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[MATH] transport during hypoxic and CO hypoxia in neonatal and adult sheep. Am. J. Physiol. 248 : H118-H124. Landauer R (1961) Irreversibility and heat generation in the computing process. IBM J. Res. Dev. |
: 183-191. Lennie P (2003) The cost of cortical computation. Curr. Biol. 13 : 493-497. Linde R, Schmalbruch IK, Paulson OB, Madsen PL (1999) The Kety-Schmidt technique for repeated measurements of global cerebral blood flow and metabolism in the conscious rat. Acta Physiol. Scand. |
165 : 395-401. Madsen PL et al (1991) Cerebral [MATH] metabolism and cerebral blood flow in humans during deep and rapid-eye-movement sleep. |
J. Appl. Physiol. 70 : 2597-2601. Marcus ML, Heistad DD (1979) Effects of sympathetic nerves on cerebral blood flow in awake dogs. Am. J. Physiol. |
236 : H549-H553. Markram H et al (1997) Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex. J. Physiol. |
500 : 409-440. Markram H, Wang Y, Tsodyks M (1998) Differential signaling via the same axon of neocortical pyramidal neurons. Proc. Natl. Acad. Sci. USA |
95 : 5323-5328. McElligott JG, Melzack R (1967) Localized thermal changes evoked in the brain by visual and auditory stimulation. Exp. Neurol. |
17 : 293-312. Murre JMJ, Sturdy DPF (1995) The connectivity of the brain: Multilevel quantitative analysis. Biol. Cybern. 73 529-545. |
Nakao M, Gadsby DC (1989) [Na] and [K] dependence of the Na/K pump current-voltage relationship in guinea pig ventricular myocytes. |
J. Gen. Physiol. 94 : 539-565. Nelson DA, Nunneley SA (1998) Brain temperature and limits on transcranial cooling in humans: quantitative modeling results. Eur. J. Appl. Physiol. |
78 : 353-359. Nybo L, Secher NH, Nielsen B (2002) Inadequate heat release from the human brain during prolonged exercise with hyperthermia. J. Physiol. |
545 : 697-704. Prothero (1997) Cortical scaling in mammals: A repeating units model. J. Brain Res. 38 : 195-207. Purves D (1988) Body and Brain. |
Cambridge, Massachusetts: Harvard Univ. Press. Raichle ME (2003) Functional brain imaging and human brain function. J. Neurosci. |
23 : 3959-3962. Rolfe DFS, Brown GC (1997) Cellular energy utilization and molecular origin of standard metabolic rate in mammals. |
Physiol. Rev. 77 : 731-758. Schmidt-Nielsen K (1984) Scaling: Why is Animal Size so Important? Cambridge: Cambridge Univ. Press. |
Siesjo B (1978) Brain Energy Metabolism . New York: Wiley. Stephan H, Baron G, Frahm HD (1981) New and revised data on volumes of brain structures in insectivores and primates. Folia Primatol. |
35 : 1-29. Stowe K (1984) Introduction to Statistical Mechanics and Thermodynamics New York: Wiley. Striedter GF (2005) Principles of Brain Evolution Sunderland, MA: Sinauer Assoc. |
Sukstanskii AL, Yablonskiy DA (2006) Theoretical model of temperature regulation in the brain during changes in functional activity. |
Proc. Natl. Acad. Sci. USA 103 : 12144-12149. Traub R, Miles R (1991) Neuronal Networks of the Hippocampus Cambridge, UK: Cambridge Univ. Press. |
Waschke K et al (1993) Local cerebral blood flow and glucose utilization after blood exchange with a hemoglobin-based [MATH] carrier in conscious rats. Am. J. Physiol. |
265 : H1243-H1248. van Leeuwen GMJ et al (2000) Numerical modeling of temperature distribution within the natal head. Pediatr. Res. |
48 : 351-356. Volgushev M, et al (2004) Probability of transmitter release at neocortical synapses at different temperatures. J. Neurophysiol. |
92 : 212-220. Yablonskiy DA, Ackerman JJH, Raichle ME (2000) Coupling between changes in human brain temperature and oxidative metabolism during prolonged visual stimulation. Proc. Natl. Acad. Sci. USA |
97 : 7603-7608. Yoshinura Y, Kimura F, Tsumoto T (1999) Estimation of single channel conductance underlying synaptic transmission between pyramidal cells in the visual cortex. |
Neuroscience 88 : 347-352. Zhang K, Sejnowski TJ (2000) A universal scaling law between gray matter and white matter of cerebral cortex. Proc. Natl. Acad. Sci. USA |
97 : 5621-5626. Figure Captions Fig. 1 Heat transfer in the brain. Brain is represented as half of the ball with three concentric layers representing (from the brain outside): cerebrospinal fluid, skull, and scalp. The heat generated in the brain is removed by cerebral blood flow (small circles), conduction through the... |
