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Linear Temporal Logic (LTL) is one of the most popular temporal logics, that comes into play in a variety of branches of computer science. Among the various reasons of its widespread use there are its strong foundational properties: LTL is equivalent to counter-free omega-automata, to star-free omega-regular expressions, and (by Kamp's theorem) to the first-order theory of one successor (S1S[FO]). Safety and co-safety languages, where a finite prefix suffices to establish whether a word does not belong or belongs to the language, respectively, play a crucial role in lowering the complexity of problems like model checking and reactive synthesis for LTL. SafetyLTL (resp., coSafetyLTL) is a fragment of LTL where only universal (resp., existential) temporal modalities are allowed, that recognises safety (resp., co-safety) languages only. The main contribution of this paper is the introduction of a fragment of S1S[FO], called SafetyFO, and of its dual coSafetyFO, which are expressively complete with respect to the LTL-definable safety and co-safety languages. We prove that they exactly characterize SafetyLTL and coSafetyLTL, respectively, a result that joins Kamp's theorem, and provides a clearer view of the characterization of (fragments of) LTL in terms of first-order languages. In addition, it gives a direct, compact, and self-contained proof that any safety language definable in LTL is definable in SafetyLTL as well. As a by-product, we obtain some interesting results on the expressive power of the weak tomorrow operator of SafetyLTL, interpreted over finite and infinite words. Moreover, we prove that, when interpreted over finite words, SafetyLTL (resp. coSafetyLTL) devoid of the tomorrow (resp., weak tomorrow) operator captures the safety (resp., co-safety) fragment of LTL over finite words.

Thanks to modern manufacturing technologies, heterogeneous materials with complex inner structures (e.g., foams) can be easily produced. However, their utilization is not straightforward, as the classical constitutive laws are not necessarily valid. According to various experimental observations, the Guyer--Krumhansl equation stands as a promising candidate to model such complex structures. However, the practical applications need a reliable and efficient algorithm that is capable of handling both complex geometries and advanced heat equations. In the present paper, we present the development of a $hp$-type finite element technique, which can be reliably applied. We investigate its convergence properties for various situations, being challenging in relation to stability and the treatment of fast propagation speeds. That algorithm is also proved to be outstandingly efficient, providing solutions four magnitudes faster than commercial algorithms.

Various cryptographic techniques are used in outsourced database systems to ensure data privacy while allowing for efficient querying. This work proposes a definition and components of a new secure and efficient outsourced database system, which answers various types of queries, with different privacy guarantees in different security models. This work starts with the survey of five order-revealing encryption schemes that can be used directly in many database indices and five range query protocols with various security / efficiency tradeoffs. The survey systematizes the state-of-the-art range query solutions in a snapshot adversary setting and offers some non-obvious observations regarding the efficiency of the constructions. In $\mathcal{E}\text{psolute}$, a secure range query engine, security is achieved in a setting with a much stronger adversary where she can continuously observe everything on the server, and leaking even the result size can enable a reconstruction attack. $\mathcal{E}\text{psolute}$ proposes a definition, construction, analysis, and experimental evaluation of a system that provably hides both access pattern and communication volume while remaining efficient. The work concludes with $k\text{-a}n\text{o}n$ -- a secure similarity search engine in a snapshot adversary model. The work presents a construction in which the security of $k\text{NN}$ queries is achieved similarly to OPE / ORE solutions -- encrypting the input with an approximate Distance Comparison Preserving Encryption scheme so that the inputs, the points in a hyperspace, are perturbed, but the query algorithm still produces accurate results. We use TREC datasets and queries for the search, and track the rank quality metrics such as MRR and nDCG. For the attacks, we build an LSTM model that trains on the correlation between a sentence and its embedding and then predicts words from the embedding.

