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ClC-1 belongs to the gene family of CLC Cl channels and Cl/H+ antiporters. It is the major skeletal muscle chloride channel and is mutated in dominant and recessive myotonia. In addition to the membrane-embedded part, all mammalian CLC proteins possess a large cytoplasmic C-terminal domain that bears two so-called CBS (from cystathionine-β-synthase) domains. Several studies indicate that these domains might be involved in nucleotide binding and regulation. In particular, Bennetts et al. (J. Biol. Chem. 2005. 280:32452–32458) reported that the voltage dependence of hClC-1 expressed in HEK cells is regulated by intracellular ATP and other nucleotides. Moreover, very recently, Bennetts et al. (J. Biol. Chem. 2007. 282:32780–32791) and Tseng et al. (J. Gen. Physiol. 2007. 130:217–221) reported that the ATP effect was enhanced by intracellular acidification. Here, we show that in striking contrast with these findings, human ClC-1, expressed in Xenopus oocytes and studied with the inside-out configuration of the patch-clamp technique, is completely insensitive to intracellular ATP at concentrations up to 10 mM, at neutral pH (pH 7.3) as well as at slightly acidic pH (pH 6.2). These results have implications for a general understanding of nucleotide regulation of CLC proteins and for the physiological role of ClC-1 in muscle excitation.

ClC-1 is the major skeletal muscle chloride channel (Steinmeyer et al., 1991a,b). Its activity accounts for the large chloride conductance of the sarcolemma at rest that is necessary to stabilize the membrane potential. Mutations in the CLCN1 gene lead to dominant and recessive myotonia (Koch et al., 1992; George et al., 1993; Steinmeyer et al., 1994; Pusch, 2002). The channel is a member of the gene family of CLC Cl channels and Cl/H+ antiporters (Zifarelli and Pusch, 2007), which are homodimeric proteins with independent ion permeation pathways in each subunit (Dutzler et al., 2002). In addition to the membrane-embedded part, all mammalian CLC proteins possess a large cytoplasmic C-terminal domain that bears two so-called CBS (from cystathionine-β-synthase) domains (Ponting, 1997). The precise role of the CBS domains is still unclear, but several recent reports indicate that CBS domains may be involved in the regulation of protein function by intracellular nucleotides like ATP, ADP, and AMP (Scott et al., 2004; Bennetts et al., 2005; Wellhauser et al., 2006; Meyer et al., 2007). Scott et al. (2004) showed that isolated CBS domains from CLC proteins are able to bind nucleotides. Similarly, Wellhauser et al. (2006) reported low affinity binding of ATP at the C terminus of ClC-5 that could be competed by 1 μM AMP. Moreover, nucleotides were found to be bound in the crystal structure of the C-terminal fragment of ClC-5 (Meyer et al., 2007). In agreement with these biochemical results, Bennetts et al. (2005) reported that the activity of ClC-1 is regulated by intracellular ATP and other nucleotides. They found that the presence of 5 mM ATP shifted the open probability (Popen) of the slow gate by ∼50 mV toward positive potentials. Moreover, very recently Bennetts et al. (2007) and Tseng et al. (2007) reported that the effect of ATP was greatly enhanced by acidification of the intracellular solution.

The studies of Bennetts et al. (2005, 2007) were performed on human ClC-1 expressed in cultured cells and measured using the whole-cell configuration of the patch clamp technique. However, this method has several drawbacks. First, the effects of different intracellular solutions and their washout are not tested on the same cell. Rather, averages of different cells are compared. Second, indirect effects of ATP in the complex cellular environment cannot be excluded. Third, if large currents are measured, as is the case for ClC-1, the whole cell configuration allows only a relatively poor control of the ion concentrations close to the plasma membrane. For example, a reduction of the intracellular chloride concentration close to the plasma membrane may decrease inward currents after long hyperpolarizing pulses because of a reduced driving force for chloride. To find out if ATP has a direct effect on ClC-1 and if acidification may eventually modulate such an effect, we tested the nucleotide on inside-out patches. This method avoids the above mentioned problems. To our surprise, we could not detect any significant effect of ATP on ClC-1 activity even at acidic pH. During the elaboration of this manuscript, Tseng et al. (2007), in a study performed in inside-out oocytes patches, reported, in rough agreement with the findings of Bennetts et al. (2007), that intracellular ATP modulates ClC-1 activity and that intracellular acidification increases this effect. The origin of the discrepancy between the results reported by Tseng et al. (2007) and our results is unclear.

WT hClC-1 (Koch et al., 1992) was expressed in Xenopus oocytes and currents were measured at 18°C (some control experiments were performed at 26°C to ensure that the temperature did not influence the results), 2–4 d after injection using the inside-out configuration of the patch clamp technique (Hamill et al., 1981) with an EPC-7 (List) amplifier and a custom acquisition program (GePulse, Visual C ++, Microsoft). Data analysis was performed using custom software (written in Visual C ++, Microsoft) and the Origin program (OriginLab Corporation).

The control internal solution contained (in mM) 100 NMDG-Cl, 2 MgCl2, 10 HEPES, 2 EGTA, pH 7.3. The extracellular (pipette) solution contained (in mM) 100 NMDG-Cl, 5 MgCl2, 10 HEPES, pH 7.3. Some control experiments were conducted with solutions identical to those used by Tseng et al. (2007) (120 mM NMDG-Cl, 1 MgCl2, 10 HEPES, 1 EGTA, pH 7.4 or 6.2). In these experiments the pH 7.4 solution was also used as the extracellular (pipette) solution. Solutions containing ATP (adenosine 5′-triphosphate bis(tris) salt dehydrate, Sigma-Aldrich) were prepared diluting the appropriate volume of ATP from a stock solution of 50 mM ATP in the internal solution. Mg2+ in the form of MgSO4 was added at the same concentration of ATP. Solutions containing MgATP (Sigma-Aldrich) were prepared in a similar way but without supplementation of Mg2+. Solutions were applied by inserting the patch pipette into perfusion tubes of 0.5 mm diameter.

The functionality of the ATP solution and the efficiency of the perfusion system were evaluated on the ΔR-CFTR construct that was reconstituted from the injection of two separate RNAs encoding the N-terminal and C-terminal half of the protein, respectively. The gating of this channel does not require phosphorylation and depends only on ATP (Bompadre et al., 2005). The ΔR-CFTR was injected in the same batch of oocytes and measured before ClC-1.

The voltage protocol used to study CFTR-mediated currents consists of voltage steps ranging from −80 to 80 mV in 20-mV increments.

To study hClC-1–mediated currents we used a tail protocol consisting of a 100-ms test pulse to a variable potential ranging from 100 to −160 mV followed by a repolarization to −140 mV for 100 ms. To study in isolation slow gating transitions the test pulses were prolonged to 200 ms, and a 200-μs pulse to 160 mV, to fully activate the fast gating, was applied before the −140-mV repolarization. For measurements at pH 6.2 the length of the test pulse was prolonged to 300 ms as in Tseng et al. (2007). In some recordings, a 20-ms prepulse to 80 mV was applied before the test pulse (e.g., Fig. 2). The presence of this prepulse did not alter the gating parameters derived from the Boltzmann fits. The open probability was derived from tail currents fitting the latter with a monoexponential function and extrapolating the current values to the beginning of the tail pulse.

Open probabilities were derived from the tail currents by fitting a modified Boltzmann function (Pusch et al., 1995):

$I(V){=}I_{\mathrm{max}}(P_{\mathrm{min}}{+}(1{-}P_{\mathrm{min}})/(1{+}\mathrm{exp}[(V_{1/2}{-}V)/k)])),$
(1)

where Imax is the (fitted) maximal current, Pmin the residual open probability at negative voltages, V1/2 is the midpoint voltage of the open probability, and k the slope factor of the voltage dependence of the open probability.

To estimate the apparent Kd for ATP activation of the ΔR-CFTR channel, we perfused inside-out patches with different concentrations of ATP and measured the current at 80 mV. Current measured in the absence of ATP was subtracted. Since not all patches allowed the application of many concentrations and because most patches showed a slow rundown over time we bracketed all measurements by recordings with 1 mM ATP and normalized the response to the current measured with 1 mM ATP. Assuming that, for a single ideal patch without rundown, the ATP dependence can be described by

$I(c){=}I_{\mathrm{max}}\frac{(c/K_{d})^{n}}{1{+}(c/K_{d})^{n}},$

where c is the concentration of ATP, Kd is the apparent dissociation constant, and n is the Hill coefficient, the normalized response, Inorm, is given by

$I_{\mathrm{norm}}{=}\frac{I(c)}{I(1{\,}\mathrm{mM})}{=}\frac{(c/K_{d})^{n}}{1{+}(c/K_{d})^{n}}\frac{1{+}(1{\,}\mathrm{mM}/K_{d})^{n}}{(1{\,}\mathrm{mM}/K_{d})^{n}}$
(2)

This equation was used to fit the data shown in Fig. 1. Data are presented as mean ± SEM except where noted.

