We introduce the \emph{Topological Stability Index} (TSI), a variance-based scalar measure for persistence barcodes that quantifies the dispersion of persistence lifetimes. Unlike persistent entropy, which depends only on normalized weights, the TSI captures absolute variability and is sensitive to heterogeneous feature scales. We establish fundamental properties of the TSI, including its scaling behavior, invariance under lifetime translation and explicit update formulas under insertion and deletion of bars. We also consider a complementary first-moment-type quantity, the Topological Signal Index (TSigI), which captures the typical scale of persistence lifetimes and provides additional interpretability alongside the TSI. We further introduce a normalized version, $cv\text{TSI}$, which is scale invariant and admits an explicit algebraic relation to the Rényi entropy of order two. In particular, $cv\text{TSI}$ is an affine function of the collision probability $\sum_i p_i^2$, and therefore a monotone reparametrization of the Rényi entropy, providing a direct link between variance-based and entropy-based summaries in topological data analysis. Numerical experiments on synthetic data and stochastic time series demonstrate that the TSI captures structural variability complementary to entropy: it is relatively insensitive to deterministic trends, while responding strongly to stochastic fluctuations and variations in persistence magnitude.

Denoising Score Matching estimates the score of a noised version of a target distribution by minimizing a regression loss and is widely used to train the popular class of Denoising Diffusion Models. A well known limitation of Denoising Score Matching, however, is that it yields poor estimates of the score at low noise levels. This issue is particularly unfavourable for problems in the physical sciences and for Monte Carlo sampling tasks for which the score of the clean original target is known. Intuitively, estimating the score of a slightly noised version of the target should be a simple task in such cases. In this paper, we address this shortcoming and show that it is indeed possible to leverage knowledge of the target score. We present a Target Score Identity and corresponding Target Score Matching regression loss which allows us to obtain score estimates admitting favourable properties at low noise levels.

Nearest neighbor-based methods are commonly used for classification tasks and as subroutines of other data-analysis methods. An attacker with the capability of inserting their own data points into the training set can manipulate the inferred nearest neighbor structure. We distill this goal to the task of performing a training-set data insertion attack against $k$-Nearest Neighbor classification ($k$NN). We prove that computing an optimal training-time (a.k.a. poisoning) attack against $k$NN classification is NP-Hard, even when $k = 1$ and the attacker can insert only a single data point. We provide an anytime algorithm to perform such an attack, and a greedy algorithm for general $k$ and attacker budget. We provide theoretical bounds and empirically demonstrate the effectiveness and practicality of our methods on synthetic and real-world datasets. Empirically, we find that $k$NN is vulnerable in practice and that dimensionality reduction is an effective defense. We conclude with a discussion of open problems illuminated by our analysis.

BENGALURU: Cloud architects, data scientists, storage systems & management specialists, and software architects are the hardest to find technology talent in India. And over the past year, the shortage of data scientists has increased dramatically because of a surge in demand. A talent supply index (TSI) developed by recruitment company Belong puts the TSI for these roles at 0.2 -- in other words, if there are 10, say, cloud architect opportunities, there are only 2 relevant cloud architects available. A cloud architect is an IT professional responsible for overseeing a company's cloud computing strategy. The TSI for data scientists has dropped dramatically from 0.7 in 2017 to 0.2 this year.

MUMBAI: With exponential uptick in adoption of Internet of Things (IoT) and machine learning related activities in the country, the demand for IoT talent has surged by 300 per cent since 2014, showed a recent report. "The demand for IoT talent rocketed by 304 per cent, between 2014 and 2017," according to Talent Supply Index (TSI) by predictive outbound hiring platform provider Belong. TSI is based on Belong's platform data and publicly-available data from a continuously growing array of hiring sources, including traditional job sites, inbound recruiting channels, online communities, tech networks, discussion forums and more. The June 2017, TSI factored more than 1.6 lakh jobs and over 260,000 candidates based in India. "What is clear is that even in the midst of all the layoffs, it is solidly a candidate-driven market for the jobs of the future. This trend will only accelerate with more companies investing aggressively in cloud and emerging technologies like artificial intelligence (AI), while supply struggles to keep pace," Belong co-founder and CEO Vijay Sharma said.