and off nonlinear interactions in the system. We predict this protocol to allow the creation of multiatom MQS by measuring the number of atoms coherently outcoupled from a two-component (spinor) Bose-Einstein condensate.Comment: 4 pages (revtex4), 2 figure

Control of ornithine decarboxylase activity in α -difluoromethylornithine-resistant L1210 cells by polyamines and synthetic analogues

The regulation of ornithine decarboxylase (ODC) activity by the polyamine derivatives N1,N8-bis(ethyl)-spermidine and N1,N12-bis(ethyl)spermine was studied using a line of L1210 cells resistant to α -difluoromethylornithine (D-R cells), which contain very high levels of ODC, and a synthetic mRNA prepared from a plasmid containing an insert corresponding to ODC mRNA adjacent to an SP6 RNA polymerase promoter. Studies in which ODC protein was labeled in the D-R cells by exposure to [35S]methionine indicated that the polyamine derivatives and their physiological counterparts led to an increased rate of degradation of ODC and to a rapid reduction in ODC synthesis without affecting the content of ODC mRNA. Direct evidence that the polyamine derivatives act by inhibiting the translation of the ODC mRNA was obtained by studying their effects on the translation of ODC mRNA in reticulocyte lysates. This translation was strongly inhibited by the addition of N1,N8-bis(ethyl)spermidine, spermidine, N1,N12-bis(ethyl)spermine, or spermine but was not affected much by putrescine. The inhibition of the translation of ODC mRNA by either of the bis(ethyl) polyamine derivatives occurred at concentrations which stimulated total protein synthesis showing the selectivity of the reduction in ODC. The effects of polyamine derivatives and polyamines on translation of the plasmid-derived ODC mRNA were identical with those found with the D-R L1210 cell mRNA. This synthetic ODC mRNA lacks 261 bases of the 5'-leader sequences and 200 bases plus the poly(A) section from the 3'-nontranslated sequence. Therefore, these regions appear not to influence sensitivity of the ODC mRNA to inhibition of translation by polyamine derivatives

Non-deterministic Gates for Photonic Single Rail Quantum Logic

We discuss techniques for producing, manipulating and measureing qubits encoded optically as vacuum and single photon states. We show that a universal set of non-deterministic gates can be constructed using linear optics and photon counting. We investigate the efficacy of a test gate given realistic detector efficiencies.Comment: 8 pages, 6 figure

On the Spectrum of Field Quadratures for a Finite Number of Photons

The spectrum and eigenstates of any field quadrature operator restricted to a finite number $N$ of photons are studied, in terms of the Hermite polynomials. By (naturally) defining \textit{approximate} eigenstates, which represent highly localized wavefunctions with up to $N$ photons, one can arrive at an appropriate notion of limit for the spectrum of the quadrature as $N$ goes to infinity, in the sense that the limit coincides with the spectrum of the infinite-dimensional quadrature operator. In particular, this notion allows the spectra of truncated phase operators to tend to the complete unit circle, as one would expect. A regular structure for the zeros of the Christoffel-Darboux kernel is also shown.Comment: 16 pages, 11 figure

Alteration of the conserved residue tyrosine-158 to histidine renders human O6-alkylguanine-DNA alkyltransferase insensitive to the inhibitor O6- benzylguanine

The DNA repair protein O6-alkylguanine-DNA alkyltransferase (AGT) protects cells from alkylation damage. O6-Benzylguanine (BG) is a potent inactivator of human AGT (ED50 of 0.1 μM) that is currently undergoing clinical trials to enhance chemotherapy by alkylating agents. In a screen of AGT mutants randomly mutated at position glycine-160, we found that the double mutant Y158H/G160A protected Escherichia coli from killing by N- methyl-N'-nitro-N-nitrosoguanidine (MNNG) even in the presence of BG and that the AGT activity of this mutant was strongly resistant to BG (ED50 of 180 μM). Because the single mutant G160A was not resistant to BG, this suggested that the presence of the charged histidine residue at position 158 was responsible. This hypothesis was confirmed by the construction of the single mutation Y158H. The Y158H-mutant AGT was slightly less active than wild-type AGT for the repair of mcthylated DNA in vitro, but it protected E. coli from killing by MNNG even in the presence of BG and had an ED50 for the inactivation by BG of 620 μM. In contrast, mutant Y158F had an ED50 of 0.2 μM. Previous studies (M. Xu-Welliver et al., Cancer Res., 58: 1936-1945, 1998) have shown that mutant P140K is highly resistant to BG (ED50 of > 1200 μM). Models of human AGT suggest that the side chain of the lysine inserted into this mutant is close to tyrosine-158 and that the positively charged lysine side-chain may interfere with BG binding. The double mutants P140K/Y158H and P140K/Y158F resembled P140K and Y158H in being highly resistant to BG, but the use of a sensitive assay for reaction of BG with AGT indicated that their abilities to react were in the order P140K/Y158H < P140K < P140K/Y158F. These results confirm that the presence of a positively charged residue close to the active site of human AGT renders it highly resistant to BG without substantially affecting activity toward methylated DNA substrates. Such mutants may limit the value of BG therapy if they arise in malignant cells during chemotherapy, but the mutant sequences may be useful for gene therapy approaches in which BG-resistant human AGTs are used to prevent hematopoietic toxicity. At least 28 AGT sequences (from 25 species) have now been described. In 25 of these, the position equivalent to 158 in the human AGT is also a tyrosine, and in the other 3, it is a phenylalanine. The importance of an aromatic ring side chain at this position is emphasized by previous studies (S. Edara et al., Carcinogenesis, 16: 1637- 1642, 1995), which show that the replacement by alanine renders human AGT inactive. Our results show that histidine can also substitute for tyrosine at this position