### Online Supplemental Material

We provide supplemental online information on the application of intracellular ATP on ClC-1 at 26 °C (Figs. S1 and S2), demonstrating the lack of a significant effect also at this elevated temperature. Furthermore, we show the result of sequencing the hClC-1 insert in the expression vector with four primers (Fig. S3).

In this work we wanted to study the effect of intracellular ATP on hClC-1 expressed in Xenopus oocytes using inside-out patches. To test whether our perfusion system and the ATP containing solutions were appropriate for this task, we used as a positive control a CFTR construct lacking the regulatory domain (ΔR-CFTR) (Bompadre et al., 2005). In this construct, activation of the Cl conductance depends only on the presence of ATP on the cytoplasmic side and does not require activation by protein kinase. We expressed ΔR-CFTR in Xenopus oocytes and performed inside-out patch experiments, perfusing with control solution and with solutions containing 0.01 (n = 11), 0.1 (n = 14), 1 mM (n = 25), and 5 mM ATP (n = 17).

In the absence of ATP, we observed only very small background currents (Fig. 1 A, top left). However, perfusion with solutions containing increasing concentrations of ATP (Fig. 1 A) progressively activated larger Cl currents, with 1 mM being already a saturating concentration. Switching back to the control solution, devoid of ATP, currents returned to background levels (not depicted).

In particular, to make sure that the ATP was prepared and delivered at the appropriate concentrations, we performed a dose–response curve for ATP activation of ΔR-CFTR. Fig. 1 B shows the ATP dependence of currents at 80 mV normalized to the current measured in 1 mM ATP. The solid line represents the best fit of Eq. 2, resulting in an apparent dissociation constant of (38 ± 4) μM and a Hill coefficient of 0.63 ± 0.03. The Kd value is in reasonable agreement with the result of Bompadre et al. (2005) who reported a Kd value of 89 μM for the ATP dependence of the single channel open probability. These results prove that we have appropriate control of the amount of ATP delivered to the patch.

Using the same recording condition, we then investigated the effect of ATP on currents mediated by hClC-1. Typical ClC-1 currents that deactivate at negative voltages are shown in Fig. 2 A. As can be seen, the macroscopic currents do not seem to be largely affected by the presence of 10 mM ATP. This was the case also for measurements performed after perfusion lasting up to 5 min. Fig. 2 B shows that the apparent open probability, derived from the analysis of the tail currents reported in Fig. 2 A, follows a modified Boltzmann distribution whose midpoint (V1/2) and minimal open probability (Pmin) are only marginally affected by the presence of 10 mM ATP as compared with control solution (see legend of Fig. 2).

Bennetts et al. (2005) reported that the effect of ATP was mostly on the slow (or common) gate, which acts simultaneously on both pores of the double-barreled channel (Miller and White, 1984; Accardi and Pusch, 2000). To isolate the voltage dependence of the common gate, we adopted the voltage protocol devised by Accardi and Pusch (Accardi et al., 2001) (see Materials and methods). Also in this case, we did not observe a significant difference between currents recorded in the presence and in the absence of ATP (traces not shown). In fact, the voltage dependence of the open probability of the slow gate is virtually unaffected by the presence of 10 mM ATP as shown for a representative patch (Fig. 2 C).

Fig. 3 displays the statistical evaluation of the parameters V1/2 and Pmin derived as described for the representative measurements in Fig. 2. The mean values of V1/2 and Pmin are not significantly changed by the presence of ATP when the overall gating of ClC-1 is considered (Fig. 3, A and B). The same conclusion holds when only the slow gating mechanism is taken into account (C and D).

Bennetts et al. (2007) and Tseng et al. (2007) recently suggested that the ATP effect was greatly enhanced by decreasing pHint. In particular at pH 6.2, ATP was reported to dramatically shift the open probability–voltage curve by >100 mV to more positive voltages, with 1 mM ATP being sufficient to reach a maximal effect. To test whether acidification of the intracellular solution could unmask an effect of ATP that was not evident at the neutral pH used in the previous experiments, we decreased the pHint from 7.3 to 6.2 and assessed the effect of 1 mM ATP. Fig. 4 shows representative current traces obtained at pH 7.3 (Fig. 4 A), pH 6.2 (Fig. 4 B), and pH 6.2 in the presence of 1 mM ATP (Fig. 4 C). In agreement with previous observations (Rychkov et al., 1996; Accardi and Pusch, 2000), switching from pH 7.3 to 6.2 slows down the deactivation kinetics and increases the steady-state value of the currents at negative potentials. Surprisingly, addition of 1 mM ATP had no detectable further effect on the kinetics and voltage dependence of the currents. The changes produced by acidification are quickly reversed upon wash with solution at pH 7.3 (Fig. 4 D). The voltage dependence of the Popen derived for the representative patch shown in Fig. 4 (A–D) is practically unaffected by the presence of 1 mM ATP (Fig. 4 E). This is confirmed by the statistical evaluation of the V1/2 and Pmin of the Boltzmann distribution describing the Popen (Fig. 5, A and B), where average values of these parameters are shown.

The lack of any effect of ATP at acidic pH was confirmed by isolating the voltage dependence of the slow gate as already described for pH 7.3 (Fig. 4 F) and by the statistical evaluation of the V1/2 and Pmin of the Boltzmann distribution (Fig. 5, C and D).

In the experiments described above we had used Tris-ATP and have added MgSO4 at the same concentration, whereas Tseng et al. (2007) and Bennetts et al. (2007) had used MgATP. To test whether the discrepancies between our results and theirs could be due to this different source of ATP, we performed additional experiments with MgATP. Also with MgATP, ΔR-CFTR could be reliably activated and no effect on ClC-1 currents could be detected (unpublished data), showing that the source of the nucleotide has no influence on our conclusions.

We also performed some experiments at 26°C to assess whether higher temperature could uncover an effect of ATP. In these experiments we employed recording solutions identical to those of Tseng et al. (see Materials and methods). At pH 7.4, the voltage dependence of opening is slightly shifted by ∼30 mV to more positive voltages, compared with the recordings at 18°C, pH 7.3 (see Figs. S1 and S2). This shift is probably caused by the combined effect of the higher temperature (Bennetts et al., 2001) and the slightly more basic pH. Interestingly, at pH 6.2 almost no effect of temperature on the gating parameters could be observed (Fig. S2). Most importantly, however, we could not observe any significant effect of 1 mM ATP on current magnitude or voltage dependence of gating at pH 7.4 or pH 6.2 (see Figs. S1 and S2).

In skeletal muscle, Cl conductance (gCl) accounts for ∼80% of the overall membrane conductance at rest (Aromataris and Rychkov, 2006) and ClC-1 is the main determinant of this conductance (Lueck et al., 2007). The Cl conductance is required to keep an appropriate resting potential and to repolarize the voltage following an action potential (Aromataris and Rychkov, 2006). This critical role is underscored by the fact that mutations in the gene coding for ClC-1 (Pusch, 2002) or aberrant splicing of ClC-1 (Charlet et al., 2002; Mankodi et al., 2002) produce muscle hyperexcitability. Several recent reports indicate that intracellular CBS domains may be involved in the regulation of CLC proteins by intracellular nucleotides like ATP, ADP, and AMP (Scott et al., 2004; Bennetts et al., 2005; Wellhauser et al., 2006; Meyer et al., 2007). In particular, Bennetts et al. reported that the activity of ClC-1 expressed in HEK cells and studied with the whole-cell configuration of the patch-clamp technique is regulated by intracellular ATP and other nucleotides. At physiological pH (7.2), ATP shifted the open probability of the slow gate of ClC-1 by ∼50 mV toward positive voltages with a half-maximal concentration of around 1 mM (Bennetts et al., 2005). Moreover, the presence of 5 mM ATP produced a sixfold reduction in the number of channels that remained open at negative voltages (Bennetts et al., 2005). On the basis of an in silico docking study of ATP binding, using the crystal structure of IMPDH (inosine-monophosphate dehydrogenase) (Zhang et al., 1999) to model the cytoplasmic region of ClC-1, they also suggested residues that modified the effect of ATP. In particular, mutating L848, predicted from the model to interact with the adenine base of ATP, to alanine, abrogated the effect of ATP.

