The problem of analytic continuation is considered for the general hypergeometric Horn series with an arbitrary number of variables. An approach is proposed that allows one to find formulas for the ...continuation of such series into the exterior of the set of their convergence in the form of linear combinations of other hypergeometric series. These new hypergeometric series belong also to the Horn class, and are solutions of the same system of partial differential equations. Using this general result, we construct formulas for the analytic continuation for a double hypergeometric series of Horn's type, which plays an important role in the theory of the Appell function
.
Mammalian hibernation in ground squirrels is characterized by periods of torpor wherein body temperature approaches ambient temperature and metabolism is reduced to as low as 1/100th of active rates. ...It is unclear how hibernation affects long-term spatial memory, as tremendous remodeling of neurons is associated with torpor use. Given the suspected links between remodeling and memory formation and retention, we examined long-term spatial memory retention throughout a hibernation season. Animals were trained on a Barnes maze before entering torpor. Animals were tested for memory retention once a month throughout a hibernation season. Results indicate marked variation between individuals. Some squirrels retained memory across multiple torpor bouts, while other squirrels did not. No relationship was found between the number of torpor bouts, duration of bouts, or time spent torpid on long-term memory retention. However, that some squirrels successfully retain memory suggests that the profound remodeling of dendritic spines during torpor does not always lead to memory loss.
In the works of Djuna Barnes, and particularly the enigmatic final paragraphs of Nightwood , animals and animalistic qualities represent the terminal incapacity of language to encompass reality. ...Georges Bataille's concept of "animality," considered as a comparative heuristic, allows for a more coherent articulation of the theoretical underpinnings and implications of this presentation of the animal as a limit to the logical, sequential ordering of coherent meaning through language, or what Bataille refers to in shorthand as "discourse." Ultimately, Bataille theorizes and Barnes embodies an animal poetics that gives expression to that which is not strictly amenable to human sense, and both mark the literary as the site where it becomes possible to gesture beyond the human toward a mode of bestial expression that emerges from the breakdown of human signification.
We give a detailed description of the Voronoi region of the Barnes-Wall lattice <inline-formula> <tex-math notation="LaTeX">\Lambda _{16} </tex-math></inline-formula>, including its vertices, ...relevant vectors, and symmetry group. The exact value of its quantizer constant is calculated, which was previously only known approximately. To verify the result, we estimate the same constant numerically and propose a new very simple method to quantify the variance of such estimates, which is far more accurate than the commonly used jackknife estimator.
Time locking between neocortical sleep slow oscillations, thalamo-cortical spindles, and hippocampal sharp-wave ripples has convincingly been shown to be a key element of systems consolidation. Here ...we investigate the role of monosynaptic projections from ventral/intermediate hippocampus to medial prefrontal cortex (mPFC) in sleep-dependent memory consolidation in male mice. Following acquisition learning in the Barnes maze, we optogenetically silenced the axonal terminals of hippocampal projections within mPFC during slow-wave sleep. This silencing during SWS selectively impaired recent but not remote memory in the absence of effects on error rate and escape latencies. Furthermore, it prevented the development of the most efficient search strategy and sleep spindle time-locking to slow oscillation. An increase in post-learning sleep sharp-wave ripple (SPWR) density and reduced time locking of learning-associated SPWR activity to sleep spindles may be a less specific response. Our results demonstrate that monosynaptic projections from hippocampus to mPFC contribute to sleep-dependent memory consolidation, potentially by affecting the temporal coupling of sleep-associated electrophysiological events.
Convincing evidence supports the role of slow-wave sleep (SWS), and the relevance of close temporal coupling of neuronal activity between brain regions for systems consolidation. Less attention has been paid so far to the specific neuronal pathways underlying these processes. Here, we optogenetically silenced the direct monosynaptic projection from ventral/intermediate hippocampus (HC) to medial prefrontal cortex (mPFC) during SWS in male mice following repeated learning trials in a weakly aversive spatial task. Our results confirm the concept that the monosynaptic projection between HC and mPFC contributes to memory consolidation and support an important functional role of this pathway in shaping the temporal precision among sleep-associated electrophysiological events.
The efficient parallelization of fast multipole-based algorithms for the N-body problem is one of the most challenging topics in high performance scientific computing. The emergence of non-local, ...irregular communication patterns generated by these algorithms can easily create an insurmountable bottleneck on supercomputers with hundreds of thousands of cores. To overcome this obstacle we have developed an innovative parallelization strategy for Barnes–Hut tree codes on present and upcoming HPC multicore architectures. This scheme, based on a combined MPI–Pthreads approach, permits an efficient overlap of computation and data exchange. We highlight the capabilities of this method on the full IBM Blue Gene/P system JUGENE at Jülich Supercomputing Centre and demonstrate scaling across 294,912 cores with up to 2,048,000,000 particles. Applying our implementation pepc to laser–plasma interaction and vortex particle methods close to the continuum limit, we demonstrate its potential for ground-breaking advances in large-scale particle simulations.
We consider the Mellin–Barnes (MB) transform of the triangle ladder-like scalar diagram in d=4 dimensions. It is shown how the multi-fold MB transform of the momentum integral corresponding to an ...arbitrary number of rungs is reduced to the two-fold MB transform. For this purpose, we use the Belokurov–Usyukina reduction method for four-dimensional scalar integrals in position space. The result is represented in terms of the Euler ψ function and its derivatives. We derive new formulas for the MB two-fold integration in the complex planes of two complex variables. We demonstrate that these formulas solve the Bethe–Salpeter equation. We comment on further applications of the solution to the Bethe–Salpeter equation for the vertices in N=4 supersymmetric Yang–Mills theory. We show that the recursive property of the MB transforms observed in the present work for that kind of diagrams has nothing to do with quantum field theory, the theory of integral transforms, or the theory of polylogarithms in general, but has its origin in a simple recursive property of smooth functions, which may be shown by using basic methods of mathematical analysis.
PDF
