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Creating accessible Virtual Reality (VR) is an ongoing concern in the Human-Computer Interaction (HCI) research community. However, there is little reflection on how accessibility should be conceptualized in the context of an experiential technology. We address this gap in our work: We first explore how accessibility is currently defined, highlighting a growing recognition of the importance of equitable and enriching experiences. We then carry out a literature study (N=28) to examine how accessibility and its relationship with experience is currently conceptualized in VR research. Our results show that existing work seldom defines accessibility in the context of VR, and that barrier-centric research is prevalent. Likewise, we show that experience - e.g., that of presence or immersion - is rarely designed for or evaluated, while participant feedback suggests that it is relevant for disabled users of VR. On this basis, we contribute a working definition of VR accessibility that considers experience a necessary condition for equitable access, and discuss the need for future work to focus on experience in the same way as VR research addressing non-disabled persons does.

As millimeter-wave cosmology experiments refine their optical chains, precisely characterizing their optical materials under cryogenic conditions becomes increasingly important. For instance, as the aperture sizes and bandwidths of millimeter-wave receivers increase, the design of antireflection coatings becomes progressively more constrained by an accurate measure of material optical properties in order to achieve forecasted performance. Likewise, understanding dielectric and scattering losses is relevant to photon noise modeling in presently-deploying receivers such as BICEP Array and especially to future experiments such as CMB-S4. Additionally, the design of refractive elements such as lenses necessitates an accurate measure of the refractive index. High quality factor Fabry-P\'{e}rot open resonant cavities provide an elegant means for measuring these optical properties. Employing a hemispherical resonator that is compatible with a quick-turnaround 4 Kelvin cryostat, we can measure the dielectric and scattering losses of low-loss materials at both ambient and cryogenic temperatures. We review the design, characterization, and metrological applications of quasioptical cavities commissioned for measuring the dielectric materials in the BICEP3 (95 GHz) and BICEP Array mid-frequency (150 GHz) optics. We also discuss the efforts to improve the finesse of said cavities, for better resolution of degenerate higher order modes, which can provide stronger constraints on cavity parameters and sample material thickness., Comment: 12 pages, 4 figures

Disabled people experience many barriers in daily life, but non-disabled people rarely pause to reflect and engage in joint action to advocate for access. In this demo, we explore the potential of Virtual Reality (VR) to sensitize non-disabled people to barriers in the built environment. We contribute a VR simulation of a major traffic hub in Karlsruhe, Germany, and we employ visual embellishments and animations to showcase barriers and potential removal strategies. Through our work, we seek to engage users in conversation on what kind of environment is accessible to whom, and what equitable participation in society requires. Additionally, we aim to expand the understanding of how VR technology can promote reflection through interactive exploration., Comment: Accepted at Mensch und Computer 2024 conference

We employ renewal processes to characterize the spatiotemporal dynamics of an active Brownian particle under stochastic orientational resetting. By computing the experimentally accessible intermediate scattering function (ISF) and reconstructing the full time-dependent distribution of the displacements, we study the interplay of rotational diffusion and resetting. The resetting process introduces a new spatiotemporal regime reflecting the directed motion of agents along the resetting direction at large length scales, which becomes apparent in an imaginary part of the ISF. We further derive analytical expressions for the low-order moments of the displacements and find that the variance displays an effective diffusive regime at long times, which decreases for increasing resetting rates. At intermediate times the dynamics are characterized by a negative skewness as well as a non-zero non-Gaussian parameter.