Very recently, two different publications reported that the effect of ATP was greatly enhanced by intracellular acidification, finding that at pH 6.2, addition of 1 mM ATP further shifted the open probability toward positive voltages (Bennetts et al., 2007; Tseng et al., 2007).

In contrast with previous findings (Rychkov et al., 1996; Accardi and Pusch, 2000), Bennetts et al. (2007) reported also a slight shift toward positive potentials of the Popen at acidic pH even in the absence of ATP.

In stark contrast to these conclusions, we have demonstrated here that direct application of ATP to the intracellular side of excised inside-out patches does not exert a significant effect on the current amplitude or on the voltage dependence of the open probability of hClC-1 expressed in Xenopus oocytes at neither neutral nor slightly acidic pH (7.3 and 6.2). In particular, we were not able to detect any significant shift in the midpoint of the voltage dependence of the open probability, or on the residual open probability at negative voltages for both fast and slow gate. We observed practically no effect for concentrations of ATP up to 10 mM, even after perfusion for up to 5 min. Moreover, in contrast with Bennetts et al. (2007) and in agreement with previous studies (Rychkov et al., 1996; Accardi and Pusch, 2000), we find that acidic pH has at most a small effect on the V1/2 of the Popen, and that inward currents are drastically increased at low pH.

As already mentioned, Bennetts et al. (2007) reported a slight shift toward positive potentials of the Popen at acidic pH even in the absence of ATP. The estimated pK for the effect of protons was found to be compatible with the pK of histidine residues. On the basis of this observation and of a structural model, they suggested that a histidine residue (H847) is important to mediate the effect of pH-dependent ATP modulation. Residue H847 was suggested to interact electrostatically with the phosphate of ATP, however the mutational analysis of Bennetts et al. failed to support this hypothesis as changing this residue to either A or to R similarly affected ATP dependence. Finally, the mutant L848A that was reported in the first work of Bennetts et al. (2005) to have the largest impact on ATP effect was not investigated in their latest work, nor in the work of Tseng et al. (2007).

The striking contrast with the results of Bennetts et al. (2007) and Tseng et al. (2007) prompted us to thoroughly control the experimental condition used in our study. We proved that we efficiently apply active ATP because we could robustly and reversibly activate currents mediated by ΔR-CFTR, a channel that is gated by intracellular ATP (Bompadre et al., 2005). Moreover, we quantitatively controlled the concentration of ATP delivered to the patches by performing a dose–response curve of the ATP activation of ΔR-CFTR, obtaining a Kd in agreement with published results (Bompadre et al., 2005).

To exclude possible sequence variations of the cDNA construct we fully sequenced the open reading frame of our hClC-1 clone and found it to be in complete agreement with the published hClC-1 cDNA (see Fig. S3).

To exclude any influence of the type of ATP salt used, we tested both Tris salt and Mg2+ salt without observing any difference. Moreover, we used pulse protocols of variable length (see Materials and methods) to ensure that the current reached a steady state during our experiments.

Finally, we proved that temperature in the range between 18 and 26°C did not influence the lack of effect of ATP on ClC-1–induced currents. Hence, we conclude that intracellular ATP does not directly affect the function of ClC-1 at both neutral and acidic pH.

The conflicting conclusions of Bennetts et al. (2005, 2007) might result from the different electrophysiological methods used and/or the different expression system adopted. In this respect, it is important to note that the whole-cell configuration used by Bennetts et al. presents some problematic aspects for the type of study that we are considering. Most importantly, in the whole-cell configuration it is normally not possible to change the internal solution, implying that the comparison between different ATP concentrations cannot be performed directly on the same cell. Furthermore, the interior of the cell, even after internal access has been established by the patch pipette, remains probably a complex and biochemically active milieu in which ATP can potentially activate signaling cascades that may indirectly modulate channel function. For example, ClC-1 activity could be regulated by protein kinases (Chen and Jockusch, 1999; Rosenbohm et al., 1999).

To assess whether the difference in the apparent ATP sensitivity of ClC-1, is caused by the different expression systems, we attempted to measure ClC-1 currents from inside-out patches of transfected HEK cells. Unfortunately, as also reported by Bennetts et al. (2007), we were not able to obtain a sufficient expression level to allow reliable measurements.

It is more difficult to explain the difference with the study of Tseng et al. (2007) in which the same expression system (Xenopus oocytes) and excised inside-out patch clamp recordings were used. We are not able to provide any reasonable explanation for the discrepancy between our study and the one of Tseng et al. Independent studies from other research groups should help to clarify this important issue.

Our results have implications for the interpretation of recent results from x-ray crystallography of CLC proteins and for the physiological role of ClC-1. In accordance with the lack of functional effects on ClC-1, Meyer and Dutzler (2006) could not detect ATP binding to the cytoplasmic domain of the highly homologous ClC-0 channel, and no nucleotides could be detected in the crystal structure of the C terminus of the ClC-Ka channel (Markovic and Dutzler, 2007). Interestingly however, the same group found that nucleotides bind with 100 μM affinity to the CBS domains of C terminus of the Cl/H+ antiporter ClC-5 (Meyer et al., 2007), in agreement with biochemical data on isolated C-terminal protein fragments (Scott et al., 2004; Wellhauser et al., 2006). Of course our results do not exclude that nucleotides can bind to the C terminus of ClC-1. However, the lack of direct functional alteration of the channel by ATP shows that if nucleotides have any effect in the physiological regulation of the skeletal muscle chloride conductance, it is of indirect nature.

Regarding the physiological role of ClC-1, an important finding is that macroscopic gCl is reduced by intracellular acidification (Pedersen et al., 2004, 2005), an effect that, in principle, could be mediated by a direct pH dependence of ClC-1. However, previous reports (Rychkov et al., 1996; Accardi and Pusch, 2000) have shown that low pHi activates rather than inhibits ClC-1, a finding that we plainly reproduce (see current traces in Fig. 4), suggesting an indirect mechanism of acidosis-induced reduction of gCl. In contrast to these findings, from apparent shifts of activation curves, Bennetts et al. (2007) deduced that ClC-1 currents are inhibited by low pHi, and speculated that acidosis directly inhibits CLC-1 and leads to hyperexcitability. Moreover, they speculated that their finding of increased effect of ATP on ClC-1 upon intracellular acidification (Bennetts et al., 2007) would explain the so far elusive link between acidification, decrease in gCl, and recovery of muscle excitability (Nielsen et al., 2001; Pedersen et al., 2004; Pedersen et al., 2005) because acidification, potentiating the effect of ATP, which is to shift the Popen toward positive potentials, would greatly decrease gCl facilitating muscle excitation (Bennetts et al., 2007). Our measurements do not support any of these speculations and point to an indirect role of ClC-1 and a more complicated mechanism of regulation of gCl that can probably be thoroughly understood only in the context of active skeletal muscle tissues.

We thank T.J. Jentsch for providing the ClC-1 cDNA, L. Csanády for providing the ΔR-CFTR clones, and G. Gaggero for help in constructing the perfusion system.

The financial support by Telethon Italy (grant GGP04018) is gratefully acknowledged.

Olaf S. Andersen served as editor.

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2008 - The Mathematical Association of America MathFest Words: 255 words ||
 Info
1. Mingus, Tabitha. and Grassl, Richard. "Validating the Warrant P(k)-->P(k+1): Does Any Means Justify the Ends?" Paper presented at the annual meeting of the The Mathematical Association of America MathFest, TBA, Madison, Wisconsin, Jul 28, 2008 <Not Available>. 2019-06-27 <http://citation.allacademic.com/meta/p275279_index.html>
Publication Type: Conference Paper/Unpublished Manuscript
Abstract: For practicing and prospective secondary mathematics teachers, the role of mathematical reasoning and proof in their mathematical training is crucial for a number of reasons: (1) formal mathematical proof serves as a tool for teachers to develop a profound understanding of mathematics and as a means for communicating their understanding; (2) reasoning and proof are featured prominently in the secondary school curricula as envisioned in the NCTM Principles; and, (3) reasoning and proof can form the basis for the development and assessment of student learning and discourse. Following the scheme suggested by the Seldens (2003), we undertook a cross-sectional study of pre- and in-service secondary mathematics teachers abilities to validate purported proofs by mathematical induction with an eye toward determining what facets they attended to when reading such an argument. Of the 82 validation attempts only 9 correctly identified that the attempt was flawed.

