We start with a simple introduction to topological data analysis where the most popular tool is called persistence diagram. Briefly, diagram multiset of points in plane describing features compact set when scale parameter varies. Since statistical methods are difficult apply directly on diagrams, various alternative functional summary statistics have been suggested, but either they do not contain full information or two-dimensional functions. suggest new statistic that one-dimensional and...

Determinantal point processes (DPPs) have recently proved to be a useful class of models in several areas statistics, including spatial statistical learning and telecommunications networks. They are for repulsive (or regular, or inhibitive) processes, the sense that nearby points process tend repel each other. We consider two ways quantify repulsiveness process, both based on its second-order properties, we address question how stationary DPP can be. determine most DPP, when intensity is...

Hidden medium-range structural features of disordered materials can be extracted through persistent homology analyses.

Automatic speech recognition (ASR) systems are known to be vulnerable adversarial attacks. This paper addresses detection and defence against targeted white-box attacks on signals for ASR systems. While existing work has utilised diffusion models (DMs) purify examples, achieving state-of-the-art results in keyword spotting tasks, their effectiveness more complex tasks such as sentence-level remains unexplored. Additionally, the impact of number forward steps performance is not well...

Monte Carlo tests are widely used for computing valid p-values without requiring known distributions of test statistics. When performing multiple tests, it is essential to maintain control the type I error. Some techniques multiplicity pose requirements on joint distribution p-values, instance independence, which can be computationally intensive achieve using na\"ive testing. We highlight in this work that testing an conformal novelty detection. Leveraging insight enables a more efficient...

Metal–organic framework (MOF) glasses feature numerous unique properties and potential applications, but many fundamental questions remain unanswered, especially concerning their glass transition. Here, we report a discovery about ZIF-62 (a typical MOF glass), namely, the hypersensitivity of its transition to pressure history. Specifically, upon quenching melt under modest 60 MPa, derived exhibited significantly lower temperature (Tg) than formed ambient pressure. The sensitivity parameter...

Glass structure remains puzzling to scientists, especially due the challenges in characterizing their structural order beyond first coordination shell, i.e., so-called medium-range order. Structural method development is therefore needed advance our understanding of, e.g., structure-property relations these disordered materials. To this end, we here review fundamentals, applications and perspectives of an interesting new approach, namely persistent homology, which a type topological data...

We introduce tests for the goodness of fit point patterns via methods from topological data analysis. More precisely, persistent Betti numbers give rise to a bivariate functional summary statistic observed that is asymptotically Gaussian in large observation windows. analyze power derived this on simulated and compare its performance with global envelope tests. Finally, we apply pattern an application context neuroscience. As main methodological contribution, derive sufficient conditions...

Methods to improve the fracture toughness and strength of glassy materials are increasingly important for a variety applications that remain limited by restrictions brittleness surface defect propensity. Here, we report on enhancement glass mechanical performance through combination tailored chemistry irradiation post-treatment. Specifically, show both experiments atomistic simulations (crack) initiation resistance as well selected calcium aluminoborosilicate glasses can be significantly...

Abstract We study minimum contrast estimation for parametric stationary determinantal point processes. These processes form a useful class of models repulsive (or regular, or inhibitive) patterns and are already applied in numerous statistical applications. Our main focus is on methods based the Ripley's K ‐function pair correlation function. Strong consistency asymptotic normality theses procedures proved under general conditions that only concern existence process its regularity with...

Stationary determinantal point processes are proved to be Brillinger mixing. This property is an important step towards asymptotic statistics for these processes. As example, a central limit theorem wide class of functionals established. result yields in particular the normality estimator intensity stationary process and kernel its pair correlation.

Abstract Motivated by the general ability of cross-validation to reduce overfitting and mean square error, we develop a cross-validation-based statistical theory for point processes. It is based on combination two novel concepts processes: prediction errors. Our approach uses thinning split process/pattern into pairs training validation sets, while our errors measure discrepancy between The new approach, which may be used model different distributional characteristics, exploits how well...

Abstract Several fundamental questions about the medium‐range order (MRO) structure of oxide glasses remain unanswered. How do we define MRO in glass? Should only consider covalently bonded rings or also repeating patterns non‐chemically atom clusters? Is first sharp diffraction peak (FSDP) factor constituted by those rings? In this study, focusing on binary silicate glasses, compare as determined using persistent homology and classical ring analysis. While latter identifies chemically...

(1) Background: The immune system has physiological antitumor activity, which is partially mediated by cytotoxic T lymphocytes (CTL). Tumor hypoxia, highly prevalent in cancers of the head and neck region, been hypothesized to inhibit infiltration tumors CTL. In situ data validating this concept have so far based solely upon visual assessment distribution Here, we established a set spatial statistical tools address problem mathematically tested their performance. (2) Patients Methods: We...

Metal-organic framework (MOF) glasses have multiple potential applications, as they combine advantages of traditional with those MOFs. The melt-quenching process used to form MOF typically leads a significant decrease in porosity, but the structural origin this thermally induced pore collapse remains largely unknown. Here, we study melting three zeolitic imidazolate frameworks (ZIFs), namely ZIF-4, ZIF-62, and ZIF-76, using ab initio molecular dynamics (MD) simulations. By analyzing MD data...

The first sharp diffraction peak (FSDP) in the reciprocal-space structure factor $S(Q)$ of glasses has been associated with their medium-range order (MRO) structure, but real-space origin remains debated. While some progress made case silicate and borate glasses, MRO phosphate not studied detail. Here, we apply persistent homology (PH), a topological data analysis method, to extract features deconvolute FSDP zinc glasses. To this end, oxygen, phosphorus, atoms atomic configurations are...

Recent developments in computing and IoT technology have enabled the daily generation of enormous amounts time series data. These to be analyzed create value. A fundamental type analysis is find temporal correlations between given sets series. To provide a robust method for solving this problem, several properties are desirable. First, should strong theoretical foundation. Second, since can occur at different scales, e.g., sub-second versus weekly, it important that capable discovering...

Abstract We establish a central limit theorem for multivariate summary statistics of nonstationary α ‐mixing spatial point processes and subsampling estimator the covariance matrix such statistics. The is crucial establishing asymptotic properties estimators in processes. flexible model free. It needed, example, to construct confidence intervals ellipsoids based on normality estimators. also provide simulation study investigating an application our results estimating functions.

This paper proposes exploiting the spatial correlation of wireless channel statistics beyond conventional received signal strength maps by constructing statistical radio to predict any relevant assist communications. Specifically, from stored samples acquired previous users in network, we use Gaussian processes (GPs) estimate quantiles distribution at a new position using non-parametric model. prior information is then used select transmission rate for some target level reliability. The...