This paper presents design methods for highly efficient optimisation of geometrically shaped constellations to maximise data throughput in optical communications. It describes methods to analytically calculate the information-theoretical loss and the gradient of this loss as a function of the input constellation shape. The gradients of the \ac{MI} and \ac{GMI} are critical to the optimisation of geometrically-shaped constellations. It presents the analytical derivative of the achievable information rate metrics with respect to the input constellation. The proposed method allows for improved design of higher cardinality and higher-dimensional constellations for optimising both linear and nonlinear fibre transmission throughput. Near-capacity achieving constellations with up to 8192 points for both 2 and 4 dimensions, with generalised mutual information (GMI) within 0.06 bit/2Dsymbol of additive white Gaussian noise channel (AWGN) capacity, are presented. Additionally, a design algorithm reducing the design computation time from days to minutes is introduced, allowing the presentation of optimised constellations for both linear AWGN and nonlinear fibre channels for a wide range of signal-to-noise ratios.

Context: Modelling satellite galaxy abundance $N_s$ in Galaxy Clusters (GCs) is a key element in modelling the Halo Occupation Distribution (HOD), which itself is a powerful tool to connect observational studies with numerical simulations. Aims: To study the impact of cosmological parameters on satellite abundance both in cosmological simulations and in mock observations. Methods: We build an emulator (HODEmu, \url{//github.com/aragagnin/HODEmu/}) of satellite abundance based on cosmological parameters $\Omega_m, \Omega_b, \sigma_8, h_0$ and redshift $z.$ We train our emulator using \magneticum hydrodynamic simulations that span 15 different cosmologies, each over $4$ redshift slices between $0<z<0.5,$ and for each setup we fit normalisation $A$, log-slope $\beta$ and Gaussian fractional-scatter $\sigma$ of the $N_s-M$ relation. The emulator is based on multi-variate output Gaussian Process Regression (GPR). Results: We find that $A$ and $\beta$ depend on cosmological parameters, even if weakly, especially on $\Omega_m,$ $\Omega_b.$ This dependency can explain some discrepancies found in literature between satellite HOD of different cosmological simulations (Magneticum, Illustris, BAHAMAS). We also show that satellite abundance cosmology dependency differs between full-physics (FP) simulations, dark-matter only (DMO), and non-radiative simulations. Conclusions: This work provides a preliminary calibration of the cosmological dependency of the satellite abundance of high mass halos, and we showed that modelling HOD with cosmological parameters is necessary to interpret satellite abundance, and we showed the importance of using FP simulations in modelling this dependency.

Electric vehicles (EVs) are key to alleviate our dependency on fossil fuels. The future smart grid is expected to be populated by millions of EVs equipped with high-demand batteries. To avoid an overload of the (current) electricity grid, expensive upgrades are required. Some of the upgrades can be averted if users of EVs participate to energy balancing mechanisms, for example through bidirectional EV charging. As the proliferation of consumer Internet-connected devices increases, including EV smart charging stations, their security against cyber-attacks and the protection of private data become a growing concern. We need to properly adapt and develop our current technology that must tackle the security challenges in the EV charging infrastructure, which go beyond the traditional technical applications in the domain of energy and transport networks. Security must balance with other desirable qualities such as interoperability, crypto-agility and energy efficiency. Evidence suggests a gap in the current awareness of cyber security in EV charging infrastructures. This paper fills this gap by providing the most comprehensive to date overview of privacy and security challenges To do so, we review communication protocols used in its ecosystem and provide a suggestion of security tools that might be used for future research.

We introduce two new tools to assess the validity of statistical distributions. These tools are based on components derived from a new statistical quantity, the $comparison$ $curve$. The first tool is a graphical representation of these components on a $bar$ $plot$ (B plot), which can provide a detailed appraisal of the validity of the statistical model, in particular when supplemented by acceptance regions related to the model. The knowledge gained from this representation can sometimes suggest an existing $goodness$-$of$-$fit$ test to supplement this visual assessment with a control of the type I error. Otherwise, an adaptive test may be preferable and the second tool is the combination of these components to produce a powerful $\chi^2$-type goodness-of-fit test. Because the number of these components can be large, we introduce a new selection rule to decide, in a data driven fashion, on their proper number to take into consideration. In a simulation, our goodness-of-fit tests are seen to be powerwise competitive with the best solutions that have been recommended in the context of a fully specified model as well as when some parameters must be estimated. Practical examples show how to use these tools to derive principled information about where the model departs from the data.