The reviews of our article submission were mixed, including one reviewer who insisted that the proposition P(k+1) can be established by any means. This sparked an in-depth analysis of the mathematical induction argumentation style using Toulmins (1958) argumentation scheme. The concept of a warrant from Toulmins scheme is the logical connection between what is given in a proof and what is concluded. In this talk we will discuss the flawed arguments presented to the participants, how Toulmins scheme can be utilized to analyze students attempts at proof by mathematical induction, and how the scheme can be used as a pedagogical tool in the undergraduate mathematics classroom.

2015 - The Native American and Indigenous Studies Association Words: 255 words ||
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2. Chang, David. "Diasporic Lives and Deaths: Kānaka and American Indians Remember the Deaths of Kānaka in California" Paper presented at the annual meeting of the The Native American and Indigenous Studies Association, Hyatt Regency on Capitol Hill, Washington, D.C., <Not Available>. 2019-06-27 <http://citation.allacademic.com/meta/p987678_index.html>
Publication Type: Conference Paper/Unpublished Manuscript
Abstract: The varying commemorations of the lives and deaths of diasporic Hawaiians in nineteenth-century California reveal the complexities of their lives and identities: both as Kānaka Maoli with deep ties to the Hawaiian nation and as men whose lives had entwined deeply with California Indian communities. By the 1840s, one-third of the Native men of the archipelago were laboring abroad, and the Gold Rush brought hundreds more to California. Many (probably most) of them lived with and among Native Americans. Many diasporic Kānaka never returned home: they died far from their homeland. From the 1850s until the end of the century, commemorative articles in Hawaiian-language newspapers about Kānaka Hawaiʻi who died in diaspora gave Kānaka a means to imagine the enduring bonds linking Kanaka to each other and to their home places—what Kānaka call their ʻone hanau, the sands of their birth. Articles in Hawaiian-language newspapers and stories of remembrance about Kānaka Hawaiʻi who died in diaspora helped make Hawaiian families and communities aware of the fate of the migrants far away and helped to keep the migrants knit into the Hawaiian national community. At the same time, the way these people were commemorated in graveyards and oral narratives by their American Indian family members and descendants makes clear their strong connection to the American Indian communities among whom they lived. Read together, both Hawaiian and Native Californian commemorations played a role in reimagining communities that could be physically far-flung, socially diverse, and tied to Hawaiian and Native Californian communities.

2018 - ICA's 68th Annual Conference Pages: unavailable || Words: unavailable ||
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3. Zhang, Ruonan. "International K-Pop Fans’ Usage of Facebook Groups for Organizational Identification With K-Pop Fan Community" Paper presented at the annual meeting of the ICA's 68th Annual Conference, Hilton Prague, Prague, Czech Republic, May 22, 2018 Online <APPLICATION/PDF>. 2019-06-27 <http://citation.allacademic.com/meta/p1361623_index.html>
Publication Type: Extended Abstract
Review Method: Peer Reviewed
Abstract: This study is designed to investigate how international fans of Korean popular (K-pop) culture construct organizational identification with K-pop fan community through interactions on Facebook fan group pages. Drawn on organizational identification scholarship and literature on the international influence of K-pop culture, this study aims to find out (1) the types of interactions conducted by international K-pop fans on Facebook fan group pages, (2) how those interactions help them build organizational identification with K-pop fan community, (3) how their organizational identification contributes to their sense of belongingness, attachment, and pleasure of being K-pop fans, and (4) the moderator of the relationship between Facebook interactions and organizational identification with K-pop fan community. A mixed-methods approach is adopted to answer the proposed research questions. A qualitative content analysis is used to determine the typology of interactions conducted on international K-pop fan groups on Facebook. A quantitative survey method is used to investigate the international K-pop fans’ organizational identification with the Facebook fan groups, including its predictors, moderators, and effects.

2007 - Mathematical Association of America Words: 77 words ||
 Info
4. Molina, Robert., McNally, Myles. and Smith, Ken. "Characterization of Randomly $P_k$-Decomposable Graphs, $2le k le11$" Paper presented at the annual meeting of the Mathematical Association of America, The Fairmont Hotel, San Jose, CA, Aug 03, 2007 <Not Available>. 2019-06-27 <http://citation.allacademic.com/meta/p206505_index.html>
Publication Type: Conference Paper/Unpublished Manuscript
Abstract: A graph G is H-decomposable if it can be expressed as an edge disjoint union of H-subgraphs. We say that G is randomly H-decomposable if every collection of edge disjoint H-subgraphs of G can be extended to an H-decomposition of G. In this paper we characteriz randomly $P_k$-decomposable graphs for $2\le k \le11$. We also prove several structural results related to these graphs. Finally, suggestions for further research in this area are given.

2015 - SRCD Biennial Meeting Words: 497 words ||
 Info
5. Valentino, Rachel. "Will Public Pre-K Really Close Achievement Gaps? Gaps in Access to Quality Pre-K between Students and Across States" Paper presented at the annual meeting of the SRCD Biennial Meeting, Pennsylvania Convention Center and the Philadelphia Marriott Downtown Hotel, Philadelphia, PA, <Not Available>. 2019-06-27 <http://citation.allacademic.com/meta/p954156_index.html>
Publication Type: Presentation
Abstract: By the time children enter kindergarten, there are already large gaps in achievement between black/Hispanic and white students, poor and non-poor students, and dual language learners (DLLs) and non-DLLs (Reardon & Robinson, 2008; NCES, 2011). Public pre-K is often touted as a means to close gaps, with the idea that enriching disadvantaged children’s early learning will level the playing field between them and their more advantaged peers. However, this end may not be realized if there are large gaps in the quality of pre-K experienced between groups. This paper seeks to understand overall quality gap magnitudes, variation in gaps across states, and what classroom- and state-level factors explain the size of quality gaps.

This paper uses data from the NCEDL Multi-State Pre-Kindergarten Study and the State-Wide Early Education Programs Study, which measured classroom quality in state-funded pre-K in 11 states in 2001-2002 and 2003-2004, respectively. At the time of data collection 80% of children in the U.S. participating in state-funded pre-K were enrolled in one of these 11 states. The study consists of a stratified random sample of 721 classrooms containing approximately 12,000 students, and collected data on classroom quality using structural and procedural measures. The current study uses OLS regression with appropriate survey weighting and jackknife standard errors to unsure unbiased parameter estimation.

First, I find that black-white, Hispanic-white, poor-non-poor, and DLL-non-DLL quality gaps in standard deviation units are large, ranging from 0.3 to 0.7 SD, with the largest gaps on measures of emotional and instructional climate (see Table 1 for an abbreviated list of raw gaps).

Second, I examine what factors explain the size of gaps on procedural measures of quality, considering three groups of variables: 1) structural characteristics such as teacher education to consider, for instance, whether variation across classrooms and groups in teacher training explains the size of gaps; 2) the initial competency of students upon entry to the program to examine whether when initial skills of the students are low, teachers target teaching to students’ ability; and 3.) classroom composition to consider, for example, whether the proportion of low SES kids in the classroom explains the size of racial quality gaps. State fixed effects are included in these models. I find that structural characteristics generally explain little to none of the size of quality gaps, while initial student ability and classroom composition each explain about 50-65% of gap magnitudes. Gaps of about 0.2 to 0.3 SD remain on most quality measures net of these factors.

Third, I consider whether there is between-state variation in the size of quality gaps, and find sizable differences across states (See figure 1 for gaps on the Early Childhood Environmental Rating Scale).

Additionally, in the presentation I will report on state-level factors, such as segregation and the rates at which states expanded their pre-K programs, that account for between-state differences in the size of quality gaps. This question is particularly important, as idiosyncratic state policies may provide insight into broader policy reform to equalize quality access across groups.

