191 research outputs found
Probabilistic Guarantees for Safe Deep Reinforcement Learning
Deep reinforcement learning has been successfully applied to many control
tasks, but the application of such agents in safety-critical scenarios has been
limited due to safety concerns. Rigorous testing of these controllers is
challenging, particularly when they operate in probabilistic environments due
to, for example, hardware faults or noisy sensors. We propose MOSAIC, an
algorithm for measuring the safety of deep reinforcement learning agents in
stochastic settings. Our approach is based on the iterative construction of a
formal abstraction of a controller's execution in an environment, and leverages
probabilistic model checking of Markov decision processes to produce
probabilistic guarantees on safe behaviour over a finite time horizon. It
produces bounds on the probability of safe operation of the controller for
different initial configurations and identifies regions where correct behaviour
can be guaranteed. We implement and evaluate our approach on agents trained for
several benchmark control problems
Hair cells use active zones with different voltage dependence of Ca<sup>2+</sup> influx to decompose sounds into complementary neural codes.
For sounds of a given frequency, spiral ganglion neurons (SGNs) with different thresholds and dynamic ranges collectively encode the wide range of audible sound pressures. Heterogeneity of synapses between inner hair cells (IHCs) and SGNs is an attractive candidate mechanism for generating complementary neural codes covering the entire dynamic range. Here, we quantified active zone (AZ) properties as a function of AZ position within mouse IHCs by combining patch clamp and imaging of presynaptic Ca2+ influx and by immunohistochemistry. We report substantial AZ heterogeneity whereby the voltage of half-maximal activation of Ca2+ influx ranged over âŒ20 mV. Ca2+ influx at AZs facing away from the ganglion activated at weaker depolarizations. Estimates of AZ size and Ca2+ channel number were correlated and larger when AZs faced the ganglion. Disruption of the deafness gene GIPC3 in mice shifted the activation of presynaptic Ca2+ influx to more hyperpolarized potentials and increased the spontaneous SGN discharge. Moreover, Gipc3 disruption enhanced Ca2+ influx and exocytosis in IHCs, reversed the spatial gradient of maximal Ca2+ influx in IHCs, and increased the maximal firing rate of SGNs at sound onset. We propose that IHCs diversify Ca2+ channel properties among AZs and thereby contribute to decomposing auditory information into complementary representations in SGNs
Irreducible decomposition for tensor prodect representations of Jordanian quantum algebras
Tensor products of irreducible representations of the Jordanian quantum
algebras U_h(sl(2)) and U_h(su(1,1)) are considered. For both the highest
weight finite dimensional representations of U_h(sl(2)) and lowest weight
infinite dimensional ones of U_h(su(1,1)), it is shown that tensor product
representations are reducible and that the decomposition rules to irreducible
representations are exactly the same as those of corresponding Lie algebras.Comment: LaTeX, 14pages, no figur
Classification of the quantum deformation of the superalgebra
We present a classification of the possible quantum deformations of the
supergroup and its Lie superalgebra . In each case, the
(super)commutation relations and the Hopf structures are explicitly computed.
For each matrix, one finds two inequivalent coproducts whether one chooses
an unbraided or a braided framework while the corresponding structures are
isomorphic as algebras. In the braided case, one recovers the classical algebra
for suitable limits of the deformation parameters but this is no
longer true in the unbraided case.Comment: 23p LaTeX2e Document - packages amsfonts,subeqn - misprints and
errors corrected, one section adde
Three dimensional quantum algebras: a Cartan-like point of view
A perturbative quantization procedure for Lie bialgebras is introduced and
used to classify all three dimensional complex quantum algebras compatible with
a given coproduct. The role of elements of the quantum universal enveloping
algebra that, analogously to generators in Lie algebras, have a distinguished
type of coproduct is discussed, and the relevance of a symmetrical basis in the
universal enveloping algebra stressed. New quantizations of three dimensional
solvable algebras, relevant for possible physical applications for their
simplicity, are obtained and all already known related results recovered. Our
results give a quantization of all existing three dimensional Lie algebras and
reproduce, in the classical limit, the most relevant sector of the complete
classification for real three dimensional Lie bialgebra structures given by X.
