336 research outputs found
Quantitative Coding and Complexity Theory of Compact Metric Spaces
Specifying a computational problem requires fixing encodings for input and
output: encoding graphs as adjacency matrices, characters as integers, integers
as bit strings, and vice versa. For such discrete data, the actual encoding is
usually straightforward and/or complexity-theoretically inessential (up to
polynomial time, say); but concerning continuous data, already real numbers
naturally suggest various encodings with very different computational
properties. With respect to qualitative computability, Kreitz and Weihrauch
(1985) had identified ADMISSIBILITY as crucial property for 'reasonable'
encodings over the Cantor space of infinite binary sequences, so-called
representations [doi:10.1007/11780342_48]: For (precisely) these does the
sometimes so-called MAIN THEOREM apply, characterizing continuity of functions
in terms of continuous realizers.
We rephrase qualitative admissibility as continuity of both the
representation and its multivalued inverse, adopting from
[doi:10.4115/jla.2013.5.7] a notion of sequential continuity for
multifunctions. This suggests its quantitative refinement as criterion for
representations suitable for complexity investigations. Higher-type complexity
is captured by replacing Cantor's as ground space with Baire or any other
(compact) ULTRAmetric space: a quantitative counterpart to equilogical spaces
in computability [doi:10.1016/j.tcs.2003.11.012]
Why Spiking Neural Networks Are Efficient: A Theorem
Current artificial neural networks are very successful in many machine learning applications, but in some cases they still lag behind human abilities. To improve their performance, a natural idea is to simulate features of biological neurons which are not yet implemented in machine learning. One of such features is the fact that in biological neural networks, signals are represented by a train of spikes. Researchers have tried adding this spikiness to machine learning and indeed got very good results, especially when processing time series (and, more generally, spatio-temporal data). In this paper, we provide a theoretical explanation for this empirical success
Computability of the Radon-Nikodym derivative
We study the computational content of the Radon-Nokodym theorem from measure
theory in the framework of the representation approach to computable analysis.
We define computable measurable spaces and canonical representations of the
measures and the integrable functions on such spaces. For functions f,g on
represented sets, f is W-reducible to g if f can be computed by applying the
function g at most once. Let RN be the Radon-Nikodym operator on the space
under consideration and let EC be the non-computable operator mapping every
enumeration of a set of natural numbers to its characteristic function. We
prove that for every computable measurable space, RN is W-reducible to EC, and
we construct a computable measurable space for which EC is W-reducible to RN
Computation with Advice
Computation with advice is suggested as generalization of both computation
with discrete advice and Type-2 Nondeterminism. Several embodiments of the
generic concept are discussed, and the close connection to Weihrauch
reducibility is pointed out. As a novel concept, computability with random
advice is studied; which corresponds to correct solutions being guessable with
positive probability. In the framework of computation with advice, it is
possible to define computational complexity for certain concepts of
hypercomputation. Finally, some examples are given which illuminate the
interplay of uniform and non-uniform techniques in order to investigate both
computability with advice and the Weihrauch lattice
A CDCL-style calculus for solving non-linear constraints
In this paper we propose a novel approach for checking satisfiability of
non-linear constraints over the reals, called ksmt. The procedure is based on
conflict resolution in CDCL style calculus, using a composition of symbolical
and numerical methods. To deal with the non-linear components in case of
conflicts we use numerically constructed restricted linearisations. This
approach covers a large number of computable non-linear real functions such as
polynomials, rational or trigonometrical functions and beyond. A prototypical
implementation has been evaluated on several non-linear SMT-LIB examples and
the results have been compared with state-of-the-art SMT solvers.Comment: 17 pages, 3 figures; accepted at FroCoS 2019; software available at
<http://informatik.uni-trier.de/~brausse/ksmt/
Computing domains of attraction for planar dynamics
In this note we investigate the problem of computing the
domain of attraction of a
ow on R2 for a given attractor. We consider
an operator that takes two inputs, the description of the
ow and a cover
of the attractors, and outputs the domain of attraction for the given
attractor. We show that: (i) if we consider only (structurally) stable
systems, the operator is (strictly semi-)computable; (ii) if we allow all
systems de ned by C1-functions, the operator is not (semi-)computable.