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# bit v1.1-15.1

0

0th

Percentile

## A Class for Vectors of 1-Bit Booleans

True boolean datatype (no NAs), coercion from and to logicals, integers and integer subscripts; fast boolean operators and fast summary statistics. With 'bit' vectors you can store true binary booleans {FALSE,TRUE} at the expense of 1 bit only, on a 32 bit architecture this means factor 32 less RAM and ~ factor 32 more speed on boolean operations. Due to overhead of R calls, actual speed gain depends on the size of the vector: expect gains for vectors of size > 10000 elements. Even for one-time boolean operations it can pay-off to convert to bit, the pay-off is obvious, when such components are used more than once. Reading from and writing to bit is approximately as fast as accessing standard logicals - mostly due to R's time for memory allocation. The package allows to work with pre-allocated memory for return values by calling .Call() directly: when evaluating the speed of C-access with pre-allocated vector memory, coping from bit to logical requires only 70% of the time for copying from logical to logical; and copying from logical to bit comes at a performance penalty of 150%. the package now contains further classes for representing logical selections: 'bitwhich' for very skewed selections and 'ri' for selecting ranges of values for chunked processing. All three index classes can be used for subsetting 'ff' objects (ff-2.1-0 and higher).

## Functions in bit

 Name Description Summary Summaries of bit vectors Extract Extract or replace part of an bit vector c.bit Concatenating bit and bitwhich vectors bitwhich A class for vectors representing asymetric selections regtest.bit Regressiontests for bit LogicBit Boolean operators and functions for class bit as.bitwhich Coercing to bitwhich as.which Coercion to (positive) integer positions as.logical.bit Coercion from bit, bitwhich and ri to logical, integer, double bbatch Balanced Batch sizes repeat.time Adaptive timer chunk Chunked range index clone Cloning ff and ram objects as.bit Coercing to bit intrle Hybrid Index, C-coded utilities vecseq Vectorized Sequences is.bit Testing for bit, bitwhich and ri selection classes unattr Attribute removal ramsort Generics for in-RAM sorting and ordering physical Physical and virtual attributes length.bit Getting and setting length of bit, bitwhich and ri objects is.sorted Generics related to cache access repfromto Virtual recycling rlepack Hybrid Index, rle-pack utilities setattributes Attribute setting by reference ri Range index bit-package A class for vectors of 1-bit booleans bit_init Initializing bit masks No Results!


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Blanchard, Gofman and Seaborg (quoted by Segre). Almost all nuclear bombs use some kind of implosion method. Bohr and Wheeler, Phys. Weapons-grade plutonium contains no more than 7.0% 240Pu. Browse our catalogue of tasks and access state-of-the-art solutions. 238U decays via alpha decay to 234Th with half-life of ~4.5×109 years. Get the most important science stories of the day, free in your inbox. • Their neutron spectra are similar to that of a fission … An attempt is made to explain the irregular behavior of the spontaneous fission half lives. 240Pu's high rate of spontaneous fission events makes it an undesirable contaminant. Plutonium-238 and plutonium-239 oxides are included and such emission rates are useful for scaling tallies from Monte Carlo simulations and estimating dose rates for health physics applications. >2. Mathematically, the criterion for whether spontaneous fission can occur in a time short enough to be observed by present methods, is approximately: [5] where Z is the atomic number and A is the mass number (e.g. Spontaneous fission of 25~Cf; prompt gamma ray emission; multipli- city distribution. 235U.

