arXiv subjects

Daniel Flores

Publications and source records attributed to Daniel Flores.

8 recordsLinked to original sources

arXiv2026

Increasing Line Outage Localization Performance with Ensemble Classifiers

In many cases, the outage of one transmission line in a system can be localized by monitoring the power flow of another line, and machine learning methods can be used to distinguish the cases under uncertainty. In this study, we examine the improvements in line outage localization performance achieved by various ensemble classifiers compared to single-model methods. In the case studies, we compared the classification results with measurement data collected at observed transmission lines (OTLs) selected using three algorithms, i.e, greedy maximum coverage problem (MCP), high-eta, and random selection, based on two sensitivity factors, i.e., line outage distribution factors (LODFs) and line outage impact factors (LOIFs). We found that the OTLs selected by the greedy MCP algorithm yielded the highest F1 score and the ensemble classifiers significantly outperformed a base kNN classifier. The extra-trees bagging technique achieved the highest F1 score in many instances. All the findings were statistically significant.

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arXiv2026

Line Outage Impact Factor (LOIF): A New Sensitivity Factor for Enhanced Transmission Observability

Transmission failures can lead to cascading failures and system blackout affecting millions of customers if not handled in time, and choosing the best locations to monitor the condition of the transmission system is crucial for power system reliability. In this paper, we propose a new sensitivity factor, the line outage impact factor (LOIF), which is especially useful for power system monitoring and can reveal the impacts of a transmission outage on the power flow of other lines more effectively than existing sensitivity factors, such as the line outage distribution factors (LODF). In this study, we apply the LOIF in transmission line outage detection in three test systems and compare it with LODF using a number of observed transmission line (OTL) selection methods based on these two sensitivity factors. Then we apply a machine learning algorithm to detect the outages of other lines by monitoring the selected OTLs, and the detection accuracy is evaluated using the F1-score. The results show that, in general, with the same number of OTLs, detection using the OTLs selected using LOIF achieved higher F1-scores. The pattern was especially consistent in large-scale systems, showing its potential in real-world applications.

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arXiv2025

Additional Constructions of Sequences of Alternating Sum and Difference Dominated Sets

A More Sums Than Differences (MSTD) set is a finite set of integers $A$ where the cardinality of its sumset, $A+A$, is greater than the cardinality of its difference set, $A-A$. We address a problem posed by Samuel Allen Alexander that asks whether there exists an infinite sequence of sets alternating between being MSTD and More Differences Than Sums (MDTS), where each set properly contains the previous. While a companion paper resolved this using `filling in' techniques, we solve the more challenging `non-filling-in' version, where any missing integer between a set's minimum and maximum elements remains missing in all subsequent sets.

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arXiv2025

Constructions of Sequences of Alternating Sum and Difference Dominated Sets

A More Sums Than Difference (MSTD) set is a finite set of integers $A$ where the cardinality of its sumset, $A+A$, is greater than the cardinality of its difference set, $A-A$. Since addition is commutative while subtraction isn't, it was conjectured that MSTD sets are rare. As Martin and O'Bryant proved a small (but positive) percentage are MSTD, it is natural to ask what additional properties can we impose on a chain of MSTD sets; in particular, can we construct a sequence of sets alternating between being MSTD and More Difference Than Sums (MDTS) where each properly contains the previous? We provide several such constructions; the first are trivial and proceed by filling in all missing elements from the minimum to maximum elements of $A$, while the last is a more involved construction that prohibits adding any such elements.

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arXiv2025

The Hasse principle for random homogeneous polynomials in thin sets

Let $d$ and $n$ be natural numbers. Let $\nu_{d,n}: \mathbb{R}^n\rightarrow \mathbb{R}^{N}$ denote the Veronese embedding with $N=N_{n,d}:=\binom{n+d-1}{d}$, defined by listing all the monomials of degree $d$ in $n$ variables using the lexicographical ordering. Let $\langle \boldsymbol{a}, \nu_{d,n}(\boldsymbol{x})\rangle\in \mathbb{Z}[\boldsymbol{x}]$ be a homogeneous polynomial in $n$ variables of degree $d$ with integer coefficients $\boldsymbol{a}$, where $\langle\cdot,\cdot\rangle$ denotes the inner product. For a non-singular form $P\in \mathbb{Z}[\boldsymbol{x}]$ of degree $k\ (\leq d)$ in $N$ variables, consider a set of integer vectors $\boldsymbol{a}\in \mathbb{Z}^N$, defined by $$\mathfrak{A}(A;P)=\{\boldsymbol{a}\in \mathbb{Z}^N:\ P(\boldsymbol{a})=0,\ \|\boldsymbol{a}\|_{\infty}\leq A\}.$$ By handling a new lattice problem via the geometry of numbers, we confirm that whenever $n> 24d$ and $d\geq 17,$ the proportion of integer coefficients $\boldsymbol{a}\in \mathfrak{A}(A;P)$, whose associated equation $f_{\boldsymbol{a}}(\boldsymbol{x})=0$ satisfies the Hasse principle, converges to $1$ as $A\rightarrow\infty$. This improves on the recent work of the second author.

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arXiv2024

Existence of $K$-multimagic squares and magic squares of $k$th powers with distinct entries

We demonstrate the existence of $K$-multimagic squares of order $N$ consisting of distinct integers whenever $N>2 K(K+1)$. This improves upon our earlier result in which we only required $N+1$ distinct integers. Additionally, we present a direct method by which our analysis of the magic square system may be used to show the existence of $N \times N$ magic squares consisting of distinct $k$ th powers when $$ N> \begin{cases}2^{k+1} & \text { if } 2 \leqslant k \leqslant 4 \\ 2\lceil k(\log k+4.20032)\rceil & \text { if } k \geqslant 5\end{cases} $$ improving on a recent result by Rome and Yamagishi.

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arXiv2024

A circle method approach to K-multimagic squares

In this paper we investigate $K$-multimagic squares of order $N$, these are $N \times N$ magic squares which remain magic after raising each element to the $k$ th power for all $2 \leqslant$ $k \leqslant K$. Given $K \geqslant 2$, we consider the problem of establishing the smallest integer $N_2(K)$ for which there exists nontrivial $K$-multimagic squares of order $N_2(K)$. Previous results on multimagic squares show that $N_2(K) \leqslant(4 K-2)^K$ for large $K$. Here we utilize the Hardy-Littlewood circle method and establish the bound $$ N_2(K) \leqslant 2 K(K+1)+1 $$ Via an argument of Granville's we additionally deduce the existence of infinitely many nontrivial prime valued $K$-multimagic squares of order $2 K(K+1)+1$.

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arXiv2023

A Quantitative Hasse Principle for Weighted Quartic Forms

We derive, via the Hardy-Littlewood method, an asymptotic formula for the number of integral zeros of a particular class of weighted quartic forms under the assumption of non-singular local solubility. Our polynomials $F({\mathbf x},{\mathbf y}) \in \mathbb{Z}[x_1,\ldots,x_{s_1},y_1,\ldots,y_{s_2}]$ satisfy the condition that $F(\lambda^2 {\mathbf x}, \lambda {\mathbf y}) = \lambda^4 F({\mathbf x},{\mathbf y})$. Our conclusions improve on those that would follow from a direct application of the methods of Birch. For example, we show that in many circumstances the expected asymptotic formula holds when $s_1 \ge 2$ and $2s_1 + s_2 > 8$.

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