Fig. 2 Sodium influx during an action potential. (A) Temporal dependence of Na (solid line) and K (dashed line) conductances and voltage (dashed-dotted line) during the action potential. (B) The correction |
[MATH] as a function of intracellular sodium concentration. (C) Dependence of sodium influx [MATH] on the effective fiber diameter [MATH] coming from a numerical integration of Eq. (6). The least square fit (solid line) yields the relationship: |
[MATH] mM, where [MATH] is in cm. This numerical fit practically confirms the theoretical dependence [MATH] in Eq. (12). Fig. 3 Dependence of the intracellular sodium concentration on time for a neuron firing repeatedly. (A) Results for [MATH] |
[MATH] m, i.e., the harmonic mean of the mouse axon diameter [MATH] [MATH] m and dendrite diameter [MATH] [MATH] m (see Sec. 2.2). (B) Results for [MATH] |
[MATH] m, i.e., for the smallest molecularly possible axons with [MATH] [MATH] m. Note that the range of variability in (B) is much larger, which reflexs higher amplitudes of Na |
influx and its faster relaxation for thin fibers. Panels (A) and (B) come from simulations of Eq. (6). (C) Simulation results for [MATH] |
[MATH] m of Eq. (13) (solid lines) and its approximation Eq. (14) (dashed and dashed-dotted lines). For all plots in (A)-(C) [MATH] |
Fig. 4 Intracellular sodium concentration as a function of firing rate. The point (diamonds) coming from a direct numerical integration of Eq. (6) are approximated well by the theoretical formula (15) (solid line). The maximal discrepancy for high frequency is about |
[MATH] [MATH] . The average [Na] av does not depend much on fiber diameter (panels A and C) nor on the Hill coefficient [MATH] (panels A and B). |
Fig. 5 ATP and glucose utilization rates, and scaling of firing rate with brain size. (A) ATP rate increases non-linearly with frequency [MATH] and saturates for high values of [MATH] . (B) CMR glu also increases non-linearly with firing rate, similar to the dependence of ATP on [MATH] (C) Scaling of the estimated firi... |
[MATH] Hz ( [MATH] [MATH] ). Estimates of frequency are based on the empirical data of CMR glu which are (in [MATH] mol/cm min): 1.07 for mouse, 0.90 for rat, 0.83 for rabbit, 0.81 for cat, 0.47 for rhesus monkey, 0.46 for baboon, 0.34 for human. These data were taken from the data gathered in the supplementary informa... |
[MATH] m, [MATH] Fig. 6 Dependence of the sodium pump power [MATH] on frequency and the effective fiber diameter. (A) Biphasic dependence of [MATH] (per neuron per surface area) on frequency. Analytical formula (19) (solid line) leads to similar results as a direct numerical integration of Eq. (6) (diamonds). Results a... |
[MATH] m. (B) [MATH] depends inversely on fiber diameter [MATH] . For extremely thin fibers [MATH] tends to diverge. Results are for |
[MATH] cm and [MATH] Hz, corresponding to human brain. In both panels A and B, the Hill coefficient [MATH] Fig. 7 Log-Log plot of the empirical dependence of the cerebral blood flow rate [MATH] on brain volume [MATH] for several mammals. The allometric dependence has the following form: [MATH] 1/sec, where [MATH] is ex... |
[MATH] [MATH] ). The [MATH] empirical data are as follows: [MATH] sec -1 for mouse (Frietsch et al, 2007); [MATH] sec -1 for rat (Waschke et al, 1993; Linde et al, 1999); |
[MATH] sec -1 for rabbit (Busija, 1984); [MATH] sec -1 for dog (Marcus and Heistad, 1979); [MATH] sec -1 for sheep (Koehler et al, 1985); |
[MATH] sec -1 for human (Madsen et al, 1991). Brain volumes were taken from Stephan et al (1981) and Karbowski (2007). Fig. 8 Brain temperature as a function of brain size, fiber diameter, and firing rate. (A) The spatial distribution of brain temperature [MATH] For very small brains [MATH] is smaller than the arterior... |
[MATH] m, [MATH] ). Solid line corresponds to human and dashed line to mouse. Fig. 9 Lower bound on the effective fiber diameter [MATH] as a function of brain size and firing rate. (A) [MATH] depends very weakly on gray matter volume. (B) The lower bound on [MATH] depends biphasically on firing rate [MATH] cm ). Weak s... |
# Source: arxiv 0906.3178 # Title: Survival of the aligned: ordering of the plant cortical microtubule array # Sections: all # Downloaded: 2026-03-03T05:15:00.416652+00:00 |
Current address: ]UMR 7600, UPMC /CNRS, 4 Place Jussieu, 75255 Paris Cedex 05 France Survival of the Aligned: Ordering of the Plant Cortical Microtubule Array |