Welcome! Spontaneous fission rates. By a system which has no purpose and goal transcending it, and which makes man its appendix.”—Erich Fromm (19001980). The SOURCES code is capable of calculating (α,n) production rates for four different problem configurations (homogeneous, interface, three region and beam problems) and neutron production rates for spontaneous fission and delayed neutron processes. Spontaneous fission can occur much more rapidly when the nucleus of an atom undergoes superdeformation. With its prodigious spontaneous fission rate, Cf-252 serves well as a compact, intense, fission-spectrum neutron source, and is thus the only isotope of californium of any significant industrial importance. The fission at low temperatures can be described mainly as a barrier-tunneling process. It is also possible to calculate fission product composition, emitted radiation and decay heat following specified periods of fission rates and cooling. Google Scholar. Abstract. Spontaneous fission (SF) is a form of radioactive decay that is found only in very heavy chemical elements. Nature In fission, an atom is split into two or more smaller, lighter atoms. Spontaneous fission, decay rates, and critical mass. Full Record; Other Related Research; Abstract. Scientists have to consider the spontaneous fission rate of each material when designing nuclear weapons. Spontaneous fission rates: Here we describe the rate and spectrum of spontaneous mutations for the fission yeast Schizosaccharomyces pombe , a key model organism with many similarities to higher eukaryotes. The main isotopes, which have to be considered in the fuel cycle of all commercial light water reactors, are: Isotopes of uranium 1. The probability of spontaneous fission is very strongly dependent upon, and increases rapidly with, the atomic number of the heavy element. In practice 239Pu will invariably contain a certain amount of 240Pu due to the tendency of 239Pu to absorb an additional neutron during production. Most of the discussion about alpha particles will also apply to spontaneous fission. Σ) by the total volume of the core (V) gives us the total number of reactions occurring in the reactor core per unit time. MEASUREMENTS of the spontaneous fission rates of nearly twenty nuclides have recently been published. Abstract. fission rate Übersetzung, Englisch - Franzosisch Wörterbuch, Siehe auch , biespiele, konjugation and JavaScript. 238U occasionally decays by spontaneous fission with probability of 0.000055%. The difference between our results and those of Segre shows that the fission probability of Np237 is evi dently considerably less than has been believed. Inactive Member. 240Pu's high rate of spontaneous fission events makes it an undesirable contaminant. Most of these are given in a paper by Segre 1 , in which he describes the work carried out at Los Alamos during the War, and also sums up the results of other experiments. Weapons-grade plutonium contains no more than 7% Pu-240. 238U. The rate at which new mutations arise in the genome is a key factor in the evolution and adaptation of species. Spontaneous fission rates [6] Nu-clide Half-life (yrs) Fission prob. Multiplying the reaction rate per unit volume (RR = Ф . Hanna, Harvey, Moss and Tunnicliffe, Phys. The spontaneous fission of 238 U occurs at a given rate, described by the decay constant. Table 1 illustrates a comparison of the rate at which different heavy nuclides produce neutrons by spontaneous fission. Despite having a half-life greater than the age of the universe, neutron emission from 240Pu becomes significant because of the quantity of material present. 240 Pu 's high rate of spontaneous fission events makes it an undesirable contaminant. In the meantime, to ensure continued support, we are displaying the site without styles The influence of a single nucleon on the barrier height is calculated from the level scheme of Nilsson. The dependence of the yields of cosmochronometer nuclei on the spontaneous fission model has been considered. Spontaneous fission of 25~Cf; prompt gamma ray emission; multipli- city distribution. NoNukes Posts Only. The rate of spontaneous fission decay of uranium-238 (λ f 238) was determined in 4π-geometry by the fission track method. (2017), Fortschritte der Physik Table 1 illustrates a comparison of the rate at which different heavy nuclides produce neutrons by spontaneous fission. Spontaneous fission is an extremely rare phenomenon. We begin by examining thirty-two different combinations of nuclear inputs: eight mass models, two types of spontaneous fission rates, and two types of fission daughter product distributions. Message 16 of 29 (647496) 01-10-2012 12:29 AM Reply to: Message 15 by RAZD 01-09-2012 1:57 PM Re: Decay rates, change, and atomic stability . 1. However, fission may be triggered by the capture of incoming neutrons by very heavy nuclei. At the temperatures found in fission bombs reaction 1 has a rate 100 times faster than the next fastest candidate (reactions 2 and 3 combined), which are in turn 10 times faster than reaction 4. Using ultrafast transient absorption spectroscopy, we discovered that for large crystallite sizes, singlet fission is significantly faster in polymorph Tc II than in Tc I, and that, unlike in Tc I films, in Tc II films the crystallite size has little or no effect on the SF rate. The rarely used gun-type atomic bomb has a critical insertion time of about one millisecond, and the probability of a fission during this time interval should be small. Therefore only 235U is suitable. Weapons-grade plutonium contains no more than 7.0% Pu . Pu-240's high rate of spontaneous fission events makes it an undesirable contaminant. Spontaneous fission rates: [6] The spontaneous, fission rates of the relevant nuclides are: zaapu 2.14 x los g-' sec-' Segrk (1952) 242Pu -10 8-l sec-l Estimated from Z2/A, see Whitehouse 241b 4.6 g-l sec-' Segrk 242b < lo4 g-' sec-' Upper limit estimated from Z2/A arecm 8 x lo8 g-' sec-' Hanna et al. Introduction When a nucleus undergoes fission, the primary fission fiagments are always formed in a state of high excitation and de-excite by successive neutron and gamma ray emission. For a nucleus like uranium 238, for instance, spontaneous fission only takes place for one decay in two million. Measurements on curium-242 have been published by Hanna et al. Introduction When a nucleus undergoes fission, the primary fission fiagments are always formed in a state of high excitation and de-excite by successive neutron and gamma ray emission. Most experimental data on the spontaneous fission are for nuclei with even numbers of protons and neutrons—called 'even-even nuclei.' You are not logged in. An attempt is made to explain the irregular behaviour of the spontaneous fission half-lives. Most of these are given in a paper by Segre1, in which he describes the work carried out at Los Alamos during the War, and also sums up the results of other experiments. Weapons-grade plutonium contains no more than 7.0% 240Pu. Full Record; Other Related Research; Authors: Whitehouse, W J; Galbraith, W Publication Date: Sat Mar 22 00:00:00 EST 1952 Research Org. Nature 169, 494 (1952). SOURCES is a computer code that determines neutron production rates and spectra from (α,n) reactions, spontaneous fission and delayed neutron emission owing to the decay of radionuclides in homogeneous media, interface problems and three-region interface problems. The neutron spectra may also be determined for all cases, if required. Most of these are given in a paper by Segre1, in which he describes the work carried out at Los Alamos during the War, and also sums up the results of other experiments. (1983). You are using a browser version with limited support for CSS. PubMed Google Scholar, WHITEHOUSE, W., GALBRAITH, W. Spontaneous Fission Rates. Spontaneous fission rates: In practice 239Puwill invariably contain a certain amount of 240Pudue to the tendency of 239Puto absorb an additional neutron during production. Presently measured spontaneous-fission rates in f/gm/hr are: 238U = 20 (1.5-10 16), 235U= 1 (3-1017), 239Pu = 40 (7-1015), 240Pu= 1.6- 106 (2- 1011); the values in parentheses are the neutron emission half-lives in years. 27 • Each fission event typically results in the emission of 2 to 4 neutrons. Spontaneous tracks have accumulated since the time of manufacture and induced tracks to determine the uranium content were produced by thermal neutron irradiations. \item[Results] Our results of spontaneous fission rates reasonably agree with other studies and experiments. No code available yet. The fission that occurs in nuclear reactors and explosive devices is induced by the neutron bombardment of certain types of nuclei. The influence of a single nucleon on the barrier height is calculated from the level scheme of Nilsson. Fusion, in contrast, occurs when two or more smaller atoms fuse together, creating a larger, heavier atom. This means that the assembly time to reach a critical mass has to be less than the rate of spontaneous fission. Here we describe the rate and spectrum of spontaneous mutations for the fission yeast Schizosaccharomyces pombe , a key model organism with many similarities to higher eukaryotes. not identified Sponsoring Org. Fission tracks are linear damage tracks that occur in minerals that are caused by the spontaneous fission of heavy, unstable nuclides (mostly 238 U in natural minerals). The stray neutrons released by a spontaneous fission can prematurely initiate a chain reaction. This physics video explains the concept of nuclear fission reaction by illustrating an example of nuclear fission of Uranium 235 atom. The mean counting rate of the fragments was equal to 0.92 particles per hour for pure Pu238, and to 7 particles per hour for the ... of the spontaneous-fission half-period of Np237, for which a value of 1018 years is indicated. Pu 's high rate of spontaneous fission events makes it an undesirable contaminant. Tip: you can also follow us on Twitter 1. Spontaneous fission (SF) is a form of radioactive decay that is found only in very heavy chemical elements.Because the nuclear binding energy of the elements reaches its maximum at an atomic mass number greater than about 58 atomic mass units (u), spontaneous breakdown into smaller nuclei and a few isolated nuclear particles becomes possible at heavier masses. Uranium-238, uranium-235, and plutonium-239 undergo spontaneous fission to a limited extent. On spontaneous fission rates Johansson, Sven A. E. Abstract. The rate at which new mutations arise in the genome is a key factor in the evolution and adaptation of species. Secondary Mode of Decay: Spontaneous fission. Weapons-grade plutonium contains no more than 7.0% 240 Pu. So long as the rates of progress held good, these bombs would double in force and number every ten years.”—Henry Brooks Adams (18381918), “Our spontaneous action is always the best. Spontaneous fission rates. the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in (1991), Zeitschrift f�r Physik A Atoms and Nuclei In uranium-238, alpha decay is about 2 million times more probable than is spontaneous fission, whereas in fermium-256, 3 percent of the nuclei undergo alpha decay and 97 percent undergo spontaneous fission. The isotopes of plutonium of even mass number, namely 238 Pu, 240 Pu, and 242 Pu, decay principally by alpha particle-emission but can also undergo spontaneous fission to a lesser extent at rates of 1100, 471, and 800 SF s −1 g −1, respectively. volume 169, page494(1952)Cite this article. Bretscher, Cook, Martin and Poole, British Report BR 384. [ Login] EvC Forum active members: 79 (8970 total) Article  The dose averaged LET for the charged particle recoil nuclei is 68 keV/µ.Conclusions: We have developed a facility to perform high LET studies in mice and rats at space relevant dose rates and career-relevant doses using neutrons emitted from the spontaneous fission of 252Cf. Spontaneous fission is invariably accompanied by the release of large amounts of energy, and it is usually accompanied by the emission of several neutrons as well. FISPIN is issued with JEF2.2 and JEFF3.1 reactor independent nuclear cross section libraries including 38 different reactions. Uranium-238, uranium-235, and plutonium-239 undergo spontaneous fission to a limited extent. Here's why: As a rule, isotopes with even-numbered masses have high spontaneous fission rates and are less fissile. Radioactivity - Radioactivity - Calculation and measurement of energy: By the method of closed energy cycles, it is possible to use measured radioactive-energy-release (Q) values for alpha and beta decay to calculate the energy release for unmeasured transitions. An example is the spontaneous fission of $$^{254}_{98}\textrm{Cf}$$, which gives a distribution of fission products; one possible set of products is shown in the following equation: I don't think it would be the case of one or the other, but both would be affected. Spontaneous Fission. Thank you for visiting nature.com. Therefore, only 235 U is suitable. Militarily, however, it's Cf-251 that really kicks butt. Google Scholar. CAS  Gamma decay often occurs from the daughter nucleus of one of the other decay modes. In practice 239Pu will invariably contain a certain amount of 240Pu due to the tendency of 239Pu to absorb an additional neutron during production. This work tabulates neutron emission rates for 80 plutonium oxide samples as reported in the literature. Spontaneous fission, in which a sufficiently heavy nucleus simply breaks in half. The first person to derive the rate of spontaneous emission accurately from first principles was Dirac in his quantum theory of radiation, the precursor to the theory which he later called quantum electrodynamics. By submitting a comment you agree to abide by our Terms and Community Guidelines. Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily. Fission is triggered by the capture of a neutron. Σ) by the total volume of the core (V) gives us the total number of reactions occurring in the reactor core per unit time. Theoretical physics forces atomic energy on us; the successful production of the fission bomb forces upon us the manufacture of the hydrogen bomb. ISSN 1476-4687 (online). To obtain The spontaneous fission rate is the probability per second that a given atom will fission spontaneously--that is, without any external intervention. MEASUREMENTS of the spontaneous fission rates of nearly twenty nuclides have recently been published. 238U belongs to the group of fertile isotopes. Fission is triggered by the capture of a neutron. 235U belongs to the group of fissile i… Spontaneous fission rates: In practice Pu-239 will invariably contain a certain amount of Pu-240 due to the tendency of Pu-239 to absorb an additional neutron during production. Keywords. Weapons-grade plutonium contains no more than 7.0% 240 Pu. Get the latest machine learning methods with code. Topic: Spontaneous fission, decay rates, and critical mass: NoNukes. Article  Its specific activity is very low ~3.4×10-7Ci/g. For example, 230 Th, which has Z = 90, has a half-life for spontaneous fission of approximately 1.5 × 10 17 years, whereas for 254 Cf, which has Z = 98, the half-life is about 60 days for this mode of decay. Spontaneous emission cannot be explained by classical electromagnetic theory and is fundamentally a quantum process. The rarely-used gun-type atomic bomb has a critical insertion time of about one millisecond, and the probability of a fission during this time interval should be small. While the fission at high temperatures has to incorporate the reflection above barriers. You cannot, with your best deliberation and heed, come so close to any question as your spontaneous glance shall bring you.”—Ralph Waldo Emerson (18031882), “The pace of science forces the pace of technique. Reaction Rate and Reactor Power Calculation. Nuclides of the same element are linked with a red line. Nature Nuclear fusion and nuclear fission are different types of reactions that release energy due to the presence of high-powered atomic bonds between particles found within a nucleus. (2006), Journal of Physics G: Nuclear and Particle Physics Browse our catalogue of tasks and access state-of-the-art solutions. Uranium-238, for example, yields almost 60 neutrons per hour per gram. We do not choose our problems, we do not choose our products; we are pushed, we are forcedby what? Internet Explorer). Plutonium 239 has a very high spontaneous fission rate compared to the spontaneous fission rate of uranium 235. SPONTANEOUS FISSION RATES. The rate at which new mutations arise in the genome is a key factor in the evolution and adaptation of species. https://doi.org/10.1038/169494a0, The European Physical Journal A Measurements on curium-242 have been published by Hanna et al.2. Multiplying the reaction rate per unit volume (RR = Ф . It has been shown that the spontaneous fission rates estimated within a phenomenological model constructed on the basis of the calculations of the spontaneous fission rates for superheavy nuclei within the macroscopic-microscopic model are in good agreement with the … Because the nuclear binding energy of the elements reaches its maximum at an atomic mass number greater than about 58 atomic mass units (u), spontaneous breakdown into smaller nuclei and a few isolated nuclear particles becomes possible at heavier masses. Data taken from French Wikipedia. Spontaneous Fission Sources General • A number of high mass even-even alpha emitting radionuclides (e.g., Pu-238, Cm-242, Cm-244, Cf-252) also undergo spontaneous fission. 240 Pu 's high rate of spontaneous fission events makes it an undesirable contaminant. = 36 for uranium-235). SOURCES 4C is a computer code that determines neutron production rates and spectra from ({alpha},n) reactions, spontaneous fission, and delayed neutron emission due to radionuclide decay. Uranium-238, for example, yields almost 60 neutrons per hour per gram. Atomic Energy Research Establishment, Harwell, Berks, You can also search for this author in The process become predominant for an handful of such heavy nuclei called fissile. Reaction Rate and Reactor Power Calculation. Read more about this topic:  Spontaneous Fission, “[The] elderly and timid single gentleman in Paris ... never drove down the Champs Elysees without expecting an accident, and commonly witnessing one; or found himself in the neighborhood of an official without calculating the chances of a bomb. Some radionuclides of interest in nuclear energy and safeguards also decay by spontaneous fission. Rev., 81, 466 (1951). In practice, Pu will invariably contain a certain amount of Pu due to the tendency of Pu to absorb an additional neutron during production. Spontaneous Fission Rates - NASA/ADS MEASUREMENTS of the spontaneous fission rates of nearly twenty nuclides have recently been published. Mathematically, the criterion for whether spontaneous fission can occur in a time short enough to be observed by present methods, is approximately: where Z is the atomic number and A is the mass number (e.g. Weapons-grade plutonium contains no … For a nucleus like uranium 238, for instance, spontaneous fission only takes place for one decay in two million. Predictions of decay modes for the superheavy nuclei most suitable for synthesis, Spontaneous fission properties of superheavy elements, Rare decay modes by cluster emission from nuclei, Evaluation of ?n/?f from cross sections of (HI, xn) reactions. Scientists had to consider the spontaneous fission rate of each material … SOURCES 4C is a computer code that determines neutron production rates and spectra from ({alpha},n) reactions, spontaneous fission, and delayed neutron emission due to radionuclide decay. Spontaneous fission rates Spontaneous fission half-life of various nuclides depending on their Z /A ratio. Traductions en contexte de "fission rate" en anglais-français avec Reverso Context : The spontaneous fission rate is too high. (1951). 240Pu's high rate of spontaneous fission events makes it an undesirable contaminant. ON SPONTANEOUS FISSION RATES. However, fission may be triggered by the capture of incoming neutrons by very heavy nuclei. Get the latest machine learning methods with code. The formation of heavy elements in the neutron star merger scenario is considered. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. Spontaneous fission is an extremely rare phenomenon. The rate at which new mutations arise in the genome is a key factor in the evolution and adaptation of species. ADS  MEASUREMENTS of the spontaneous fission rates of nearly twenty nuclides have recently been published. In such a scenario, the duration of the r-process is long and when the nucleosynthesis wave passes through the region of actinides, beta-delayed, neutron-induced, and spontaneous fission are added to the main r-process reaction channels. The green line shows the upper limit of half-life. GENETICS | INVESTIGATION The Spontaneous Mutation Rate in the Fission Yeast Schizosaccharomyces pombe Ashley Farlow,*,†,1,2 Hongan Long,‡,1 Stéphanie Arnoux,* Way Sung,‡ Thomas G. Doak,‡,§ Magnus Nordborg,* and Michael Lynch‡,2 *Gregor Mendel Institute of Molecular Plant Biology, 1030 Vienna, Austria, †Institute of Population Genetics, 1210 Vetmeduni Vienna, Rev., 55, 426 (1939). Uranium glasses of known age of manufacture were used. 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Technical Article

