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We introduce the notion of birth and death cochains as generalized versions of birth and death simplices in persistent cohomology. We show that birth and death cochains (unlike birth and death simplices) are always unique for a given persistent cohomology class. We use birth and death cochains to define birth and death content as generalizations of birth and death times. We then demonstrate the advantages of using that birth and death content as loss functions on a variety of topological optimization tasks with point clouds, time series and scalar fields. We close with a novel application of topological optimization to a dataset of arctic ice images.
We develop a likelihood-based inference for finite-state birth-death processes with composite birth rates, in which multiple distinct mechanisms contribute additively to the total birth intensity. Our main motivating example is an SIS epidemic model with pairwise and higher-order transmission. The process is observed through a single aggregate trajectory, and in the main setting of interest, birth events are unmarked. This creates a deconvolution problem in event space: the state is one-dimensional, but the mechanism underlying each birth is latent. We formulate the inference under a Doob $h$-transformed $Q$-process, which is time-homogeneous and ergodic and which provides a time-homogeneous asymptotic surrogate for the law of the original process conditioned on long survival. We derive the corresponding conditional likelihood and study both the conditional maximum likelihood estimator and a quasi-maximum likelihood estimator which is based on a simplified working score. Under the Doob-transform law, we prove consistency and asymptotic normality for both estimators, with asymptotic covariance determined by the inverse Fisher and inverse Godambe information matrices, respectively. W
Preterm birth is associated with significant mortality and a risk for lifelong morbidity. The complex multifactorial aetiology hampers accurate prediction and thus optimal care. A pipeline consisting of bespoke machine learning methods for data imputation, feature selection, and regression models to predict gestational age (GA) at birth was developed and evaluated from comprehensive multi-modal morphological and functional fetal MRI data from 333 control cases and 93 preterm birth cases. The GA at birth predictions were classified into term and preterm categories and their accuracy, sensitivity, and specificity were reported. An ablation study was performed to further validate the design of the pipeline. Performance was evaluated using stratified 10-fold cross-validation. The pipeline achieves an R2 score of 0.13 and a mean absolute error of 2.74 weeks. It also achieves a 0.77 accuracy, 0.59 sensitivity, and 0.82 specificity across folds. The predominant features selected by the pipeline include cervical length and statistics derived from placental T2* values. The confluence of fast, motion-robust and multi-modal fetal MRI techniques and machine learning prediction allowed the pred
A birth and death process is a continuous-time Markov chain with the minimal state space $\mathbb N$, whose transition matrix is standard and whose density matrix is the given birth-death matrix. Birth and death process is unique if and only if $\infty$ is an entrance or natural. When $\infty$ is neither an entrance nor natural, there are two ways in the literature to obtain all birth and death processes. The first one is an analytic treatment proposed by Feller in 1959, and the second one is a probabilistic construction completed by Wang in 1958. In this paper we will give another way to study birth and death processes using the Ray-Knight compactification. This way has the advantage of both the analytic and probabilistic treatments above. By applying the Ray-Knight compactification, every birth and death process can be modified into a càdlàg Ray process on $\mathbb N\cup \{\infty\}\cup\{\partial\}$, which is either a Doob processes or a Feller $Q$-process. Every birth and death process in the second class has a modification that is a Feller process on $\mathbb N\cup\{\infty\}\cup \{\partial\}$. We will derive the expression of its infinitesimal generator, which explains its bound
The Sun is thought to be formed within a star cluster. The coexistence of $^{26}{\rm Al}$-rich and $^{26}{\rm Al}$-poor calcium--aluminum-rich inclusions indicates that a direct injection of $^{26}{\rm Al}$-rich materials from a nearby core-collapse supernova should occur in the first $10^5$ years of the solar system. Therefore, at least one core-collapse supernova should occur within the duration of star formation in the Sun's birth cluster. Here we revisit the number of stars in the Sun's birth cluster from the point of view of the probability for acquiring at least one core-collapse supernova within the finite duration of star formation in the birth cluster. We find that the number of stars in the birth cluster can be significantly larger than that previously considered, depending on the duration of star formation.
Evolutionary models on graphs, as an extension of the Moran process, have two major implementations: birth-death (BD) models (or the invasion process) and death- birth (DB) models (or voter models). The isothermal theorem states that the fixation probability of mutants in a large group of graph structures (known as isothermal graphs, which include regular graphs) coincides with that for the mixed population. This result has been proven by Lieberman et al (Nature 433: 312-316, 2005) in the case of BD processes, where mutants differ from the wild types by their birth rate (and not by their death rate). In this paper we discuss to what extent the isothermal theorem can be formulated for DB processes, proving that it only holds for mutants that differ from the wild type by their death rate (and not by their birth rate). For more general BD and DB processes with arbitrary birth and death rates of mutants, we show that the fixation probabilities of mutants are different from those obtained in the mass-action populations. We focus on spatial lattices and show that the difference between BD and DB processes on 1D and 2D lattices are non-small even for large population sizes. We support the
The researchers have drawn much attention about the birth weight of newborn babies in the last three decades. The birth weight is one of the vital roles in the babys health. So many researchers such as (2),(1) and (4) analyzed the birth weight of babies. The aim of this paper is to analyze the birth weight and some other birth weight related variable, using singular value decomposition and multiple linear regression.