Abstract The cortical array is a structure consisting of highly aligned microtubules which plays a crucial role in the characteristic uniaxial expansion of all growing plant cells. Recent experiments have shown polymerization-driven collisions between the membrane-bound cortical microtubules, suggesting a possible mech... |
pacs: 87.16.Ka, 87.16.ad, 87.16.af, 87.16.Ln Microtubules are a ubiquitous component of the cytoskeleton of eukaryotic cells. These dynamic filamentous protein aggregates, in association with a host of microtubule associated proteins (MAPs), are able to self-organize into dynamic, spatially extended stable structures o... |
In contrast to the more commonly studied animal cells, plant cells are encased in a cellulosic cell wall, and generally only expand along a single well-defined growth axis. A crucial component in this anisotropic growth process is a plant-unique microtubule structure called the cortical array Ehrhardt and Shaw ( 2006 .... |
In this Letter we address the question of whether, as has been posited by Dixit and Cyr Dixit and Cyr ( 2004 , these interactions are sufficient to explain the alignment of microtubules in the cortical array. To do so we construct a model for the microtubule dynamics and interactions, and evaluate it using two compleme... |
Our model differs from existing models for 2D organization of filamentous proteins in two important ways. Firstly, in most of these models the filaments are both free to rotate and translate as a whole |
Geigant et al. ( 1998 ); Zumdieck et al. ( 2005 ); Kruse et al. ( 2005 ); Aranson and Tsimring ( 2006 ); Rühle et al. ( 2008 , which is inconsistent with the experimental observations on the cortical array. Secondly, our model explicitly takes into account the dynamic instability of the individual microtubules, providi... |
For the intrinsic microtubule dynamics in our model, we use the standard two-state dynamic instability model Dogterom and Leibler ( 1993 in which each microtubule plus end is assumed to be either growing with a speed [MATH] or shrinking with a speed [MATH] . This plus end can switch stochastically from growing to shrin... |
Because the persistence length [MATH] of microtubules is long ( [MATH] ) compared to the average length of a microtubule ( [MATH] ) and thermal motion is inhibited by the attachment to the plasma membrane, microtubules are modelled as straight rods with kinks at positions where a zippering event has occurred. A microtu... |
for the segment attached to the nucleation site. In light of the available evidence, we assume that the angle-dependent collision outcome probabilities [MATH] (zippering), [MATH] (induced catastrophe) and [MATH] (crossover) are independent of the polarity of the microtubules and are therefore fully defined on the inter... |
We first analyze this system using a coarse-grained theory, in which we consider densities of microtubule segments instead of individual microtubules. From the outset we assume the system is, and remains, spatially homogeneous, and later restrict ourselves to steady-state solutions. Because microtubules are nucleated i... |
(0) segments that form the ‘body’ and tail of the microtubule. Our variables are thus the areal number densities [MATH] of segments in state [MATH] with segment index [MATH] , having length [MATH] and orientation [MATH] (measured from an arbitrary axis) at time |
[MATH] . From these, we compute the total length density [MATH] as [EQUATION] The segment densities obey a set of evolution equations that can symbolically be written as |
[EQUATION] The arguments in square brackets explicitly display the functional dependencies of the terms on the right hand side. Below, we explain each of these terms briefly, and refer the reader to Hawkins et al. ( 2009 for a full derivation and an in-depth analysis. The dynamics of the active growing ( [MATH] ) and s... |
[MATH] and [MATH] , and the advective terms [MATH] and [MATH] due to growth and shrinkage respectively Dogterom and Leibler ( 1993 . Collisions between microtubules that lead to an induced catastrophe cause growing segments to switch to the shrinking state, at a rate given by [MATH] , where [MATH] is the collision angl... |
In the steady state, the infinite set of equations ( with the boundary conditions reduces to a set of four coupled non-linear integral equations. These relate the length density [MATH] to the average segment length, active segment density and ratio between inactive and active segments, each being a function of the angl... |