# The 16 Boolean Logic Functions of Two-Input Systems

March 01, 2020 by Sneha H.L.

## Learn about all 16 possible logic functions that can be realized for two binary inputs.

Boolean logic has been ruling the world of computational digital systems for many decades. Nonetheless, a few logic functions have been overlooked considerably.

In this article, I make an attempt to shed light on some of the forgotten logic functions concerned with two-input variables.

### Number of Boolean Functions

Before proceeding any further, let's try to remember the logical operations associated with a single input variable. NOT – yes, that’s right.

Is that all?

The answer from a majority of us would be “Yes.”

Well now, let's try to answer the same question when the number of inputs changes to two instead of one. This time, we seem to have a handful of operations: AND, OR, XOR, XNOR, NAND, NOR, and of course, NOT.

Are we done…? The answer would again be a resounding “Yes.” But, sorry to say, the correct answer is “No” for both cases.

Actually, there can be $$2^{2^{n}}$$ logic functions for n input variables. This means there can be $$4 (= 2^{2^{1}} = 2^2)$$ possible outcomes of a single input variable; $$16 (= 2^{2^{2}} = 2^4)$$ outputs from two-input system; $$256(= 2^{2^{3}} = 2^8)$$ outputs from three-input system, and so on.

Accordingly, there should be three and nine more logical functions corresponding to one-input and two-input systems apart from the one and seven quoted above, respectively.

### Complete List of Boolean Functions for 1- and 2- Input Variables

The complete list of Boolean functions for a system with input A and another system with inputs A and B are shown in Tables 1 and 2, respectively.

 Name of the Boolean Function Boolean Function Meaning Null 0 Always 0 Identity 1 Always 1 Transfer A Pass value of A NOT Ā Pass negated value of A
##### Table 1. Complete list of Boolean functions for a single input system

 Name of the Boolean Function Boolean Function Meaning Null $$0$$ Always 0 Identity $$1$$ Always 1 Transfer $$A$$ Pass value of A $$B$$ Pass value of B NOT $$\bar{A}$$ Pass negated value of A $$\bar{B}$$ Pass negated value of B AND $$A \bullet B$$ 1 only if A and B both are 1 NAND $$\overline {A \bullet B}$$ 0 only if A and B both are 1 OR $$A + B$$ 0 only if A and B both are 0 NOR $$\overline {A + B}$$ 1 only if A and B both are 0 Implication $$A + \bar {B}$$ If B, then A $$\bar {A} + B$$ If A, then B Inhibition $$A \bullet \bar {B}$$ A but not B $$\bar {A} \bullet B$$ B but not A EX-OR $$A \oplus B$$ A or B, but not both EX-NOR $$\overline {A \oplus B}$$ 1 if A equals B
##### Table 2. Complete list of Boolean functions for a dual input system

Having known the list now, let's try to quite deeply dive into their meaning, implementation, and usage (in terms of electronics). Actually, although the discussion presented is based on the two-input system, it is applicable even for a single-input system.

#### Null and Identity

Null and identity Boolean functions result in 0 (low) and 1 (high) output respectively, no matter what value the input variable holds. Implementation-wise, they require zero switches as they just need to pull the output line either to low or high.

Certain IC pins that demand to be pulled low or high to ensure satisfactory functioning stand as an example application for null and identity logic functions.

#### Transfer

The transfer Boolean function is the one in which the output promptly reflects the input. In the case of two-inputs, A and B, the output can be a replica of either A or B. Even in this case, we require no switches as there is no switching action to be performed.

The transfer logic function finds its application in power amplifiers where the output of the preceding section is connected as an input to the successive one.

