300 research outputs found
Phase of Firing as a Local Window for Efficient Neuronal Computation: Tonic and Phasic Mechanisms in the Control of Theta Spike Phase
Operator system quotients of matrix algebras and their tensor products
An operator system modulo the kernel of a completely positive linear map of
the operator system gives rise to an operator system quotient. In this paper,
operator system quotients and quotient maps of certain matrix algebras are
considered. Some applications to operator algebra theory are given, including a
new proof of Kirchberg's theorem on the tensor product of B(H) with the group
C*-algebra of a countable free group. We also show that an affirmative solution
to the Connes Embedding Problem is implied by various matrix-theoretic
problems, and we give a new characterisation of unital C*-algebras that have
the weak expectation property.Comment: To appear in Mathematica Scandinavic
Classical and nonclassical randomness in quantum measurements
The space of positive operator-valued measures on the Borel sets of a compact
(or even locally compact) Hausdorff space with values in the algebra of linear
operators acting on a d-dimensional Hilbert space is studied from the
perspectives of classical and non-classical convexity through a transform
that associates any positive operator-valued measure with a certain
completely positive linear map of the homogeneous C*-algebra
into . This association is achieved by using an operator-valued integral
in which non-classical random variables (that is, operator-valued functions)
are integrated with respect to positive operator-valued measures and which has
the feature that the integral of a random quantum effect is itself a quantum
effect. A left inverse for yields an integral representation,
along the lines of the classical Riesz Representation Theorem for certain
linear functionals on , of certain (but not all) unital completely
positive linear maps . The extremal and
C*-extremal points of the space of POVMS are determined.Comment: to appear in Journal of Mathematical Physic
Bone Dielectric Property Variation as a Function of Mineralization at Microwave Frequencies
A critical need exists for new imaging tools to more accurately characterize bone quality beyond the conventional modalities of dual energy X-ray absorptiometry (DXA), ultrasound speed of sound, and broadband attenuation measurements. In this paper we investigate the microwave dielectric properties of ex vivo trabecular bone with respect to bulk density measures. We exploit a variation in our tomographic imaging system in conjunction with a new soft prior regularization scheme that allows us to accurately recover the dielectric properties of small, regularly shaped and previously spatially defined volumes. We studied six excised porcine bone samples from which we extracted cylindrically shaped trabecular specimens from the femoral heads and carefully demarrowed each preparation. The samples were subsequently treated in an acid bath to incrementally remove volumes of hydroxyapatite, and we tested them with both the microwave measurement system and a micro-CT scanner. The measurements were performed at five density levels for each sample. The results show a strong correlation between both the permittivity and conductivity and bone volume fraction and suggest that microwave imaging may be a good candidate for evaluating overall bone health
Decomposition of the tensor product of two Hilbert modules
Given a pair of positive real numbers and a sesqui-analytic
function on a bounded domain , in this paper,
we investigate the properties of the sesqui-analytic function taking values in matrices. One of the key findings
is that is non-negative definite whenever
and are non-negative definite. In this case, a realization
of the Hilbert module determined by the kernel is
obtained. Let , be two Hilbert modules over the
polynomial ring . Then acts naturally on the tensor product . The restriction of this action to the polynomial ring obtained using the restriction map leads
to a natural decomposition of the tensor product , which is investigated. Two of the initial pieces in this decomposition
are identified
Neuronal oscillations and the rate-to-phase transform: mechanism, model and mutual information
Theoretical and experimental studies suggest that oscillatory modes of processing play an important role in neuronal computations. One well supported idea is that the net excitatory input during oscillations will be reported in the phase of firing, a ‘rate-to-phase transform’, and that this transform might enable a temporal code. Here, we investigate the efficiency of this code at the level of fundamental single cell computations. We first develop a general framework for the understanding of the rate-to-phase transform as implemented by single neurons. Using whole cell patch-clamp recordings of rat hippocampal pyramidal neurons in vitro, we investigated the relationship between tonic excitation and phase of firing during simulated theta frequency (5 Hz) and gamma frequency (40 Hz) oscillations, over a range of physiological firing rates. During theta frequency oscillations, the phase of the first spike per cycle was a near-linear function of tonic excitation, advancing through a full 180 deg, from the peak to the trough of the oscillation cycle as excitation increased. In contrast, this relationship was not apparent for gamma oscillations, during which the phase of firing was virtually independent of the level of tonic excitatory input within the range of physiological firing rates. We show that a simple analytical model can substantially capture this behaviour, enabling generalization to other oscillatory states and cell types. The capacity of such a transform to encode information is limited by the temporal precision of neuronal activity. Using the data from our whole cell recordings, we calculated the information about the input available in the rate or phase of firing, and found the phase code to be significantly more efficient. Thus, temporal modes of processing can enable neuronal coding to be inherently more efficient, thereby allowing a reduction in processing time or in the number of neurons required
The role of red and processed meat in colorectal cancer development : a perspective
Peer reviewe
CAG repeat not polyglutamine length determines timing of Huntington’s disease onset
Variable, glutamine-encoding, CAA interruptions indicate that a property of the uninterrupted HTT CAG repeat sequence, distinct from the length of huntingtin’s polyglutamine segment, dictates the rate at which Huntington’s disease (HD) develops. The timing of onset shows no significant association with HTT cis-eQTLs but is influenced, sometimes in a sex-specific manner, by polymorphic variation at multiple DNA maintenance genes, suggesting that the special onset-determining property of the uninterrupted CAG repeat is a propensity for length instability that leads to its somatic expansion. Additional naturally occurring genetic modifier loci, defined by GWAS, may influence HD pathogenesis through other mechanisms. These findings have profound implications for the pathogenesis of HD and other repeat diseases and question the fundamental premise that polyglutamine length determines the rate of pathogenesis in the “polyglutamine disorders.
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