We develop the theory of a metric, which we call the $\nu$-based Wasserstein metric and denote by $W_\nu$, on the set of probability measures $\mathcal P(X)$ on a domain $X \subseteq \mathbb{R}^m$. This metric is based on a slight refinement of the notion of generalized geodesics with respect to a base measure $\nu$ and is relevant in particular for the case when $\nu$ is singular with respect to $m$-dimensional Lebesgue measure; it is also closely related to the concept of linearized optimal transport. The $\nu$-based Wasserstein metric is defined in terms of an iterated variational problem involving optimal transport to $\nu$; we also characterize it in terms of integrations of classical Wasserstein distance between the conditional probabilities and through limits of certain multi-marginal optimal transport problems. As we vary the base measure $\nu$, the $\nu$-based Wasserstein metric interpolates between the usual quadratic Wasserstein distance and a metric associated with the uniquely defined generalized geodesics obtained when $\nu$ is sufficiently regular. When $\nu$ concentrates on a lower dimensional submanifold of $\mathbb{R}^m$, we prove that the variational problem in the definition of the $\nu$-based Wasserstein distance has a unique solution. We establish geodesic convexity of the usual class of functionals and of the set of source measures $\mu$ such that optimal transport between $\mu$ and $\nu$ satisfies a strengthening of the generalized nestedness condition introduced in \cite{McCannPass20}.We finally introduce a slight variant of the dual metric mentioned above in order to prove convergence of an iterative scheme to solve a variational problem arising in game theory.

We show that under minimal assumptions on a random vector $X\in\mathbb{R}^d$, and with high probability, given $m$ independent copies of $X$, the coordinate distribution of each vector $(\langle X_i,\theta \rangle)_{i=1}^m$ is dictated by the distribution of the true marginal $\langle X,\theta \rangle$. Formally, we show that with high probability, \[\sup_{\theta \in S^{d-1}} \left( \frac{1}{m}\sum_{i=1}^m \left|\langle X_i,\theta \rangle^\sharp - \lambda^\theta_i \right|^2 \right)^{1/2} \leq c \left( \frac{d}{m} \right)^{1/4},\] where $\lambda^{\theta}_i = m\int_{(\frac{i-1}{m}, \frac{i}{m}]} F_{ \langle X,\theta \rangle }^{-1}(u)^2 \,du$ and $a^\sharp$ denotes the monotone non-decreasing rearrangement of $a$. The proof follows from the optimal estimate on the worst Wasserstein distance between a marginal of $X$ and its empirical counterpart, $\frac{1}{m} \sum_{i=1}^m \delta_{\langle X_i, \theta \rangle}$. We then use the accurate information on the structures of the vectors $(\langle X_i,\theta \rangle)_{i=1}^m$ to construct the first non-gaussian ensemble that yields the optimal estimate in the Dvoretzky-Milman Theorem: the ensemble exhibits almost Euclidean sections in arbitrary normed spaces of the same dimension as the gaussian embedding -- despite being very far from gaussian (in fact, it happens to be heavy-tailed).

We consider a potential outcomes model in which interference may be present between any two units but the extent of interference diminishes with spatial distance. The causal estimand is the global average treatment effect, which compares outcomes under the counterfactuals that all or no units are treated. We study a class of designs in which space is partitioned into clusters that are randomized into treatment and control. For each design, we estimate the treatment effect using a Horvitz-Thompson estimator that compares the average outcomes of units with all or no neighbors treated, where the neighborhood radius is of the same order as the cluster size dictated by the design. We derive the estimator's rate of convergence as a function of the design and degree of interference and use this to obtain estimator-design pairs that achieve near-optimal rates of convergence under relatively minimal assumptions on interference. We prove that the estimators are asymptotically normal and provide a variance estimator. For practical implementation of the designs, we suggest partitioning space using clustering algorithms.