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The graph parameter vertex integrity measures how vulnerable a graph is to a removal of a small number of vertices. More precisely, a graph with small vertex integrity admits a small number of vertex removals to make the remaining connected components small. In this paper, we initiate a systematic study of structural parameterizations of the problem of computing the unweighted/weighted vertex integrity. As structural graph parameters, we consider well-known parameters such as clique-width, treewidth, pathwidth, treedepth, modular-width, neighborhood diversity, twin cover number, and cluster vertex deletion number. We show several positive and negative results and present sharp complexity contrasts. We also show that the vertex integrity can be approximated within an $\mathcal{O}(\log \mathsf{opt})$ factor., Comment: 24 pages, 6 figures, WALCOM 2024

We study a modification of the primordial black hole (PBH) formation model from axion bubbles. We assume that the Peccei-Quinn scalar rolls down in the radial direction from a large field value to the potential minimum during inflation, which suppresses the axion fluctuations and weakens the clustering of PBHs on large scales. We find that the modified model can produce a sufficient number of PBHs that seed the supermassive black holes while avoiding the observational constraints from isocurvature perturbations and angular correlation of the high-redshift quasars., Comment: 17 pages, 8 figures

This paper describes an overview of the techniques of Hibikino-Musashi@Home, which intends to participate in the domestic standard platform league. The team has developed a dataset generator for the training of a robot vision system and an open-source development environment running on a human support robot simulator. The robot system comprises self-developed libraries including those for motion synthesis and open-source software works on the robot operating system. The team aims to realize a home service robot that assists humans in a home, and continuously attend the competition to evaluate the developed system. The brain-inspired artificial intelligence system is also proposed for service robots which are expected to work in a real home environment.

WhatsApp has introduced a novel avenue for smartphone users to engage with and disseminate news stories. The convenience of forming interest-based groups and seamlessly sharing content has rendered WhatsApp susceptible to the exploitation of misinformation campaigns. While the process of fact-checking remains a potent tool in identifying fabricated news, its efficacy falters in the face of the unprecedented deluge of information generated on the Internet today. In this work, we explore automatic ranking-based strategies to propose a "fakeness score" model as a means to help fact-checking agencies identify fake news stories shared through images on WhatsApp. Based on the results, we design a tool and integrate it into a real system that has been used extensively for monitoring content during the 2018 Brazilian general election. Our experimental evaluation shows that this tool can reduce by up to 40% the amount of effort required to identify 80% of the fake news in the data when compared to current mechanisms practiced by the fact-checking agencies for the selection of news stories to be checked., Comment: This is a preprint version of an accepted manuscript on the Brazilian Symposium on Multimedia and the Web (WebMedia). Please, consider to cite it instead of this one

The existence of a stochastic gravitational wave background is indicated by the recent pulsar timing array (PTA) experiments. We study the enhanced production of second-order gravitational waves from the scalar perturbations when the universe experiences a transition from the early matter-dominated era to the radiation-dominated era due to Q-ball decay. We extend the analysis in previous work by including the frequency range where density perturbations go non-linear and find that the resultant gravitational wave spectrum can be consistent with that favored by the recent PTA experiment results., Comment: 22 pages, 7 figures

Given a rational polytope $P \subset \mathbb R^d$, the numerical function counting lattice points in the integral dilations of $P$ is known to become a quasi-polynomial, called the Ehrhart quasi-polynomial $\mathrm{ehr}_P$ of $P$. In this paper we study the following problem: Given a rational $d$-polytope $P \subset \mathbb R^d$, is there a nice way to know Ehrhart quasi-polynomials of translated polytopes $P+ \mathbf v$ for all $\mathbf v \in \mathbb Q^d$? We provide a way to compute such Ehrhart quasi-polynomials using a certain toric arrangement and lattice point counting functions of translated cones of $P$. This method allows us to visualize how constituent polynomials of $\mathrm{ehr}_{P+\mathbf v}$ change in the torus $\mathbb R^d/\mathbb Z^d$. We also prove that information of $\mathrm{ehr}_{P+\mathbf v}$ for all $\mathbf v \in \mathbb Q^d$ determines the rational $d$-polytope $P \subset \mathbb R^d$ up to translations by integer vectors, and characterize all rational $d$-polytopes $P \subset \mathbb R^d$ such that $\mathrm{ehr}_{P+\mathbf v}$ is symmetric for all $\mathbf v \in \mathbb Q^d$., Comment: 28 pages, to appear in Combinatorial Theory

