Frequency control in synchronized networks of inhibitory neurons

We analyze the control of frequency for a synchronized inhibitory neuronal network. The analysis is done for a reduced membrane model with a biophysically-based synaptic influence. We argue that such a reduced model can quantitatively capture the frequency behavior of a larger class of neuronal models. We show that in different parameter regimes, the network frequency depends in different ways on the intrinsic and synaptic time constants. Only in one portion of the parameter space, called `phasic', is the network period proportional to the synaptic decay time. These results are discussed in connection with previous work of the authors, which showed that for mildly heterogeneous networks, the synchrony breaks down, but coherence is preserved much more for systems in the phasic regime than in the other regimes. These results imply that for mildly heterogeneous networks, the existence of a coherent rhythm implies a linear dependence of the network period on synaptic decay time, and a much weaker dependence on the drive to the cells. We give experimental evidence for this conclusion.Comment: 18 pages, 3 figures, Kluwer.sty. J. Comp. Neurosci. (in press). Originally submitted to the neuro-sys archive which was never publicly announced (was 9803001

Synchronization and oscillatory dynamics in heterogeneous mutually inhibited neurons

We study some mechanisms responsible for synchronous oscillations and loss of synchrony at physiologically relevant frequencies (10-200 Hz) in a network of heterogeneous inhibitory neurons. We focus on the factors that determine the level of synchrony and frequency of the network response, as well as the effects of mild heterogeneity on network dynamics. With mild heterogeneity, synchrony is never perfect and is relatively fragile. In addition, the effects of inhibition are more complex in mildly heterogeneous networks than in homogeneous ones. In the former, synchrony is broken in two distinct ways, depending on the ratio of the synaptic decay time to the period of repetitive action potentials ($\tau_s/T$), where $T$ can be determined either from the network or from a single, self-inhibiting neuron. With $\tau_s/T > 2$, corresponding to large applied current, small synaptic strength or large synaptic decay time, the effects of inhibition are largely tonic and heterogeneous neurons spike relatively independently. With $\tau_s/T < 1$, synchrony breaks when faster cells begin to suppress their less excitable neighbors; cells that fire remain nearly synchronous. We show numerically that the behavior of mildly heterogeneous networks can be related to the behavior of single, self-inhibiting cells, which can be studied analytically.Comment: 17 pages, 6 figures, Kluwer.sty. Journal of Compuational Neuroscience (in press). Originally submitted to the neuro-sys archive which was never publicly announced (was 9802001

Irredundant Triangular Decomposition

Triangular decomposition is a classic, widely used and well-developed way to represent algebraic varieties with many applications. In particular, there exist sharp degree bounds for a single triangular set in terms of intrinsic data of the variety it represents, and powerful randomized algorithms for computing triangular decompositions using Hensel lifting in the zero-dimensional case and for irreducible varieties. However, in the general case, most of the algorithms computing triangular decompositions produce embedded components, which makes it impossible to directly apply the intrinsic degree bounds. This, in turn, is an obstacle for efficiently applying Hensel lifting due to the higher degrees of the output polynomials and the lower probability of success. In this paper, we give an algorithm to compute an irredundant triangular decomposition of an arbitrary algebraic set $W$ defined by a set of polynomials in C[x_1, x_2, ..., x_n]. Using this irredundant triangular decomposition, we were able to give intrinsic degree bounds for the polynomials appearing in the triangular sets and apply Hensel lifting techniques. Our decomposition algorithm is randomized, and we analyze the probability of success

Finiteness and orbifold Vertex Operator Algebras

In this paper, I investigate the ascending chain condition of right ideals in the case of vertex operator algebras satisfying a finiteness and/or a simplicity condition. Possible applications to the study of finiteness of orbifold VOAs is discussed.Comment: 12 pages, comments are welcom

The first version Buffered Large Analog Bandwidth (BLAB1) ASIC for high luminosity collider and extensive radio neutrino detectors

Future detectors for high luminosity particle identification and ultra high energy neutrino observation would benefit from a digitizer capable of recording sensor elements with high analog bandwidth and large record depth, in a cost-effective, compact and low-power way. A first version of the Buffered Large Analog Bandwidth (BLAB1) ASIC has been designed based upon the lessons learned from the development of the Large Analog Bandwidth Recorder and Digitizer with Ordered Readout (LABRADOR) ASIC. While this LABRADOR ASIC has been very successful and forms the basis of a generation of new, large-scale radio neutrino detectors, its limited sampling depth is a major drawback. A prototype has been designed and fabricated with 65k deep sampling at multi-GSa/s operation. We present test results and directions for future evolution of this sampling technique.Comment: 15 pages, 26 figures; revised, accepted for publication in NIM

