Search results for "complex"
showing 10 items of 5889 documents
Characteristics of neuronal systems in the visual cortex
1987
The coupling complexity of cortical areas makes it very difficult to analyse them experimentally. Studies of model systems provide the possibility of adapting the analysis to the available data base and elaborating the fundamental properties that depend on the structure of the system. We propose a model system of variable complexity that is spatially two-dimensional and time-dependent, uses feedback for iteration and smoothing, includes the mapping of the cortical networks and can be nonlinear as the case requires. Combining such elementary systems on the basis of neuroanatomical findings enables us to simulate cortical mappings and to interpret neurophysiological data. The decisive factor …
Forma mentis networks map how nursing and engineering students enhance their mindsets about innovation and health during professional growth
2020
Reconstructing a “forma mentis”, a mindset, and its changes, means capturing how individuals perceive topics, trends and experiences over time. To this aim we use forma mentis networks (FMNs), which enable direct, microscopic access to how individuals conceptually perceive knowledge and sentiment around a topic, providing richer contextual information than machine learning. FMNs build cognitive representations of stances through psycholinguistic tools like conceptual associations from semantic memory (free associations, i.e., one concept eliciting another) and affect norms (valence, i.e., how attractive a concept is). We test FMNs by investigating how Norwegian nursing and engineering stude…
Exact results for accepting probabilities of quantum automata
2001
One of the properties of Kondacs-Watrous model of quantum finite automata (QFA) is that the probability of the correct answer for a QFA cannot be amplified arbitrarily. In this paper, we determine the maximum probabilities achieved by QFAs for several languages. In particular, we show that any language that is not recognized by an RFA (reversible finite automaton) can be recognized by a QFA with probability at most 0.7726...
Amount of nonconstructivity in deterministic finite automata
2010
AbstractWhen D. Hilbert used nonconstructive methods in his famous paper on invariants (1888), P. Gordan tried to prevent the publication of this paper considering these methods as non-mathematical. L.E.J. Brouwer in the early twentieth century initiated intuitionist movement in mathematics. His slogan was “nonconstructive arguments have no value for mathematics”. However, P. Erdös got many exciting results in discrete mathematics by nonconstructive methods. It is widely believed that these results either cannot be proved by constructive methods or the proofs would have been prohibitively complicated. The author (Freivalds, 2008) [10] showed that nonconstructive methods in coding theory are…
On the function of cell systems in area 18. Part I
1981
In addition to the asymmetry of the spatial coupling and of the specific temporal combination of excitation and inhibition, the non-linearity is very pronounced in area 18. Taking the sequence of a linear operation and a stationary nonlinear characteristic as a model, the experimental findings can be systematized and a cell classification specified which departs from the customary ones. The hypercomplex cell system probably originates in recurrent inhibition and leads to differentiation of the patterns along their contour line. Problems of cell classification and of the type of parallelism in the visual cortex are discussed.
Classifying G-graded algebras of exponent two
2019
Let F be a field of characteristic zero and let $$\mathcal{V}$$ be a variety of associative F-algebras graded by a finite abelian group G. If $$\mathcal{V}$$ satisfies an ordinary non-trivial identity, then the sequence $$c_n^G(\mathcal{V})$$ of G-codimensions is exponentially bounded. In [2, 3, 8], the authors captured such exponential growth by proving that the limit $$^G(\mathcal{V}) = {\rm{lim}}_{n \to \infty} \sqrt[n]{{c_n^G(\mathcal{V})}}$$ exists and it is an integer, called the G-exponent of $$\mathcal{V}$$ . The purpose of this paper is to characterize the varieties of G-graded algebras of exponent greater than 2. As a consequence, we find a characterization for the varieties with …
F-singularities via alterations
2011
For a normal F-finite variety $X$ and a boundary divisor $\Delta$ we give a uniform description of an ideal which in characteristic zero yields the multiplier ideal, and in positive characteristic the test ideal of the pair $(X,\Delta)$. Our description is in terms of regular alterations over $X$, and one consequence of it is a common characterization of rational singularities (in characteristic zero) and F-rational singularities (in characteristic $p$) by the surjectivity of the trace map $\pi_* \omega_Y \to \omega_X$ for every such alteration $\pi \: Y \to X$. Furthermore, building on work of B. Bhatt, we establish up-to-finite-map versions of Grauert-Riemenscheneider and Nadel/Kawamata-V…
Accessible parts of boundary for simply connected domains
2018
For a bounded simply connected domain $\Omega\subset\mathbb{R}^2$, any point $z\in\Omega$ and any $0<\alpha<1$, we give a lower bound for the $\alpha$-dimensional Hausdorff content of the set of points in the boundary of $\Omega$ which can be joined to $z$ by a John curve with a suitable John constant depending only on $\alpha$, in terms of the distance of $z$ to $\partial\Omega$. In fact this set in the boundary contains the intersection $\partial\Omega_z\cap\partial\Omega$ of the boundary of a John sub-domain $\Omega_z$ of $\Omega$, centered at $z$, with the boundary of $\Omega$. This may be understood as a quantitative version of a result of Makarov. This estimate is then applied to obta…
Real quadrics in C n , complex manifolds and convex polytopes
2006
In this paper, we investigate the topology of a class of non-Kähler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics Cn which are invariant with respect to the natural action of the real torus (S1)n onto Cn. The quotient space is a simple convex polytope. The problem reduces thus to the study of the topology of certain real algebraic sets and can be handled using combinatorial results on convex polytopes. We prove that the homology groups of these compact complex manifolds can have arbitrary amount of torsion so that their topology is extremely rich. We also resolve an associated wall-cros…
Curve packing and modulus estimates
2018
A family of planar curves is called a Moser family if it contains an isometric copy of every rectifiable curve in $\mathbb{R}^{2}$ of length one. The classical "worm problem" of L. Moser from 1966 asks for the least area covered by the curves in any Moser family. In 1979, J. M. Marstrand proved that the answer is not zero: the union of curves in a Moser family has always area at least $c$ for some small absolute constant $c > 0$. We strengthen Marstrand's result by showing that for $p > 3$, the $p$-modulus of a Moser family of curves is at least $c_{p} > 0$.