Gomez in J. Math. Phys. Vol. 41. (2000) 4939.Comment: LaTeX, 15 page
Stochastic electrotransport selectively enhances the transport of highly electromobile molecules
Nondestructive chemical processing of porous samples such as fixed biological tissues typically relies on molecular diffusion. Diffusion into a porous structure is a slow process that significantly delays completion of chemical processing. Here, we present a novel electrokinetic method termed stochastic electrotransport for rapid nondestructive processing of porous samples. This method uses a rotational electric field to selectively disperse highly electromobile molecules throughout a porous sample without displacing the low-electromobility molecules that constitute the sample. Using computational models, we show that stochastic electrotransport can rapidly disperse electromobile molecules in a porous medium. We apply this method to completely clear mouse organs within 1â3 days and to stain them with nuclear dyes, proteins, and antibodies within 1 day. Our results demonstrate the potential of stochastic electrotransport to process large and dense tissue samples that were previously infeasible in time when relying on diffusion.Simons Foundation. Postdoctoral FellowshipLife Sciences Research FoundationBurroughs Wellcome Fund (Career Awards at the Scientific Interface)Searle Scholars ProgramMichael J. Fox Foundation for Parkinson's ResearchUnited States. Defense Advanced Research Projects AgencyJPB FoundationNational Institutes of Health (U.S.)National Institutes of Health (U.S.) (Grant 1-U01-NS090473-01
Maps between Deformed and Ordinary Gauge Fields
In this paper, we introduce a map between the q-deformed gauge fields defined
on the GL-covariant quantum hyperplane and the ordinary gauge fields.
Perturbative analysis of the q-deformed QED at the classical level is presented
and gauge fixing la BRST is discussed. An other star product
defined on the hybrid % -plane is explicitly constructed .Comment: 10 page
Contractions, deformations and curvature
The role of curvature in relation with Lie algebra contractions of the
pseudo-ortogonal algebras so(p,q) is fully described by considering some
associated symmetrical homogeneous spaces of constant curvature within a
Cayley-Klein framework. We show that a given Lie algebra contraction can be
interpreted geometrically as the zero-curvature limit of some underlying
homogeneous space with constant curvature. In particular, we study in detail
the contraction process for the three classical Riemannian spaces (spherical,
Euclidean, hyperbolic), three non-relativistic (Newtonian) spacetimes and three
relativistic ((anti-)de Sitter and Minkowskian) spacetimes. Next, from a
different perspective, we make use of quantum deformations of Lie algebras in
order to construct a family of spaces of non-constant curvature that can be
interpreted as deformations of the above nine spaces. In this framework, the
quantum deformation parameter is identified as the parameter that controls the
curvature of such "quantum" spaces.Comment: 17 pages. Based on the talk given in the Oberwolfach workshop:
Deformations and Contractions in Mathematics and Physics (Germany, january
2006) organized by M. de Montigny, A. Fialowski, S. Novikov and M.
Schlichenmaie
Quantum Symmetries and Marginal Deformations
We study the symmetries of the N=1 exactly marginal deformations of N=4 Super
Yang-Mills theory. For generic values of the parameters, these deformations are
known to break the SU(3) part of the R-symmetry group down to a discrete
subgroup. However, a closer look from the perspective of quantum groups reveals
that the Lagrangian is in fact invariant under a certain Hopf algebra which is
a non-standard quantum deformation of the algebra of functions on SU(3). Our
discussion is motivated by the desire to better understand why these theories
have significant differences from N=4 SYM regarding the planar integrability
(or rather lack thereof) of the spin chains encoding their spectrum. However,
our construction works at the level of the classical Lagrangian, without
relying on the language of spin chains. Our approach might eventually provide a
better understanding of the finiteness properties of these theories as well as
help in the construction of their AdS/CFT duals.Comment: 1+40 pages. v2: minor clarifications and references added. v3: Added
an appendix, fixed minor typo
eIF5A Promotes Translation Elongation, Polysome Disassembly and Stress Granule Assembly
Stress granules (SGs) are cytoplasmic foci at which untranslated mRNAs accumulate in cells exposed to environmental stress. We have identified ornithine decarboxylase (ODC), an enzyme required for polyamine synthesis, and eIF5A, a polyamine (hypusine)-modified translation factor, as proteins required for arsenite-induced SG assembly. Knockdown of deoxyhypusine synthase (DHS) or treatment with a deoxyhypusine synthase inhibitor (GC7) prevents hypusine modification of eIF5A as well as arsenite-induced polysome disassembly and stress granule assembly. Time-course analysis reveals that this is due to a slowing of stress-induced ribosome run-off in cells lacking hypusine-eIF5A. Whereas eIF5A only marginally affects protein synthesis under normal conditions, it is required for the rapid onset of stress-induced translational repression. Our results reveal that hypusine-eIF5A-facilitated translation elongation promotes arsenite-induced polysome disassembly and stress granule assembly in cells subjected to adverse environmental conditions
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