868 research outputs found
A model of transport nonuniversality in thick-film resistors
We propose a model of transport in thick-film resistors which naturally
explains the observed nonuniversal values of the conductance exponent t
extracted in the vicinity of the percolation transition. Essential ingredients
of the model are the segregated microstructure typical of thick-film resistors
and tunneling between the conducting grains. Nonuniversality sets in as
consequence of wide distribution of interparticle tunneling distances.Comment: 3 pages, 1 figur
Poly-Bernoulli numbers and lonesum matrices
A lonesum matrix is a matrix that can be uniquely reconstructed from its row
and column sums. Kaneko defined the poly-Bernoulli numbers by a
generating function, and Brewbaker computed the number of binary lonesum
-matrices and showed that this number coincides with the
poly-Bernoulli number . We compute the number of -ary lonesum
-matrices, and then provide generalized Kaneko's formulas by using
the generating function for the number of -ary lonesum -matrices.
In addition, we define two types of -ary lonesum matrices that are composed
of strong and weak lonesum matrices, and suggest further researches on lonesum
matrices. \Comment: 27 page
Anisotropic random resistor networks: a model for piezoresistive response of thick-film resistors
A number of evidences suggests that thick-film resistors are close to a
metal-insulator transition and that tunneling processes between metallic grains
are the main source of resistance. We consider as a minimal model for
description of transport properties in thick-film resistors a percolative
resistor network, with conducting elements governed by tunneling. For both
oriented and randomly oriented networks, we show that the piezoresistive
response to an applied strain is model dependent when the system is far away
from the percolation thresold, while in the critical region it acquires
universal properties. In particular close to the metal-insulator transition,
the piezoresistive anisotropy show a power law behavior. Within this region,
there exists a simple and universal relation between the conductance and the
piezoresistive anisotropy, which could be experimentally tested by common
cantilever bar measurements of thick-film resistors.Comment: 7 pages, 2 eps figure
Cerebellar lesions: is there a lateralisation effect on memory deficits?
Summary: Background. Until recently, neurosurgeons eagerly removed cerebellar lesions without consideration of future cognitive impairment that might be caused by the resection. In children, transient cerebellar mutism after resection has lead to a diminished use of midline approaches and vermis transection, as well as reduced retraction of the cerebellar hemispheres. The role of the cerebellum in higher cognitive functions beyond coordination and motor control has recently attracted significant interest in the scientific community, and might change the neurosurgical approach to these lesions. The aim of this study was to investigate the specific effects of cerebellar lesions on memory, and to assess a possible lateralisation effect. Methods. We studied 16 patients diagnosed with a cerebellar lesion, from January 1997 to April 2005, in the "Centre Hospitalier Universitaire Vaudois (CHUV)”, Lausanne, Switzerland. Different neuropsychological tests assessing short term and anterograde memory, verbal and visuo-spatial modalities were performed pre-operatively. Results. Severe memory deficits in at least one modality were identified in a majority (81%) of patients with cerebellar lesions. Only 1 patient (6%) had no memory deficit. In our series lateralisation of the lesion did not lead to a significant difference in verbal or visuo-spatial memory deficits. Findings. These findings are consistent with findings in the literature concerning memory deficits in isolated cerebellar lesions. These can be explained by anatomical pathways. However, the cross-lateralisation theory cannot be demonstrated in our series. The high percentage of patients with a cerebellar lesion who demonstrate memory deficits should lead us to assess memory in all patients with cerebellar lesion
Link and subgraph likelihoods in random undirected networks with fixed and partially fixed degree sequence
The simplest null models for networks, used to distinguish significant
features of a particular network from {\it a priori} expected features, are
random ensembles with the degree sequence fixed by the specific network of
interest. These "fixed degree sequence" (FDS) ensembles are, however, famously
resistant to analytic attack. In this paper we introduce ensembles with
partially-fixed degree sequences (PFDS) and compare analytic results obtained
for them with Monte Carlo results for the FDS ensemble. These results include
link likelihoods, subgraph likelihoods, and degree correlations. We find that
local structural features in the FDS ensemble can be reasonably well estimated
by simultaneously fixing only the degrees of few nodes, in addition to the
total number of nodes and links. As test cases we use a food web, two protein
interaction networks (\textit{E. coli, S. cerevisiae}), the internet on the
autonomous system (AS) level, and the World Wide Web. Fixing just the degrees
of two nodes gives the mean neighbor degree as a function of node degree,
, in agreement with results explicitly obtained from rewiring. For
power law degree distributions, we derive the disassortativity analytically. In
the PFDS ensemble the partition function can be expanded diagrammatically. We
obtain an explicit expression for the link likelihood to lowest order, which
reduces in the limit of large, sparse undirected networks with links and
with to the simple formula . In a
similar limit, the probability for three nodes to be linked into a triangle
reduces to the factorized expression .Comment: 17 pages, includes 11 figures; first revision: shortened to 14 pages
(7 figures), added discussion of subgraph counts, deleted discussion of
directed network
Gauge factor of thick film resistors: outcomes of the variable range hopping model
Despite a large amount of data and numerous theoretical proposals, the
microscopic mechanism of transport in thick film resistors remains unclear.
