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A one-dimensional cellular automaton $\tau : A^\mathbb{Z} \to A^\mathbb{Z}$ is a transformation of the full shift defined via a finite neighborhood $S \subset \mathbb{Z}$ and a local function $\mu : A^S \to A$. We study the family of cellular automata whose finite neighborhood $S$ is an interval containing $0$, and there exists a pattern $p \in A^S$ satisfying that $\mu(z) = z(0)$ if and only if $z \neq p$; this means that these cellular automata have a unique \emph{active transition}. Despite its simplicity, this family presents interesting and subtle problems, as the behavior of the cellular automaton completely depends on the structure of $p$. We show that every cellular automaton $\tau$ with a unique active transition $p \in A^S$ is either idempotent or strictly almost equicontinuous, and we completely characterize each one of these situations in terms of $p$. In essence, the idempotence of $\tau$ depends on the existence of a certain subpattern of $p$ with a translational symmetry., Comment: 14 pages

The main purpose of this work is the derivation of a functional partial differential equation (FPDE) for the calculations of equity-linked insurance policies, where the payment stream may depend on the whole past history of the financial asset. To this end, we employ variational techniques from the theory of functional It\^o calculus.

Background: Human Emotion Recognition (HER) has been a popular field of study in the past years. Despite the great progresses made so far, relatively little attention has been paid to the use of HER in autism. People with autism are known to face problems with daily social communication and the prototypical interpretation of emotional responses, which are most frequently exerted via facial expressions. This poses significant practical challenges to the application of regular HER systems, which are normally developed for and by neurotypical people. Objective: This study reviews the literature on the use of HER systems in autism, particularly with respect to sensing technologies and machine learning methods, as to identify existing barriers and possible future directions. Methods: We conducted a systematic review of articles published between January 2011 and June 2023 according to the 2020 PRISMA guidelines. Manuscripts were identified through searching Web of Science and Scopus databases. Manuscripts were included when related to emotion recognition, used sensors and machine learning techniques, and involved children with autism, young, or adults. Results: The search yielded 346 articles. A total of 65 publications met the eligibility criteria and were included in the review. Conclusions: Studies predominantly used facial expression techniques as the emotion recognition method. Consequently, video cameras were the most widely used devices across studies, although a growing trend in the use of physiological sensors was observed lately. Happiness, sadness, anger, fear, disgust, and surprise were most frequently addressed. Classical supervised machine learning techniques were primarily used at the expense of unsupervised approaches or more recent deep learning models., Comment: 21 pages, 9 figures

There is a growing interest in reconstructing the density matrix of photoelectron wavepackets, in particular in complex systems where decoherence can be introduced either by a partial measurement of the system or through coupling with a stochastic environment. To this end, several methods to reconstruct the density matrix, quantum state tomography protocols, have been developed and tested on photoelectrons ejected from noble gases following absorption of extreme ultraviolet (XUV) photons from attosecond pulses. It remains a challenge to obtain model-free, single scan protocols that can reconstruct the density matrix with high fidelities. Current methods require extensive measurements or involve complex fitting of the signal. Efficient single-scan reconstructions would be of great help to increase the number of systems that can be studied. We propose a new and more efficient protocol that is able to reconstruct the continuous variable density matrix of a photoelectron in a single time delay scan. It is based on measuring the coherences of a photoelectron created by absorption of an XUV pulse using a broadband infrared (IR) probe that is scanned in time and a narrowband IR reference that is temporally fixed to the XUV pulse. We illustrate its performance for a Fano resonance in He as well as mixed states in Ar arising from spin-orbit splitting. We show that the protocol results in excellent fidelities and near-perfect estimation of the purity., Comment: 23 pages, 13 figures, 1 table

In August 2023, IT experts and scientists came together for a workshop to discuss the possibilities of building a computer cluster fully on renewable energies, as a test-case at Havana University in Cuba. The discussion covered the scientific needs for a computer cluster for particle physics at the InSTEC institute at Havana University, the possibilities to use solar energy, new developments in computing technologies, and computer cluster operation as well as operational needs for computing in particle physics. This computer cluster on renewable energies at the InSTEC institute is seen as a prototype for a large-scale computer cluster on renewable energies for scientific computing in the Caribbean, hosted in Cuba. The project is called "Humboldt Highway", to remember Alexander von Humboldt's achievements in bringing cultures of the American and European continents closer together by exchange and travel. In this spirit, we propose a project that enables and intensifies the scientific exchange between research laboratories and universities in Europe and the Caribbean, in particular Cuba.