[MATH] , the remaining parameters can be absorbed into a single dimensionless control parameter [MATH] , defined as [EQUATION] Here we only consider the case [MATH] , for which the length of the microtubules is intrinsically bounded even in the absence of collisions. In this case, the average length of |
non-interacting microtubules is given by [MATH] Dogterom and Leibler ( 1993 and the control parameter [MATH] can be interpreted as [MATH] , implicitly defining an interaction length scale [MATH] . As [MATH] increases towards 0, the number of interactions between microtubules increases. |
For any value of [MATH] there exists an isotropic solution to ( ), for which the total length density [MATH] satisfies [MATH] where [MATH] denotes the [MATH] -th Fourier cosine coefficient of the product [MATH] . The isotropic length density is therefore an increasing function of the control parameter [MATH] that only ... |
[MATH] , this solution is only stable for large negative values of [MATH] . As [MATH] increases, the number of interactions between microtubules increases, until the isotropic solution becomes unstable. This happens at the bifurcation point [MATH] , given by |
[EQUATION] We note that the location of the bifurcation point is determined solely by the properties of the induced catastrophe probability [MATH] , and, like the density in the isotropic phase, does not depend on zippering. |
To quantify the degree of alignment we use the standard 2D nematic order parameter [MATH] , defined as [MATH] The full bifurcation diagram can be computed by numerically tracing the ordered solution branch from the bifurcation point, provided that the products [MATH] and |
[MATH] have finite Fourier expansions. We restrict ourselves to an expansion up to [MATH] . The coefficients are constrained by [MATH] and |
[MATH] . In line with experimental observations Dixit and Cyr ( 2004 we choose the remaining parameters such that [MATH] is monotonically increasing to a maximum at |
[MATH] and is maximally biased towards steep collision angles (see Hawkins et al. ( 2009 for other choices), and [MATH] . The magnitudes of [MATH] and [MATH] |
is similar to that observed in experiments, and the crossover probability is fixed by the requirement [MATH] . The resulting interaction probabilities are illustrated in Fig. b. We argue that the apparent discrepancy with experiments, caused by setting |
[MATH] , is not very significant for the ordering transition, as collisions between near-parallel microtubules are infrequent and cause only slight changes of orientation in the case they lead to zippering. |
Given our choice for [MATH] , we have [MATH] and [MATH] so that [MATH] . The results are representative for a large class of interaction probabilities with |
[MATH] . Higher modes do not affect the bifurcation point ) and appear to have only minor effects on the bifurcation diagram. Also, any changes to the overall magnitude of |
[MATH] and [MATH] result only in a scaling of the [MATH] -axis. Comparing the computed solutions (solid lines) for systems with (Fig. b) and without ( a) zippering, we note that zippering has only a minor effect on the ordering beyond the bifurcation point (see also Hawkins et al. ( 2009 ). This shows that the ‘weeding... |
In parallel with the coarse-grained theoretical approach described above, we performed stochastic particle-based simulations of the interacting microtubules. Fig. shows the resulting steady-state alignment as a function of [MATH] , for systems with and without zippering. In the simulations, the presence of zippering tr... |
In the absence of zippering Fig. a, shows that the theoretical predictions and simulation results agree well. As expected, the agreement is less good when zippering is enabled (Fig. b), because zippering leads to strong spatial correlations in the form of microtubule bundles, which are not accounted for in our mean-fie... |
Finally we investigated the limit of weak interactions ( [MATH] ; data not shown) in which the discrepancies due to the mean-field nature of our model should decrease. Without zippering simulation results rapidly converge to the theoretical predictions. In the presence of zippering the results for the ‘single’ interact... |
Our model of interacting cortical microtubules displays both isotropic and aligned phases and is based on experimentally observed microscopic effects. The kinetic parameters appearing in the control parameter [MATH] may be regulated by the cell via MAPs, suggesting a mechanism for cellular control over creation, mainte... |
