Comparing Two Approaches in Heteroscedastic Regression Models

Recently, a generalized test approach is proposed by Sadooghi-alvandi et al. (2016) and a fiducial approach is proposed by Xu and Li (2018) to test the equality of coefficients in several regression models with unequal variances. In this paper, it is shown that the considered quantities in these approaches are identically distributed and therefore, these approaches are same. Also, this result satisfies for the one-way ANOVA problem

On Locally ϕ\phi -semisymmetric Kenmotsu Manifolds

The object of the present paper is to study the locally $\phi$- semisymmetric Kenmotsu manifolds along with the characterization of such notion.Comment: Paper contains 10 pages and already published in Palestine Journal of Mathematic

Predicting the Gender of Indonesian Names

We investigated a way to predict the gender of a name using character-level Long-Short Term Memory (char-LSTM). We compared our method with some conventional machine learning methods, namely Naive Bayes, logistic regression, and XGBoost with n-grams as the features. We evaluated the models on a dataset consisting of the names of Indonesian people. It is not common to use a family name as the surname in Indonesian culture, except in some ethnicities. Therefore, we inferred the gender from both full names and first names. The results show that we can achieve 92.25% accuracy from full names, while using first names only yields 90.65% accuracy. These results are better than the ones from applying the classical machine learning algorithms to n-grams.Comment: Submitted to ICoDIS 201

A Novel/Old Modification of the First Zagreb Index

In the paper [I. Gutman, N. Trinajsti\'c, Chem. Phys. Lett. 17 (1972), 535], it was shown that total $\pi$-electron energy ($E$) of a molecule $M$ depends on the quantity $\sum_{v\in V(G)}d_{v}^{2}$ (nowadays known as the "first Zagreb index"), where $G$ is the graph corresponding to $M$, $V(G)$ is the vertex set of $G$ and $d_{v}$ is degree of the vertex $v$. In the same paper, the graph invariant $\sum_{v\in V(G)}d_{v}\tau_{v}$ (where $\tau_{v}$ is the connection number of $v$, that is the number of vertices at distance 2 from $v$) was also proved to influence $E$, but this invariant was never restudied explicitly. We call it "modified first Zagreb connection index" and denote it by $ZC_{1}^{*}$. In this paper, we characterize the extremal elements with respect to the graph invariant $ZC_{1}^{*}$ among the collection of all $n$-vertex chemical trees.Comment: 12 Page

On the zeroth-order general Randi\'c index, variable sum exdeg index and trees having vertices with prescribed degree

The zeroth-order general Randi\'c index (usually denoted by $R_{\alpha}^{0}$) and variable sum exdeg index (denoted by $SEI_{a}$) of a graph $G$ are defined as $R_{\alpha}^{0}(G)= \sum_{v\in V(G)} (d_{v})^{\alpha}$ and $SEI_{a}(G)= \sum_{v\in V(G)}d_{v}a^{d_{v}}$ where $d_{v}$ is degree of the vertex $v\in V(G)$, $a$ is a positive real number different from 1 and $\alpha$ is a real number other than $0$ and $1$. A segment of a tree is a path $P$, whose terminal vertices are branching or pendent, and all non-terminal vertices (if exist) of $P$ have degree 2. For $n\ge6$, let $\mathbb{PT}_{n,n_1}$, $\mathbb{ST}_{n,k}$, $\mathbb{BT}_{n,b}$ be the collections of all $n$-vertex trees having $n_1$ pendent vertices, $k$ segments, $b$ branching vertices, respectively. In this paper, all the trees with extremum (maximum and minimum) zeroth-order general Randi\'c index and variable sum exdeg index are determined from the collections $\mathbb{PT}_{n,n_1}$, $\mathbb{ST}_{n,k}$, $\mathbb{BT}_{n,b}$. The obtained extremal trees for the collection $\mathbb{ST}_{n,k}$ are also extremal trees for the collection of all $n$-vertex trees having fixed number of vertices with degree 2 (because it is already known that the number of segments of a tree $T$ can be determined from the number of vertices of $T$ with degree 2 and vise versa).Comment: 10 page