Interest in the inference of evolutionary networks relating species or populations has grown with the increasing recognition of the importance of hybridization, gene flow and admixture, and the availability of large-scale genomic data. However, what network features may be validly inferred from various data types under different models remains poorly understood. Previous work has largely focused on level-1 networks, in which reticulation events are well separated, and on a general network's tree of blobs, the tree obtained by contracting every blob to a node. An open question is the identifiability of the topology of a blob of unknown level. We consider the identifiability of the circular order in which subnetworks attach to a blob, first proving that this order is well-defined for outer-labeled planar blobs. For this class of blobs, we show that the circular order information from 4-taxon subnetworks identifies the full circular order of the blob. Similarly, the circular order from 3-taxon rooted subnetworks identifies the full circular order of a rooted blob. We then show that subnetwork circular information is identifiable from certain data types and evolutionary models. This provides a general positive result for high-level networks, on the identifiability of the ordering in which taxon blocks attach to blobs in outer-labeled planar networks. Finally, we give examples of blobs with different internal structures which cannot be distinguished under many models and data types.

When hybridization or other forms of lateral gene transfer have occurred, evolutionary relationships of species are better represented by phylogenetic networks than by trees. While inference of such networks remains challenging, several recently proposed methods are based on quartet concordance factors -- the probabilities that a tree relating a gene sampled from the species displays the possible 4-taxon relationships. Building on earlier results, we investigate what level-1 network features are identifiable from concordance factors under the network multispecies coalescent model. We obtain results on both topological features of the network, and numerical parameters, uncovering a number of failures of identifiability related to 3-cycles in the network., Comment: 27 pages + 11 pages Supplementary Materials

In this study, we present our latest findings regarding azimuthal distributions in vector boson + jets and multi-jet production at the Large Hadron Collider (LHC). These findings result from matching next-to-leading order (NLO) perturbative matrix elements with transverse momentum dependent (TMD) parton branching. We conduct a comprehensive comparative analysis of azimuthal correlations between Z boson-jet and jet-jet systems in the back-to-back region. These distinct azimuthal correlation patterns can help identify potential factorization-breaking effects in this region. Such effects depend on the different color and spin structures of the final states and their interactions with the initial states., Comment: Presented at "The European Physical Society Conference on High Energy Physics (EPS-HEP2023)", 21-25 August 2023, Hamburg, Germany, Submitted to PoS - Proceedings of Science

Given a finite set $A$ and a group homomorphism $\phi : H \to G$, a $\phi$-cellular automaton is a function $\mathcal{T} : A^G \to A^H$ that is continuous with respect to the prodiscrete topologies and $\phi$-equivariant in the sense that $h \cdot \mathcal{T}(x) = \mathcal{T}( \phi(h) \cdot x)$, for all $x \in A^G, h \in H$, where $\cdot$ denotes the shift actions of $G$ and $H$ on $A^G$ and $A^H$, respectively. When $G=H$ and $\phi = \text{id}$, the definition of $\text{id}$-cellular automata coincides with the classical definition of cellular automata. The purpose of this paper is to expand the theory of $\phi$-cellular automata by focusing on the differences and similarities with their classical counterparts. After discussing some basic results, we introduce the following definition: a $\phi$-cellular automaton $\mathcal{T} : A^G \to A^H$ has the unique homomorphism property (UHP) if $\mathcal{T}$ is not $\psi$-equivariant for any group homomorphism $\psi : H \to G$, $\psi \neq \phi$. We show that if the difference set $\Delta(\phi, \psi)$ is infinite, then $\mathcal{T}$ is not $\psi$-equivariant; it follows that when $G$ is torsion-free abelian, every non-constant $\mathcal{T}$ has the UHP. Furthermore, inspired by the theory of classical cellular automata, we study $\phi$-cellular automata over quotient groups, as well as their restriction and induction to subgroups and supergroups, respectively., Comment: 15 pages