Acknowledgements. We thank Kostya Shundyak, Jan Vos and Jelmer Lindeboom for helpful discussions. SHT was supported by the NWO programme “Computational Life Sciences” (Contract: CLS 635.100.003). RJH was supported by the EU Network of Excellence “Active Biomics” (Contract: NMP4-CT-2004-516989). This work is part of the... |
# Source: arxiv 0906.5339 # Title: Asymmetric Quantum Cyclic Codes # Sections: all # Downloaded: 2026-03-03T02:20:31.637082+00:00 |
Asymmetric Quantum Cyclic Codes Abstract. It is recently conjectured that phase-shift errors occur with high probability than qubit-flip errors, hence phase-shift errors are more disturbing to quantum information than qubit-flip errors. This leads to construct asymmetric quantum error-correcting codes (AQEC) to protect... |
Construction of AQEC (Main Results). The following theorem shows the CSS construction of asymmetric quantum error control codes over [MATH] |
Theorem 1 (CSS AQEC) Let [MATH] and [MATH] be two classical codes with parameters [MATH] and [MATH] respectively, and [MATH] [MATH] . If |
[MATH] , then i) there exists an AQEC with parameters [MATH] that is [MATH] Also, there exists a QEC with parameters [MATH] ii) there exists an asymmetric subsystem code with parameters [MATH] for [MATH] |
Furthermore, all constructed codes are pure to their minimum distances. Therefore, it is straightforward to derive asymmetric quantum control codes from two classical codes as shown in Theorem as well as a subsystem code. Of course, one wishes to increase the values of [MATH] vers. [MATH] for the same code length and d... |
Lemma 2 An [MATH] asymmetric quantum code corrects all qubit-flip errors up to [MATH] and all phase-shift errors up to [MATH] Theorem 3 |
Let [MATH] be a cyclic code with parameters [MATH] and a generator polynomial [MATH] . Let [MATH] be a cyclic code defined by the polynomial [MATH] such that [MATH] , then there exists AQEC with parameters |
[MATH] , s.t. [MATH] and [MATH] . Furthermore the code can correct [MATH] qubit-flip errors and [MATH] phase-shift errors. Theorem 4 |
Let [MATH] be a [MATH] -dimensional cyclic code of length [MATH] over [MATH] . Let [MATH] and [MATH] respectively denote the defining sets of [MATH] and [MATH] . If [MATH] is a subset of |
[MATH] that is the union of cyclotomic cosets, then one can define a cyclic code [MATH] of length [MATH] over [MATH] by the defining set [MATH] . If [MATH] is in the range [MATH] then there exists asymmetric quantum code with parameters |
[MATH] where [MATH] and [MATH] The usefulness of the previous theorem is that one can directly derive asymmetric quantum codes from the set of roots (defining set) of a classical cyclic code. We also notice that the integer [MATH] represents a size of a cyclotomic coset (set of roots), in other words, it does not repre... |
AQEC and Connection with Subsystem Codes. We establish the connection between AQEC and subsystem codes. Furthermore we derive a larger class of quantum codes called asymmetric subsystem codes (ASSC). |
Theorem 5 (ASSC Euclidean Construction) If [MATH] is a [MATH] -dimensional [MATH] -linear code of length [MATH] that has a [MATH] -dimensional subcode [MATH] and |
[MATH] , then there exist [EQUATION] subsystem codes, where [MATH] and [MATH] From this result, we can see that any two classical codes [MATH] and [MATH] such that [MATH] , in which they can be used to construct a subsystem code (SSC), can also be used to construct asymmetric quantum code (AQEC). Asymmetric subsystem c... |
The interested readers may look at the previous work in constructions of asymmetric quantum error control codes (AQEC) . The CSS construction of QEC is well explained in , and in the list of references presented in |
# Source: arxiv 0907.0974 # Title: Modeling and simulation of Ran-mediated nuclear import # Sections: all # Downloaded: 2026-03-03T05:14:47.937000+00:00 |
Università di Milano–Bicocca Quaderni di Matematica Modeling and simulation of Ran-mediated nuclear import Andrea Cangiani Quaderno n. 10/2009 |
Stampato nel mese di aprile 2007 presso il Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, via R. Cozzi 53, 20125 Milano, ITALIA |
Disponibile in formato elettronico sul sito Segreteria di redazione : Ada Osmetti - Giuseppina Cogliandro tel.: +39 02 6448 5755-5758 fax: +39 02 6448 5705 |
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