arXiv subjects
Publications and source records attributed to Iuliana Teodorescu.
This article extends the known restricted isometric projection of sparse datasets in Euclidean spaces $\mathbb{R}^N$ down into low-dimensional subspaces $\mathbb{R}^k, k \ll N,$ to the case of low-dimensional varieties $\mathcal{M} \subset \mathbb{R}^N,$ of codimension $N - k = ω(N)$. Applications to structured/hierarchical datasets are considered.
We review the zeta-function representation of codewords allowed by a parity-check code based on a bipartite graph, and then investigate the effect of disorder on the effective distribution of codewords. The randomness (or disorder) is implemented by sampling the graph from an ensemble of random graphs, and computing the average zeta function of the ensemble. In the limit of arbitrarily large size for the vertex set of the graph, we find an exponential decay of the likelihood for nontrivial codewords corresponding to graph cycles. This result provides a quantitative estimate of the effect of randomization in cybersecurity applications.
In this study, we investigate the problem of classifying, characterizing, and designing efficient algorithms for hard inference problems on planar graphs, in the limit of infinite size. The problem is considered hard if, for a deterministic graph, it belongs to the NP class of computational complexity. A typical example rich in applications is that of connectivity loss in evacuation models for natural hazards management (e.g. coastal floods, hurricanes). Algorithmically, this model reduces to solving a min-cut (or max-flow) problem, with is known to be intractable. The current work covers several generalizations: posing the same problem for non-directed networks subject to random fluctuations (specifically, random graphs from the Erdös-Rényi class); finding efficient convex classifiers for the associated decision problem (deciding whether the graph had become disconnected or not); and the role played by choice of topology (on the space of random graphs) in designing efficient, convex approximation algorithms (in the infinite-size limit of the graph).
This paper is a continuation of the statistical modeling of the nonlinear relationship between atmospheric CO2 and attributable variables that can account for emissions, based on data from EU countries, in order to compare the relevant findings to those obtained in the case of US data, in [1, 2]. The current study was initiated in [3], leading to the optimal second-order model, based on three linear terms and five second-order terms. We conclude this study in the present work, by finding the canonical decomposition of the nonlinear model, and by computing the specific two-dimensional confidence regions that it leads to. We then use the model in order to quantify the net effect of various risk factors, and compare to the results obtained in the US case.
Starting from the atmospheric CO2 measurements taken in Hawaii between 1959 and 2008, a quadratic model with interactions was fitted, using 5 attributable variables. Surface response analysis returned the eigenvalues and eigenvectors at the critical point, which turns out to be of mixed type, with two positive eigenvalues, one null, and the rest negative. From these data, it is derived that the confidence regions in two variables are of various types (elliptic, hyperbolic, and degenerate). Based on these results we indicate how to determine two-dimensional confidence regions for statistically-significant variables which are relevant contributors to the atmospheric CO2 emissions.
Carbon dioxide, along with atmospheric temperature are interacting to cause what we have defined as global warming. In the present study we develop a statistical model using real data to identify the attributable variables (risk factors) that cause the CO2 emissions in the atmosphere in Europe. Some scientists believe that there are more than nineteen attributable variables that cause the CO2 in our atmosphere. However, our study has identified only three individual risk factors and five interactions among the attributable variables that cause almost all the CO2 emissions in the atmosphere in Europe. We rank the risk factors and interactions according to the amount of CO2 they generate. In addition, we compare the present findings of the European data with a similar study for the Continental United States [1, 2]. For example, in the US, liquid fuels ranks number one, while in Europe is gas fuels. In fact, liquid fuels in Europe is the least contributable variable of CO2 in the atmosphere, and gas fuels ranks seventh.
A new approach for optimal estimation of Markov chains with sparse transition matrices is presented.