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Success in academia hinges on publishing in top tier journals. This requires innovative results. And this requires clear and convincing presentation of said results. Presentation can make the difference of one tier in journal level. A lot…
This article focuses on the identification of the number of paths with different lengths between pairs of nodes in complex networks and how, by providing comprehensive information about the network topology, such an information can be…
In this note, we prove a theorem covering Chartrand, Kaigars, and Lick's theorem in [Proc. Amer. Math. Soc. 32 (1972), 63-68]. As an application, we give a simpler proof of theorem proved by Mader [J. Graph Theory 65 (2010), 61-69. (Theorem…
In this article, we take a closer look at the reliability of large minimal networks constructed by repeated compositions of the simplest possible networks. For a given number of devices $n=2^m$ we define the set of all the possible…
This doc provides some proofs in our submitted journal paper.
The Sensitivity Conjecture is a long-standing problem in theoretical computer science that seeks to fit the sensitivity of a Boolean function into a unified framework formed by the other complexity measures of Boolean functions, such as…
Connectomics - the mapping of neural connections in an organism's brain - currently requires extraordinary human effort to proofread the data collected from imaging and machine-learning assisted segmentation. With the growing excitement…
Inhomogeneity in networks can be detected by the analysis of the correlation of the total degree of nearest neighbors. This is illustrated by two models. The first one is a random multi-partitions network that the Aboav Weaire law, which…
Proof nets are a syntax for linear logic proofs which gives a coarser notion of proof equivalence with respect to syntactic equality together with an intuitive geometrical representation of proofs. In this paper we give an alternative…
Due to space limitations, our submission "Source Separation and Clustering of Phase-Locked Subspaces", accepted for publication on the IEEE Transactions on Neural Networks in 2011, presented some results without proof. Those proofs are…
The literature review presented below on Image Compression, Transmission of 3D data over wireless networks and tracking of objects is the in depth study of Research Papers done in Multimedia lab. Most of the papers presented in this…
These lecture notes provide an introduction to the verification of neural networks from a theoretical perspective. We discuss feed-forward neural networks, recurrent neural networks, attention mechanisms, and transformers, together with…
These notes pose a "proof challenge": a proof, or disproof, of the proposition that "For any given body of information, I, expressed as a one-dimensional sequence of atomic symbols, a multiple alignment concept, described in the document,…
Networks offer a powerful approach to modeling complex systems by representing the underlying set of pairwise interactions. Link prediction is the task that predicts links of a network that are not directly visible, with profound…
If we use LLMs as judges to evaluate the complex decisions of other LLMs, who or what monitors the judges? Infinite monitoring chains are inevitable whenever we do not know the ground truth of the decisions by experts and we do not want to…
The paper discusses fundamental detectability properties associated with the problem of distributed state estimation using networked observers. The main result of the paper establishes connections between detectability of the plant through…
In is paper we present a labelled tableau proof system that serves a wide class of interpretability logics. The system is proved sound and complete for any interpretability logic characterised by a frame condition given by a set of…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
This article gives an overview of the field of LLM text recognition. Different approaches and implemented detectors for the recognition of LLM-generated text are presented. In addition to discussing the implementations, the article focuses…
Inference of the network structure (e.g., routing topology) and dynamics (e.g., link performance) is an essential component in many network design and management tasks. In this paper we propose a new, general framework for analyzing and…