#### NOT

In the NOT function, the output will be the negated value of the input, i.e., logic low output for logic high input, and vice versa. Further, if there are two inputs, A and B, the output can be the complemented version of either A or B. Implementation of a single-variable NOT function demands two switches.

NOT gates are used as a primary component while designing square wave oscillators.

#### AND and NAND

The AND function generates a high output only if all of its inputs go high. The complementary version of the AND is referred to as NAND. Thus, the NAND function yields low output only when both of its inputs are high.

A two-input AND gate can be implemented using two switches connected in series; a slightly different arrangement of the same resources would realize a NAND function.

AND (and thus NAND) gates find employment in gating circuits used in most digital circuits to ensure clock synchronization.

#### OR and NOR

The OR function yields low output only when all of its inputs go low. The inversion of this, i.e., the output going high when all of the inputs go low, represents the NOR function.

The realization of OR and NOR for two-input variables requires two switches to be connected in parallel.

OR (and hence NOR) functions form an important part of control systems where some safety measures must be initiated based on the output from sensory systems.

#### EX-OR and EX-NOR

The EX-OR Boolean function produces high output when only one of the inputs is high. Equivalently, if both inputs go high/low, the output would be low.

By contrast, the output of EX-NOR function goes high when both inputs assume same value—either low or high. These functions are employed as parity generators.

#### Implication

In implication logic, the output will either be driven to a high or would replicate the state of one of the inputs, depending on the value of the other input. That is, for a two-input case (A and B), the output (Y) will assume the same state as that of the second input (B) when the first input (A) would go high.

Next, if A is 0, then the output (Y) will be driven high irrespective of the state of B

The truth table corresponding to this implication logic is as shown in Table 3.

 Inputs Output A B Y 0 0 1 0 1 1 1 0 0 1 1 1
##### Table 3. Truth table of implication logic for A implies B case

By drawing a K-map as seen in Figure 1, the simplified logic function can be obtained as $$\bar {A} + B$$, and is referred to as A implies B. Similarly, we can even have B implies A function with the logic expression, $$A + \bar {B}$$.

##### Figure 1. K-map for A implies B implication logic

The implication function can be realized using a relatively simple circuit comprising of a combination of memristors and a conventional resistor. This logic can effectively function as a non-volatile memory as depicted in this research paper by S K Vatinsky et al.

#### Inhibition

The inhibition function is the complementary version of implication and thus has its truth table as defined by Table 4 for A inhibits B case.

 Inputs Output A B Y 0 0 0 0 1 0 1 0 1 1 1 0
##### Table 4. Truth table of inhibition logic for A inhibits B case

With this, the logic expression for the function would result as $$A \bullet \bar {B}$$ as shown by the K-map of Figure 2.

##### Figure 2. K-map for A inhibits B inhibition logic

Likewise, for B inhibits A, the expression would be $$\bar {A} \bullet B$$. Application of inhibition logic in the field of artificial neural networks is explained in detail in the Springer supplement authored by R. Rojas.

### Conclusion

Every Boolean function has its own meaning and serves a purpose. Widespread use of a few of them need not necessarily imply that the others are not also useful.


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# characteristic polynomial based on differential equation

I have this differential equation:

$$\ddot{x}-\frac{1}{6} \dot{x} - \frac{1}{6}x = e^t$$

When I DSolve it looks like this:

DSolve[x''[t] - 1/6 x'[t] - 1/6 x[t] == Exp[t], x[t], t]

Which gives me the correct answer. With that, we know I have the characteristic polynomial:

z^2 - 1/6 z - 1/6

I also find the roots:

Root[%,1]
Root[%%,2]

So all the results are correct. My question is, how can make this more easy for me, so I don't need to type manually the characteristic polynomial with its roots? I have tried with the function StringReplace to rewrite my differential equation into the characteristic polynomial, but it was messy and not functioning properly.

-

Let the ODE

ode=x''[t] - 1/6*x'[t] - 1/6*x[t] == Exp[t]

to get the characteristic polynomial we follow the literature:

cpoly = Simplify[(ode[[1]]/.x->(Exp[r*#]&))/Exp[r*t]]

now we calculate the roots:

{Root[cpoly,1], Root[cpoly,2]}

or

Solve[cpoly==0, r]

Also for the odes of the form

 ode=t^2*x''[t] - 1/6*t*x'[t] - 1/6 x[t] == Exp[t]

the only change is on the substitution:

cpoly2 = Simplify[(ode[[1]]/.x->(#^r&))/t^r]

Finally, if you want to have the multiplicity of the root handy you can use Tally:

Tally[Solve[cpoly==0, r]//Flatten]

-
what if the characteristic polynomial has a different number of roots than 2? It might have 1, 3 or 4? –  Jens Jensen Apr 17 '13 at 8:28
Thats why I gave also Solve. –  Spawn1701D Apr 17 '13 at 8:38

First,

t1 = x''[t] - x'[t]/6 - x[t]/6 /. {Derivative[k_Integer][x][__] :> z^k, x[__] :> 1}
-1/6 - z/6 + z^2

t2 = x'''[t] - 5 x'[t]/6 - 3 x[t] /. {Derivative[k_Integer][x][__] :> z^k, x[__] :> 1}
-3 - 5 z/6 + z^3

Then,

z /. Solve[t1 == 0, z]
{-1/3, 1/2}

z /. Solve[t2 == 0, z, Cubics -> False]
{Root[-18 - 5 #1 + 6 #1^3 &, 1], Root[-18 - 5 #1 + 6 #1^3 &, 2],
Root[-18 - 5 #1 + 6 #1^3 &, 3]}

Remove Cubics -> False to see the actual Cardano solution.

-
Thank you. But it only answer half of my question. It doesn't write the roots. {Root[%, 1], Root[%, 2]}could be added the line under. However I don't have 2 roots every time. Other times I have 1, 3 or 4. –  Jens Jensen Apr 17 '13 at 8:35


text:
# American Institute of Mathematical Sciences

doi: 10.3934/dcdss.2021045
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

## Resampled ensemble Kalman inversion for Bayesian parameter estimation with sequential data

 1 School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dongchuan Rd, Shanghai 200240, China 2 School of Mathematics, University of Birmingham, Edgbaston Birmingham, B15 2TT, UK

* Corresponding author: Jinglai Li

Received  January 2021 Revised  February 2021 Early access April 2021

Fund Project: The work was supported by NSFC under grant number 11771289

Many real-world problems require to estimate parameters of interest in a Bayesian framework from data that are collected sequentially in time. Conventional methods to sample the posterior distributions, such as Markov Chain Monte Carlo methods can not efficiently deal with such problems as they do not take advantage of the sequential structure. To this end, the Ensemble Kalman inversion (EnKI), which updates the particles whenever a new collection of data arrive, becomes a popular tool to solve this type of problems. In this work we present a method to improve the performance of EnKI, which removes some particles that significantly deviate from the posterior distribution via a resampling procedure. Specifically we adopt an idea developed in the sequential Monte Carlo sampler, and simplify it to compute an approximate weight function. Finally we use the computed weights to identify and remove those particles seriously deviating from the target distribution. With numerical examples, we demonstrate that, without requiring any additional evaluations of the forward model, the proposed method can improve the performance of standard EnKI in certain class of problems.

Citation: Jiangqi Wu, Linjie Wen, Jinglai Li. Resampled ensemble Kalman inversion for Bayesian parameter estimation with sequential data. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2021045
##### References:

show all references

##### References:
The simulated data for $\sigma = 0.4$ (left) and $\sigma = 0.6$ (right). The lines show the simulated states in continuous time and the dots are the noisy observations
The results for the case where noise variance is $0.4^2$. Left: the error for the simulation with $100$ particles. Right: the error for simulation with $500$ particles
The results for the case where noise variance is $0.6^2$. Left: the error for the simulation with $100$ particles. Right: the error for simulation with $500$ particles
$\Delta = 0.05.$ Top: the average estimation error of the simulation with 2000 particles. Bottom: the average estimation error of the simulation with 5000 particles. In both rows, the left figure shows the results of the observed dimensions and the right one shows the unobserved ones
$\Delta = 0.1.$ Top: the average estimation error of the simulation with 2000 particles. Bottom: the average estimation error of the simulation with 5000 particles. In both rows, the left figure shows the results of the observed dimensions and the right one shows the unobserved ones
Left: The ground truth for x. Right: Both the noise-free and the noisy data at t = 3
The estimation error for the high dimensional nonlinear example. Left: the results for $M = 2000$; Right: the results for $M = 5000$
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