Here the term "high frequency" refers to daily, weekly or monthly birth data. The fluctuations of daily birth numbers show a succession of spikes and dips which, at least at first sight, looks almost as random as white noise. However in recent times several studies were published, including by the present authors, which have given better insight into how birth is affected by exogenous factors. One of them concerns the way adverse conditions (e.g. famines, diseases, earthquakes, heat waves) temporarily affect the conception capacity of populations, thus producing birth rate troughs 9 months after mortality waves. In addition, religious interdicts (e.g. during the Lent period) lead to reduced conceptions. These as well as other effects raise the hope that we will soon be able to "read" and interpret birth rate patterns just as the Egyptologist Jean-Francois Champollion managed to decipher many (though not all) hieroglyphs.
This paper reviews our current understanding of the possible birth environments of our Solar System. Since most stars form within groups and clusters, the question becomes one of determining the nature of the birth aggregate of the Sun. This discussion starts by reviewing Solar System properties that provide constraints on our environmental history. We then outline the range of star-forming environments that are available in the Galaxy, and discuss how they affect star and planet formation. The nature of the solar birth cluster is constrained by many physical considerations, including radiation fields provided by the background environment, dynamical scattering interactions, and by the necessity of producing the short-lived radioactive nuclear species inferred from meteoritic measurements. Working scenarios for the solar birth aggregate can be constructed, as discussed herein, although significant uncertainties remain.
We report the detection of diffuse gamma-ray emission toward the young massive star cluster Berkeley 87 using Fermi data. The emission has an angular extension of 0.36 degree and a photon index of 2.68. The hadronic scenario is favored given the dense gas and the cluster's strong stellar winds.
We report a detailed analysis on the young stellar cluster Berkeley 59 using Fermi-LAT. Using up-to-date source catalog and background models, we found significant extended GeV emission around Berkeley 59, which can be modeled by a radial disk of 1.02 degree radius with a significance of the extension of 10.6 sigma. We investigated the molecular, neutral and ionized gas content and the hadronic origin. The gamma-ray spectrum of Berkeley 59 has a photon index of 2.88. The derived gas mass from H2 and HII around Berkeley 59 is about 289 solar mass. We derived the relationship between cosmic ray acceleration efficiency and diffusion coefficient. Our results suggest that the extended gamma-ray emission originates from cosmic rays accelerated by cluster winds interacting with surrounding gas.
We present a comprehensive chemo-dynamical analysis of the old, metal-poor open cluster Berkeley 32 based on Gaia DR3 astrometry and Gaia-ESO Survey DR5.1 spectroscopy. Cluster membership is determined using a Gaussian Mixture Model applied to proper-motion components and trigonometric parallaxes. Isochrone fitting yields an age of 4.9 +/- 0.5 Gyr, a heliocentric distance of 3325 pc, and an extinction of A_V = 0.38 +/- 0.12 mag. Spectroscopic member stars exhibit a mean metallicity of [Fe/H] = -0.39 +/- 0.02 dex, near-solar alpha-element abundances, and a weighted mean radial velocity of V_rad = 106.26 +/- 0.03 km s^-1. The [Y/Mg] chemical clock yields an age of 4.73 +/- 2.39 Gyr, consistent with the isochrone estimate. Orbital integration indicates a moderately eccentric orbit (e = 0.268 +/- 0.004) with a guiding radius of R_g = 8.82 kpc. The inferred chemical birth radius, R_b = 9.82 kpc, together with DeltaR ~ -1 kpc, suggests moderate inward radial migration, while the offsets among R_b, R_g, and R_GC are consistent with both churning and blurring processes. A photometric analysis identifies a binary fraction of f_b = 0.449 +/- 0.017 for systems with mass ratios q >= 0.5, im
In a first part, we prove a Lyapunov-type criterion for the $ξ\_1$-positive recurrence of absorbed birth and death processes and provide new results on the domain of attraction of the minimal quasi-stationary distribution. In a second part, we study the ergodicity and the convergence of a Fleming-Viot type particle system whose particles evolve independently as a birth and death process and jump on each others when they hit $0$. Our main result is that the sequence of empirical stationary distributions of the particle system converges to the minimal quasi-stationary distribution of the birth and death process.