We also address the problem of computing limit cycles on these systems
Language, Life, Limits
In the context of second-order polynomial-time computability, we prove that
there is no general function space construction. We proceed to identify
restrictions on the domain or the codomain that do provide a function space
with polynomial-time function evaluation containing all polynomial-time
computable functions of that type.
As side results we show that a polynomial-time counterpart to admissibility
of a representation is not a suitable criterion for natural representations,
and that the Weihrauch degrees embed into the polynomial-time Weihrauch
degrees
D-4F, an apoA-1 mimetic, decreases airway hyperresponsiveness, inflammation, and oxidative stress in a murine model of asthma
Asthma is characterized by oxidative stress and inflammation of the airways. Although proinflammatory lipids are involved in asthma, therapies targeting them remain lacking. Ac-DWFKAFYDKVAEKFKEAFNH2 (4F) is an apolipoprotein (apo)A-I mimetic that has been shown to preferentially bind oxidized lipids and improve HDL function. The objective of the present study was to determine the effects of 4F on oxidative stress, inflammation, and airway resistance in an established murine model of asthma. We show here that ovalbumin (OVA) -sensitization increased airway hyperresponsiveness, eosinophil recruitment, and collagen deposition in lungs of C57BL/6J mice by a mechanism that could be reduced by 4F. OVA sensitization induced marked increases in transforming growth factor (TGF)β-1, fibroblast specific protein (FSP)-1, anti-T15 autoantibody staining, and modest increases in 4-hydroxynonenal (4-HNE) Michael\u27s adducts in lungs of OVA-sensitized mice. 4F decreased TGFβ-1, FSP-1, anti-T15 autoantibody, and 4-HNE adducts in the lungs of the OVA-sensitized mice. Eosinophil peroxidase (EPO) activity in bronchial alveolar lavage fluid (BALF), peripheral eosinophil counts, total IgE, and proinflammatory HDL (p-HDL) were all increased in OVA-sensitized mice. 4F decreased BALF EPO activity, eosinophil counts, total IgE, and p-HDL in these mice. These data indicate that 4F reduces pulmonary inflammation and airway resistance in an experimental murine model of asthma by decreasing oxidative stress
Robust computations with dynamical systems
In this paper we discuss the computational power of Lipschitz
dynamical systems which are robust to in nitesimal perturbations.
Whereas the study in [1] was done only for not-so-natural systems from
a classical mathematical point of view (discontinuous di erential equation
systems, discontinuous piecewise a ne maps, or perturbed Turing
machines), we prove that the results presented there can be generalized
to Lipschitz and computable dynamical systems.
In other words, we prove that the perturbed reachability problem (i.e. the
reachability problem for systems which are subjected to in nitesimal perturbations)
is co-recursively enumerable for this kind of systems. Using
this result we show that if robustness to in nitesimal perturbations is
also required, the reachability problem becomes decidable. This result
can be interpreted in the following manner: undecidability of veri cation
doesn't hold for Lipschitz, computable and robust systems.
We also show that the perturbed reachability problem is co-r.e. complete
even for C1-systems
Combining Interval and Probabilistic Uncertainty: What Is Computable?
In many practical problems, we need to process measurement results. For example, we need such data processing to predict future values of physical quantities. In these computations, it is important to take into account that measurement results are never absolutely exact, that there is always measurement uncertainty, because of which the measurement re-sults are, in general, somewhat different from the actual (unknown) values of the corresponding quantities. In some cases, all we know about mea-surement uncertainty is an upper bound; in this case, we have an interval uncertainty, meaning that all we know about the actual value is that is belongs to a certain interval. In other cases, we have some information – usually partial – about the corresponding probability distribution. New data processing challenges appear all the time; in many of these cases, it is important to come up with appropriate algorithms for taking uncertainty into account
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