However, recent low temperature measurements point toward a possible variable
range hopping mechanism of transport. Here we examine how such a mechanism
affects the gauge factor of thick film resistors. We find that at sufficiently
low temperatures , for which the resistivity follows the Mott's law
, the gauge factor GF is proportional to
. Moreover, the inclusion of Coulomb gap effects leads to at lower temperatures. In addition, we study a simple
model which generalizes the variable range hopping mechanism by taking into
account the finite mean inter-grain spacing. Our results suggest a possible
experimental verification of the validity of the variable range hopping in
thick film resistors.Comment: 7 pages, 3 eps figures, submitted to Journal of Applied Physic
Rainbow matchings in Dirac bipartite graphs
This is the peer reviewed version of the following article: Coulson, M, Perarnau, G. Rainbow matchings in Dirac bipartite graphs. Random Struct Alg. 2019; 55: 271– 289., which has been published in final form at https://doi.org/10.1002/rsa.20835. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived VersionsWe show the existence of rainbow perfect matchings in µn-bounded edge colorings of Dirac bipartite graphs, for a sufficiently small µ¿>¿0. As an application of our results, we obtain several results on the existence of rainbow k-factors in Dirac graphs and rainbow spanning subgraphs of bounded maximum degree on graphs with large minimum degree
Decision and function problems based on boson sampling
Boson sampling is a mathematical problem that is strongly believed to be
intractable for classical computers, whereas passive linear interferometers can
produce samples efficiently. So far, the problem remains a computational
curiosity, and the possible usefulness of boson-sampling devices is mainly
limited to the proof of quantum supremacy. The purpose of this work is to
investigate whether boson sampling can be used as a resource of decision and
function problems that are computationally hard, and may thus have
cryptographic applications. After the definition of a rather general
theoretical framework for the design of such problems, we discuss their
solution by means of a brute-force numerical approach, as well as by means of
non-boson samplers. Moreover, we estimate the sample sizes required for their
solution by passive linear interferometers, and it is shown that they are
independent of the size of the Hilbert space.Comment: Close to the version published in PR
Solution of the tunneling-percolation problem in the nanocomposite regime
We noted that the tunneling-percolation framework is quite well understood at
the extreme cases of percolation-like and hopping-like behaviors but that the
intermediate regime has not been previously discussed, in spite of its
relevance to the intensively studied electrical properties of nanocomposites.
Following that we study here the conductivity of dispersions of particle
fillers inside an insulating matrix by taking into account explicitly the
filler particle shapes and the inter-particle electron tunneling process. We
show that the main features of the filler dependencies of the nanocomposite
conductivity can be reproduced without introducing any \textit{a priori}
imposed cut-off in the inter-particle conductances, as usually done in the
percolation-like interpretation of these systems. Furthermore, we demonstrate
that our numerical results are fully reproduced by the critical path method,
which is generalized here in order to include the particle filler shapes. By
exploiting this method, we provide simple analytical formulas for the composite
conductivity valid for many regimes of interest. The validity of our
formulation is assessed by reinterpreting existing experimental results on
nanotube, nanofiber, nanosheet and nanosphere composites and by extracting the
characteristic tunneling decay length, which is found to be within the expected
range of its values. These results are concluded then to be not only useful for
the understanding of the intermediate regime but also for tailoring the
electrical properties of nanocomposites.Comment: 13 pages with 8 figures + 10 pages with 9 figures of supplementary
material (Appendix B
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