Edmund C. Berkeley is usually remembered as a mediator between symbolic logic and early computing, yet that standard description understates the scope of his work. This paper argues for a stronger reading: Berkeley should also be understood as an early theorist of embodied machine intelligence. Across Berkeley's major writings on symbolic logic, machine intelligence, living robots, and Squee, intelligence appears not as disembodied symbol manipulation alone but as the organized coordination of sensing, storage, calculation, control, state, and action in physically realized machines. The paper's first contribution is interpretive: it reconstructs Berkeley as a thinker of machine architecture, temporally extended behavior, and environment-coupled control. Its second contribution is comparative: it reads Berkeley alongside David L. Heiserman to recover a shared descriptive scheme centered on sensing, state or memory, control, action, and adaptation. Its third contribution is critical: it uses that scheme to assess current embodied-AI discourse. The broader claim is that contemporary LLM-centered robotics often demonstrates impressive capability without an equally explicit account of p
We report a detailed investigation of three intermediate-to-old age open clusters, Berkeley 17, Berkeley 18, and Berkeley 39, utilizing precise astrometric and photometric data from Gaia DR3. Cluster membership was robustly determined through a probabilistic proper-motion analysis, yielding statistically significant samples of 600, 1042, and 907 stars, respectively. From the mean parallaxes of these members, we determine astrometric distances ranging from approximately 3.40 kpc for Berkeley 17 to 5.80 kpc for Berkeley 18. Isochrone fitting applied to the decontaminated color-magnitude diagrams constrains the cluster ages to 9.12 +/- 1.00 Gyr, 3.36 +/- 0.50 Gyr, and 5.10 +/- 0.50 Gyr, respectively. Interstellar reddening spans a wide range, from E(B-V) = 0.17 mag in Berkeley 39 to 0.58 mag in Berkeley 17. Structural parameters derived from King model fits to the radial density profiles, combined with mass function analyses, indicate that the clusters are dynamically relaxed systems with mass distributions broadly consistent with the canonical Salpeter slope. Our kinematic analysis reveals that Berkeley 17, Berkeley 18, and Berkeley 39 are part of the outer disk population.
Accurate measurements of young stellar cluster internal dynamics provide crucial insights into their formation. With Gaia, we are now able to trace stellar motions and study the dynamics of star clusters with unprecedented precision, but this requires a reliable list of probable members. We examine a 2 deg-radius region in Cepheus OB4, centered on the young cluster Berkeley 59, to build a reliable candidate member list, enabling the study of the cluster's structure, kinematics, and stellar population. We compiled a catalog of optical and near-infrared photometry, along with precise positions and proper motions from Gaia DR3, for sources in the Cepheus OB4 field. Membership probabilities were determined using a probabilistic random forest algorithm and further refined by requiring HR diagram positions consistent with a young age. From a list of 1030 probable members, we estimate a distance of 1009+-12 pc to Berkeley 59. Masses, extinction, and ages were derived by fitting the spectral energy distributions to atmospheric and evolutionary models, while internal dynamics was analyzed using proper motions relative to the cluster's mean motion. Berkeley 59 exhibits an asymmetric expansio
A crucial test any proposed evolutionary scenario must pass is can the birth rate of the sources we see be sustained by the proposed progenitor population? In this review, I investigate the methods used to determine the birth rates of normal and millisecond radio pulsars and summarise recent results for these two distinct neutron star populations.
As a tutorial to the spatial aspects of Spontaneous Parametric Downconversion (SPDC), we present a detailed first-principles derivation of the transverse correlation width of photon pairs in degenerate collinear SPDC. This width defines the size of a biphoton birth zone, the region where the signal and idler photons are likely to be found when conditioning on the position of the destroyed pump photon. Along the way, we discuss the quantum-optical calculation of the amplitude for the SPDC process, as well as its simplified form for nearly collinear degenerate phase matching. Following this, we show how this biphoton amplitude can be approximated with a Double-Gaussian wavefunction, and give a brief discussion of the measurement statistics (and subsequent convenience) of such Double-Gaussian wavefunctions. Next, we use this approximation to get a simplified estimation of the transverse correlation width, and compare it to more accurate calculations as well as experimental results. We then conclude with a discussion of the concept of a biphoton birth zone, using it to develop intuition for the tradeoff between the first-order spatial coherence and bipohoton correlations in SPDC.
Reasoning about fairness through correlation-based notions is rife with pitfalls. The 1973 University of California, Berkeley graduate school admissions case from Bickel et. al. (1975) is a classic example of one such pitfall, namely Simpson's paradox. The discrepancy in admission rates among males and female applicants, in the aggregate data over all departments, vanishes when admission rates per department are examined. We reason about the Berkeley graduate school admissions case through a causal lens. In the process, we introduce a statistical test for causal hypothesis testing based on Pearl's instrumental-variable inequalities (Pearl 1995). We compare different causal notions of fairness that are based on graphical, counterfactual and interventional queries on the causal model, and develop statistical tests for these notions that use only observational data. We study the logical relations between notions, and show that while notions may not be equivalent, their corresponding statistical tests coincide for the case at hand. We believe that a thorough case-based causal analysis helps develop a more principled understanding of both causal hypothesis testing and fairness.
We consider a dynamic model of interconnected banks. New banks can emerge, and existing banks can default, creating a birth-and-death setup. Microscopically, banks evolve as independent geometric Brownian motions. Systemic effects are captured through default contagion: as one bank defaults, reserves of other banks are reduced by a random proportion. After examining the long-term stability of this system, we investigate mean-field limits as the number of banks tends to infinity. Our main results concern the measure-valued scaling limit which is governed by a McKean-Vlasov jump-diffusion. The default impact creates a mean-field drift, while the births and defaults introduce jump terms tied to the current distribution of the process. Individual dynamics in the limit is described by the propagation of chaos phenomenon. In certain cases, we explicitly characterize the limiting average reserves.