The main purpose of the paper is to derive Thiele's differential equation for unit-linked policies in the Heston-Hawkes stochastic volatility model introduced in arXiv:2210.15343. This model is an extension of the well-known Heston model that incorporates the volatility clustering feature by adding a compound Hawkes process in the volatility. Since the model is arbitrage-free, pricing unit-linked policies via the equivalence principle under a risk neutral probability measure is possible. Studying the moments of the variance and certain stochastic exponentials, a suitable family of risk neutral probability measures is found. The established and practical method to compute reserves in life insurance is by solving Thiele's equation, which is crucial to guarantee the solvency of the insurance company., Comment: 26 pages

We consider the stochastic volatility model obtained by adding a compound Hawkes process to the volatility of the well-known Heston model. A Hawkes process is a self-exciting counting process with many applications in mathematical finance, insurance, epidemiology, seismology and other fields. We prove a general result on the existence of a family of equivalent (local) martingale measures. We apply this result to a particular example where the sizes of the jumps are exponentially distributed., Comment: 23 pages

We discuss our recent results on azimuthal distributions in vector boson + jets and multi-jet production at the LHC, obtained from the matching of next-to-leading order (NLO) perturbative matrix elements with transverse momentum dependent (TMD) parton branching. We present a comparative analysis of boson-jet and jet-jet correlations in the back to-back region, and a study of the theoretical systematic uncertainties associated with the matching scale in the cases of TMD and collinear parton showers., Comment: 6 pages, 2 figures, contribution to proceedings of ICHEP 2022

In recent decades, there has been an increase in polypharmacy, the concurrent administration of multiple drugs per patient. Studies have shown that polypharmacy is linked to adverse patient outcomes and there is interest in elucidating the exact causes behind this observation. In this paper, we are studying the relationship between drug prescriptions, drug-drug interactions (DDIs) and patient mortality. Our focus is not so much on the number of prescribed drugs, the typical metric in polypharmacy research, but rather on the specific combinations of drugs leading to a DDI. To learn the space of real-world drug combinations, we first assessed the drug prescription landscape of the UK Biobank, a large patient data registry. We observed distinct drug constellation patterns driven by the UK Biobank participants' disease status. We show that these drug prescription clusters matter in terms of the number and types of expected DDIs, and may possibly explain observed differences in health outcomes.

Inference of species networks from genomic data under the Network Multispecies Coalescent Model is currently severely limited by heavy computational demands. It also remains unclear how complicated networks can be for consistent inference to be possible. As a step toward inferring a general species network, this work considers its tree of blobs, in which non-cut edges are contracted to nodes, so only tree-like relationships between the taxa are shown. An identifiability theorem, that most features of the unrooted tree of blobs can be determined from the distribution of gene quartet topologies, is established. This depends upon an analysis of gene quartet concordance factors under the model, together with a new combinatorial inference rule. The arguments for this theoretical result suggest a practical algorithm for tree of blobs inference, to be fully developed in a subsequent work., Comment: 18 pages, 8 figures

Azimuthal correlations in Z+jet production at large transverse momenta are computed by matching Parton - Branching (PB) TMD parton distributions and showers with NLO calculations via MCatNLO. The predictions are compared with those for dijet production in the same kinematic range. The azimuthal correlations $\Delta\phi$ between the Z boson and the leading jet are steeper compared to those in dijet production at transverse momenta ${\cal O}(100)$ GeV, while they become similar for very high transverse momenta ${\cal O}(1000)$ GeV. The different patterns of Z+jet and dijet azimuthal correlations can be used to search for potential {\it factorization - breaking} effects in the back-to-back region, which depend on the different color and spin structure of the final states and their interferences with the initial states. In order to investigate these effects experimentally, we propose to measure the ratio of the distributions in $\Delta\phi$ for Z+jet - and multijet production at low and at high transverse momenta, and compare the results to predictions obtained assuming factorization. We examine the role of theoretical uncertainties by performing variations of the factorization scale, renormalization scale and matching scale. In particular, we present a comparative study of matching scale uncertainties in the cases of PB-TMD and collinear parton showers., Comment: Replaced with version accepted for publication in EPJC

