DATABASE DEVELOPMENT LIFE CYCLE

A software development life cycle model (SDLC) consists of a set of processes (planning, requirements, design, development, testing, installation and maintenance) defined to accomplish the task of developing a software application that is functionally correct and satisfies the user’s needs. These set of processes, when arranged in different orders, characterize different types of life cycles. When developing a database, the order of these tasks is very important to efficiently and correctly transform the user’s requirements into an operational database. These SDLCs are generally defined very broadly and are not specific for a particular type of application. In this paper the authors emphasize that there should be a SDLC that is specific to database applications. Database applications do not have the same characteristics as other software applications and thus a specific database development life cycle (DBDLC) is needed. A DBDLC should accommodate properties like scope restriction, progressive enhancement, incremental planning and pre-defined structure.Software Development, Database, DBMS, lifecycle model, traditional lifecycles

Walker-Breaker Games on Gn,pG_{n,p}

The Maker-Breaker connectivity game and Hamilton cycle game belong to the best studied games in positional games theory, including results on biased games, games on random graphs and fast winning strategies. Recently, the Connector-Breaker game variant, in which Connector has to claim edges such that her graph stays connected throughout the game, as well as the Walker-Breaker game variant, in which Walker has to claim her edges according to a walk, have received growing attention. For instance, London and Pluh\'ar studied the threshold bias for the Connector-Breaker connectivity game on a complete graph $K_n$, and showed that there is a big difference between the cases when Maker's bias equals $1$ or $2$. Moreover, a recent result by the first and third author as well as Kirsch shows that the threshold probability $p$ for the $(2:2)$ Connector-Breaker connectivity game on a random graph $G\sim G_{n,p}$ is of order $n^{-2/3+o(1)}$. We extent this result further to Walker-Breaker games and prove that this probability is also enough for Walker to create a Hamilton cycle

Multi-Set Inoculation: Assessing Model Robustness Across Multiple Challenge Sets

Language models, given their black-box nature, often exhibit sensitivity to input perturbations, leading to trust issues due to hallucinations. To bolster trust, it's essential to understand these models' failure modes and devise strategies to enhance their performance. In this study, we propose a framework to study the effect of input perturbations on language models of different scales, from pre-trained models to large language models (LLMs). We use fine-tuning to train a robust model to perturbations, and we investigate whether exposure to one perturbation improves or degrades the model's performance on other perturbations. To address multi-perturbation robustness, we suggest three distinct training strategies. We also extend the framework to LLMs via a chain of thought(COT) prompting with exemplars. We instantiate our framework for the Tabular-NLI task and show that the proposed strategies train the model robust to different perturbations without losing accuracy on a given dataset.Comment: 13 pages, 2 Figure, 12 Table

rr-cross tt-intersecting families via necessary intersection points

Given integers $r\geq 2$ and $n,t\geq 1$ we call families $\mathcal{F}_1,\dots,\mathcal{F}_r\subseteq\mathscr{P}([n])$ $r$-cross $t$-intersecting if for all $F_i\in\mathcal{F}_i$, $i\in[r]$, we have $\vert\bigcap_{i\in[r]}F_i\vert\geq t$. We obtain a strong generalisation of the classic Hilton-Milner theorem on cross intersecting families. In particular, we determine the maximum of $\sum_{j\in [r]}\vert\mathcal{F}_j\vert$ for $r$-cross $t$-intersecting families in the cases when these are $k$-uniform families or arbitrary subfamilies of $\mathscr{P}([n])$. Only some special cases of these results had been proved before. We obtain the aforementioned theorems as instances of a more general result that considers measures of $r$-cross $t$-intersecting families. This also provides the maximum of $\sum_{j\in [r]}\vert\mathcal{F}_j\vert$ for families of possibly mixed uniformities $k_1,\ldots,k_r$.Comment: 13 page

A general approach to transversal versions of Dirac-type theorems

Given a collection of hypergraphs $\textbf{H}=(H_1,\ldots,H_m)$ with the same vertex set, an $m$-edge graph $F\subset \cup_{i\in [m]}H_i$ is a transversal if there is a bijection $\phi:E(F)\to [m]$ such that $e\in E(H_{\phi(e)})$ for each $e\in E(F)$. How large does the minimum degree of each $H_i$ need to be so that $\textbf{H}$ necessarily contains a copy of $F$ that is a transversal? Each $H_i$ in the collection could be the same hypergraph, hence the minimum degree of each $H_i$ needs to be large enough to ensure that $F\subseteq H_i$. Since its general introduction by Joos and Kim [Bull. Lond. Math. Soc., 2020, 52(3):498-504], a growing body of work has shown that in many cases this lower bound is tight. In this paper, we give a unified approach to this problem by providing a widely applicable sufficient condition for this lower bound to be asymptotically tight. This is general enough to recover many previous results in the area and obtain novel transversal variants of several classical Dirac-type results for (powers of) Hamilton cycles. For example, we derive that any collection of $rn$ graphs on an $n$-vertex set, each with minimum degree at least $(r/(r+1)+o(1))n$, contains a transversal copy of the $r$-th power of a Hamilton cycle. This can be viewed as a rainbow version of the P\'osa-Seymour conjecture.Comment: 21 pages, 4 figures; final version as accepted for publication in the Bulletin of the London Mathematical Societ