Understanding Sample Generation Strategies for Learning Heuristic Functions in Classical Planning

We study the problem of learning good heuristic functions for classical planning tasks with neural networks based on samples that are states with their cost-to-goal estimates. It is well known that the learned model quality depends on the training data quality. Our main goal is to understand better the influence of sample generation strategies on the performance of a greedy best-first heuristic search guided by a learned heuristic function. In a set of controlled experiments, we find that two main factors determine the quality of the learned heuristic: the regions of the state space included in the samples and the quality of the cost-to-goal estimates. Also, these two factors are interdependent: having perfect estimates of cost-to-goal is insufficient if an unrepresentative part of the state space is included in the sample set. Additionally, we study the effects of restricting samples to only include states that could be evaluated when solving a given task and the effects of adding samples with high-value estimates. Based on our findings, we propose practical strategies to improve the quality of learned heuristics: three strategies that aim to generate more representative states and two strategies that improve the cost-to-goal estimates. Our resulting neural network heuristic has higher coverage than a basic satisficing heuristic. Also, compared to a baseline learned heuristic, our best neural network heuristic almost doubles the mean coverage and can increase it for some domains by more than six times.Comment: 27 page

The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of the generalized Riemann type hierarchy are also discussed.Comment: 18 page

Protein Kinase CK2α Maintains Extracellular Signal-regulated Kinase (ERK) Activity in a CK2α Kinase-independent Manner to Promote Resistance to Inhibitors of RAF and MEK but Not ERK in BRAF Mutant Melanoma

The protein kinase casein kinase 2 (CK2) is a pleiotropic and constitutively active kinase that plays crucial roles in cellular proliferation and survival. Overexpression of CK2, particularly the α catalytic subunit (CK2α, CSNK2A1), has been implicated in a wide variety of cancers and is associated with poorer survival and resistance to both conventional and targeted anticancer therapies. Here, we found that CK2α protein is elevated in melanoma cell lines compared with normal human melanocytes. We then tested the involvement of CK2α in drug resistance to Food and Drug Administration-approved single agent targeted therapies for melanoma. In BRAF mutant melanoma cells, ectopic CK2α decreased sensitivity to vemurafenib (BRAF inhibitor), dabrafenib (BRAF inhibitor), and trametinib (MEK inhibitor) by a mechanism distinct from that of mutant NRAS. Conversely, knockdown of CK2α sensitized cells to inhibitor treatment. CK2α-mediated RAF-MEK kinase inhibitor resistance was tightly linked to its maintenance of ERK phosphorylation. We found that CK2α post-translationally regulates the ERK-specific phosphatase dual specificity phosphatase 6 (DUSP6) in a kinase dependent-manner, decreasing its abundance. However, we unexpectedly showed, by using a kinase-inactive mutant of CK2α, that RAF-MEK inhibitor resistance did not rely on CK2α kinase catalytic function, and both wild-type and kinase-inactive CK2α maintained ERK phosphorylation upon inhibition of BRAF or MEK. That both wild-type and kinase-inactive CK2α bound equally well to the RAF-MEK-ERK scaffold kinase suppressor of Ras 1 (KSR1) suggested that CK2α increases KSR facilitation of ERK phosphorylation. Accordingly, CK2α did not cause resistance to direct inhibition of ERK by the ERK1/2-selective inhibitor SCH772984. Our findings support a kinase-independent scaffolding function of CK2α that promotes resistance to RAF- and MEK-targeted therapies

Quartz Cherenkov Counters for Fast Timing: QUARTIC

We have developed particle detectors based on fused silica (quartz) Cherenkov radiators read out with micro-channel plate photomultipliers (MCP-PMTs) or silicon photomultipliers (SiPMs) for high precision timing (Sigma(t) about 10-15 ps). One application is to measure the times of small angle protons from exclusive reactions, e.g. p + p - p + H + p, at the Large Hadron Collider, LHC. They may also be used to measure directional particle fluxes close to external or stored beams. The detectors have small areas (square cm), but need to be active very close (a few mm) to the intense LHC beam, and so must be radiation hard and nearly edgeless. We present results of tests of detectors with quartz bars inclined at the Cherenkov angle, and with bars in the form of an "L" (with a 90 degree corner). We also describe a possible design for a fast timing hodoscope with elements of a few square mm.Comment: 24 pages, 14 figure