We show that the baryon asymmetry of the Universe cannot be explained by a large initial value before inflation because it inevitably predicts correlated baryon isocurvature perturbations that are already excluded by cosmic microwave background observations. Similar arguments can generally be applied to some models of dark matter., Comment: 4 pages

A new era of exploring the early Universe may have begun with the recent strong evidence for the stochastic gravitational wave (GW) background from the data reported by NANOGrav, EPTA, PPTA, and CPTA. Inspired by this, we propose a new potential source of stochastic GWs in the minimal supersymmetric standard model (MSSM), which could be the theory at a very high energy scale. This source is the "axion" field in the Higgs multiplets when the Higgs field takes a large value along the D-flat direction in the early Universe, for example, during inflation. The axion motion triggers the instability of the standard model ${\rm U}(1)$ and/or ${\rm SU}(3)$ gauge fields, producing stochastic GWs during the inflation. This scenario can be seen as a simple UV completion of the commonly studied models where an axion spectator/inflaton is coupled to a hidden ${\rm U}(1)$ or ${\rm SU}(N)$ gauge field without matter fields. Thus the nanohertz GWs may be a sign of supersymmetry. Primordial magnetic field production is also argued. In addition, we point out the simple possibility that this axion within the MSSM drives inflation., Comment: 17pages, 1 figure, 1 table, comments are welcome

We study for the first time the gravitational waves generated during the collapse of domain walls, incorporating the potential bias in the lattice simulations. The final stages of domain wall collapse are crucial for the production of gravitational waves, but have remained unexplored due to computational difficulties. As a significant application of this new result, we show that the observed NANOGrav, EPTA, PPTA, and CPTA data, which indicate stochastic gravitational waves in the nanohertz regime, can be attributed to axion domain walls coupled to QCD. In our model, non-perturbative effects of QCD induce a temperature-dependent bias around the QCD crossover, inducing the rapid collapse of the domain walls. We use sophisticated lattice simulations that account for the temperature-dependent bias to measure the gravitational waves resulting from the domain wall annihilation. We also discuss the future prospects for accelerator-based searches for the axion and the potential for the formation and detection of primordial black holes., Comment: v2: 9 pages, 6figures, 1 table, Lattice resolution significantly improved. Conclusions unchanged

A conjecture of Kalai asserts that for $d\geq 4$, the affine type of a prime simplicial $d$-polytope $P$ can be reconstructed from the space of affine $2$-stresses of $P$. We prove this conjecture for all $d\geq 5$. We also prove the following generalization: for all pairs $(i,d)$ with $2\leq i\leq \lceil \frac d 2\rceil-1$, the affine type of a simplicial $d$-polytope $P$ that has no missing faces of dimension $\geq d-i+1$ can be reconstructed from the space of affine $i$-stresses of $P$. A consequence of our proofs is a strengthening of the Generalized Lower Bound Theorem: it was proved by Nagel that for any simplicial $(d-1)$-sphere $\Delta$ and $1\leq k\leq \lceil\frac{d}{2}\rceil-1$, $g_k(\Delta)$ is at least as large as the number of missing $(d-k)$-faces of $\Delta$; here we show that, for $1\leq k\leq \lfloor\frac{d}{2}\rfloor-1$, equality holds if and only if $\Delta$ is $k$-stacked. Finally, we show that for $d\geq 4$, any simplicial $d$-polytope $P$ that has no missing faces of dimension $\geq d-1$ is redundantly rigid, that is, for each edge $e$ of $P$, there exists an affine $2$-stress on $P$ with a non-zero value on $e$., Comment: 21 pages. Added a few remarks and examples (see Remark 3.6, Examples 2.5 and 3.3-3.5). To appear in IMRN