As part of the DESY summer student program 2021, transverse momentum dependent (TMD) parton distributions obtained from the Parton Branching (PB) method were combined with next-to-leading-order (NLO) using the POWHEG method. Computations of the resulting Drell-Yan (DY) transverse momentum spectrum were performed. A good agreement of the theoretical predictions with the measurement performed by the CMS experiment at the center-of-mass energy of 13 TeV is found, at low and intermediate DY $p_{\rm T}$. The new scale choice option for the matching has been included in the CASCADE event generator., Comment: Part of the DESY summerstudent program 2021 (DESYsummer2021)

During the DESY summer student program 2021, young scientists from more than 13 different countries worked together, connecting from remote, to provide computer codes within the Rivet framework for 19 HERA measurements. Most of these measurements were originally available within the HZTool package, but no longer accessible for modern analysis packages such as Rivet. The temporary RivetHZTool interface was used to validate most of the new Rivet plugins., Comment: Part of the DESY summerstudent program 2021 (DESYsummer2021)

The azimuthal correlation, $\Delta \phi_{12}$, of high transverse momentum jets in pp collisions at $\sqrt{s}=13$ TeV is studied by applying PB-TMD distributions to NLO calculations via MCatNLO together with the PB-TMD parton shower. A very good description of the cross section as a function of $\Delta \phi_{12}$ is observed. In the back-to-back region of $\Delta \phi_{12} \to \pi$, a very good agreement is observed with the PB-TMD Set 2 distributions while significant deviations are obtained with the PB-TMD Set 1 distributions. Set 1 uses the evolution scale while Set 2 uses transverse momentum as an argument in $\alpha_s$, and the above observation therefore confirms the importance of an appropriate soft-gluon coupling in angular ordered parton evolution. The total uncertainties of the predictions are dominated by the scale uncertainties of the matrix element, while the uncertainties coming from the PB-TMDs and the corresponding PB-TMD shower are very small. The $\Delta \phi_{12}$ measurements are also compared with predictions using MCatNLO together PYTHIA8, illustrating the importance of details of the parton shower evolution., Comment: 15 pages, 8 Figures

Calculations of Drell-Yan (DY) production at next-to-leading (NLO) order have been combined with Transverse Momentum Dependent (TMD) distributions obtained with the Parton Branching (PB). The predictions show a remarkable agreement with DY measurement from E605 experiment, consistent with previous results we obtained for R209, PHENIX, CMS and ATLAS experiments. We also present predictions for Z+jet measurements showing the importance of TMD parton shower contributions to the jet multiplicity. We show that PB-TMD parton density and the corresponding PB-TMD parton shower can be combined with leading-order (LO) matrix element using the newly developed TMD merging algorithm to obtain a very good description of measurements over a wide kinematic range., Comment: 6 pages, 3 figures, conference paper

Inference of network-like evolutionary relationships between species from genomic data must address the interwoven signals from both gene flow and incomplete lineage sorting. The heavy computational demands of standard approaches to this problem severely limit the size of datasets that may be analyzed, in both the number of species and the number of genetic loci. Here we provide a theoretical pointer to more efficient methods, by showing that logDet distances computed from genomic-scale sequences retain sufficient information to recover network relationships in the level-1 ultrametric case. This result is obtained under the Network Multispecies Coalescent model combined with a mixture of General Time-Reversible sequence evolution models across individual gene trees, but does not depend on partitioning sequences by genes. Thus under standard stochastic models statistically justifiable inference of network relationships from sequences can be accomplished without consideration of individual genes or gene trees., Comment: 25 pages