Candidates for non-zero Betti numbers of monomial ideals

Let $I$ be a monomial ideal in the polynomial ring $S$ generated by elements of degree at most $d$. In this paper, it is shown that, if the $i$-th syzygy of $I$ has no element of degrees $j, \ldots, j+(d-1)$ (where $j \geq i+d$), then $(i+1)$-syzygy of $I$ does not have any element of degree $j+d$. Then we give several applications of this result, including an alternative proof for Green-Lazarsfeld index of the edge ideals of graphs as well as an alternative proof for Fr\"oberg's theorem on classification of square-free monomial ideals generated in degree two with linear resolution. Among all, we describe the possible indices $i, j$ for which $I$ may have non-zero Betti numbers $\beta_{i,j}$

Two Irregularity Measures Possessing High Discriminatory Ability

An $n$-vertex graph whose degree set consists of exactly $n-1$ elements is called antiregular graph. Such type of graphs are usually considered opposite to the regular graphs. An irregularity measure ($IM$) of a connected graph $G$ is a non-negative graph invariant satisfying the property: $IM(G) = 0$ if and only if $G$ is regular. The total irregularity of a graph $G$, denoted by $irr_t(G)$, is defined as $irr_t(G)= \sum_{\{u,v\} \subseteq V(G)} |d_u - d_v|$ where $V(G)$ is the vertex set of $G$ and $d_u$, $d_v$ denote the degrees of the vertices $u$, $v$, respectively. Antiregular graphs are the most nonregular graphs according to the irregularity measure $irr_t$; however, various non-antiregular graphs are also the most nonregular graphs with respect to this irregularity measure. In this note, two new irregularity measures having high discriminatory ability are devised. Only antiregular graphs are the most nonregular graphs according to the proposed measures.Comment: 11 pages and 2 figure

Relation between the Usual Order and the Enumeration Orders of Elements of r.e. Sets

In this paper, we have compared r.e. sets based on their enumeration orders with Turing machines. Accordingly, we have defined novel concept uniformity for Turing machines and r.e. sets and have studied some relationships between uniformity and both one-reducibility and Turing reducibility. Furthermore, we have defined type-2 uniformity concept and studied r.e. sets and Turing machines based on this concept. In the end, we have introduced a new structure called Turing Output Binary Search Tree that helps us lighten some ideas.Comment: 15 pages; submitted to Mathematical Logic Quarterl

Cherenkov in the Sky: Measuring the Sound Speed of Primordial Scalar Fluctuations

We consider production of additional relativistic particles coupled to the inflaton. We show that the imprints of these particles on the spectrum of primordial perturbations can be used for the direct measurement of the speed of sound of scalar perturbations, regardless of the mechanism of the production of this species. We study a model where these relativistic localized sources are decay products of heavier particles generated via a resonance mechanism. These particles emit in-phase inflaton particles which interfere constructively on the the so-called sound boom, leading to an "inflationary Cherenkov effect". The resulting shock waves lead to distinctive patterns on the temperature anisotropies of the cosmic microwave background. Moreover, we show that the model predicts unique features on the power spectrum of curvature perturbation and sizeable flattened non-gaussianity for a suitable range of parameters.Comment: 18 pages, 3 figure

Single-Field Consistency relation and δN\delta N-Formalism

According to the equivalence principal, the long wavelength perturbations must not have any dynamical effect on the short scale physics up to ${\cal O} (k_L^2/k_s^2)$. Their effect can be always absorbed to a coordinate transformation locally. So any physical effect of such a perturbation appears only on scales larger than the scale of the perturbation. The bispectrum in the squeezed limit of the curvature perturbation in single-field slow-roll inflation is a good example, where the long wavelength effect is encoded in the spectral index through Maldacena's consistency relation. This implies that one should be able to derive the bispectrum in the squeezed limit without resorting to the in-in formalism in which one computes perturbative corrections field-theoretically. In this short paper, we show that the $\delta N$ formalism as it is, or more generically the separate universe approach, when applied carefully can indeed lead to the correct result for the bispectrum in the squeezed limit. Hence despite the common belief that the $\delta N$ formalism is incapable of recovering the consistency relation within itself, it is in fact self-contained and consistent.Comment: 4 pages, 1 figur