1,300 research outputs found
Irregularity of expansions and Pell graphs
For a graph the imbalance of an edge of is
. Irregularity of a graph is defined as the sum of
imbalances over all edges of . In this paper we consider expansions and Pell
graphs. If is an expansion of with respect to the sets and ,
we express the irregularity of using and . For Pell graphs
the imbalance of their edges is studied. The number of edges of a Pell graph
with a fixed imbalance is expressed. Using these results the irregularity
and the -index of Pell graphs are given
A sharp threshold for random graphs with a monochromatic triangle in every edge coloring
Let be the set of all finite graphs with the Ramsey property that
every coloring of the edges of by two colors yields a monochromatic
triangle. In this paper we establish a sharp threshold for random graphs with
this property. Let be the random graph on vertices with edge
probability . We prove that there exists a function with
, as tends to infinity
Pr[G(n,(1-\eps)\hat c/\sqrt{n}) \in \R ] \to 0 and Pr [ G(n,(1+\eps)\hat
c/\sqrt{n}) \in \R ] \to 1. A crucial tool that is used in the proof and is
of independent interest is a generalization of Szemer\'edi's Regularity Lemma
to a certain hypergraph setting.Comment: 101 pages, Final version - to appear in Memoirs of the A.M.
Detecting Irregular Patterns in IoT Streaming Data for Fall Detection
Detecting patterns in real time streaming data has been an interesting and
challenging data analytics problem. With the proliferation of a variety of
sensor devices, real-time analytics of data from the Internet of Things (IoT)
to learn regular and irregular patterns has become an important machine
learning problem to enable predictive analytics for automated notification and
decision support. In this work, we address the problem of learning an irregular
human activity pattern, fall, from streaming IoT data from wearable sensors. We
present a deep neural network model for detecting fall based on accelerometer
data giving 98.75 percent accuracy using an online physical activity monitoring
dataset called "MobiAct", which was published by Vavoulas et al. The initial
model was developed using IBM Watson studio and then later transferred and
deployed on IBM Cloud with the streaming analytics service supported by IBM
Streams for monitoring real-time IoT data. We also present the systems
architecture of the real-time fall detection framework that we intend to use
with mbientlabs wearable health monitoring sensors for real time patient
monitoring at retirement homes or rehabilitation clinics.Comment: 7 page
Oka's conjecture on irreducible plane sextics
We partially prove and partially disprove Oka's conjecture on the fundamental
group/Alexander polynomial of an irreducible plane sextic. Among other results,
we enumerate all irreducible sextics with simple singularities admitting
dihedral coverings and find examples of Alexander equivalent Zariski pairs of
irreducible sextics.Comment: Final version accepted for publicatio
Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons
Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data
Advances in Discrete Applied Mathematics and Graph Theory
The present reprint contains twelve papers published in the Special Issue “Advances in Discrete Applied Mathematics and Graph Theory, 2021” of the MDPI Mathematics journal, which cover a wide range of topics connected to the theory and applications of Graph Theory and Discrete Applied Mathematics. The focus of the majority of papers is on recent advances in graph theory and applications in chemical graph theory. In particular, the topics studied include bipartite and multipartite Ramsey numbers, graph coloring and chromatic numbers, several varieties of domination (Double Roman, Quasi-Total Roman, Total 3-Roman) and two graph indices of interest in chemical graph theory (Sombor index, generalized ABC index), as well as hyperspaces of graphs and local inclusive distance vertex irregular graphs
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