Manipulating individual trapped ions at the single quantum level has become standard practice in radio-frequency ion traps, enabling applications from quantum information processing to precision metrology. The key ingredient is ground-state cooling of the particle's motion through resolved-sideband laser cooling. Ultra-high-presicion experiments using Penning ion traps will greatly benefit from the reduction of systematic errors offered by full motional control, with applications to atomic masses and $g$-factor measurements, determinations of fundamental constants or related tests of fundamental physics. In addition, it will allow to implement quantum logic spectroscopy, a technique that has enabled a new class of precision measurements in radio-frequency ion traps. Here we demonstrate resolved-sideband laser cooling of the axial motion of a single $^9$Be$^+$ ion in a cryogenic 5 Tesla Penning trap system using a two-photon stimulated-Raman process, reaching a mean phonon number of $\bar{n}_z = 0.10(4)$. This is a fundamental step in the implementation of quantum logic spectroscopy for matter-antimatter comparison tests in the baryonic sector of the Standard Model and a key step towards improved precision experiments in Penning traps operating at the quantum limit., Comment: 6 pages, 5 figures

High precision mass and $g$-factor measurements in Penning traps have enabled groundbreaking tests of fundamental physics. The most advanced setups use multi-trap methods, which employ transport of particles between specialized trap zones. Present developments focused on the implementation of sympathetic laser cooling will enable significantly shorter duty cycles and better accuracies in many of these scenarios. To take full advantage of these increased capabilities, we implement fast adiabatic transport concepts developed in the context of trapped-ion quantum information processing in a cryogenic Penning trap system. We show adiabatic transport of a single $^9\mathrm{Be}^+$ ion initially cooled to 2 mK over a 2.2 cm distance within 15 ms and with less than 10\,mK energy gain at a peak velocity of 3 m/s. These results represent an important step towards the implementation of quantum logic spectroscopy in the \ppbar system. Applying these developments to other multi-trap systems has the potential to considerably increase the data-sampling rate in these experiments., Comment: 15 pages, 7 figures

We describe how some differential geometric bifurcation problems can be treated with the MATLAB continuation and bifurcation toolbox pde2path. The basic setup consists in solving the PDEs for the normal displacement of an immersed surface $X\subset\mathbb{R}^3$ and subsequent update of $X$ in each continuation step, combined with bifurcation detection and localization, followed by possible branch switching. Examples treated include some minimal surfaces such as Enneper's surface and a Schwarz-P-family, some non-zero constant mean curvature surfaces such as liquid bridges and nodoids, and some 4th order biomembrane models. In all of these we find interesting symmetry breaking bifurcations. Some of these are (semi)analytically known and thus are used as benchmarks.

We demonstrate optical sideband spectroscopy of a single $^9$Be$^+$ ion in a cryogenic 5 Tesla Penning trap using two-photon stimulated-Raman transitions between the two Zeeman sublevels of the $1s^{2}2s$ ground state manifold. By applying two complementary coupling schemes, we accurately measure Raman resonances with and without contributions from motional sidebands. From the latter we obtain an axial sideband spectrum with an effective mode temperature of (3.1 $\pm$ 0.4)~mK. This results are a key step for quantum logic operations in Pennings traps, applicable to high precision matter-antimatter comparisons tests in the baryonic sector of the standard model., Comment: 7 pages, 5 figures

Internet analysis is a major challenge due to the volume and rate of network traffic. In lieu of analyzing traffic as raw packets, network analysts often rely on compressed network flows (netflows) that contain the start time, stop time, source, destination, and number of packets in each direction. However, many traffic analyses benefit from temporal aggregation of multiple simultaneous netflows, which can be computationally challenging. To alleviate this concern, a novel netflow compression and resampling method has been developed leveraging GraphBLAS hyperspace traffic matrices that preserve anonymization while enabling subrange analysis. Standard multitemporal spatial analyses are then performed on each subrange to generate detailed statistical aggregates of the source packets, source fan-out, unique links, destination fan-in, and destination packets of each subrange which can then be used for background modeling and anomaly detection. A simple file format based on GraphBLAS sparse matrices is developed for storing these statistical aggregates. This method is scale tested on the MIT SuperCloud using a 50 trillion packet netflow corpus from several hundred sites collected over several months. The resulting compression achieved is significant (<0.1 bit per packet) enabling extremely large netflow analyses to be stored and transported. The single node parallel performance is analyzed in terms of both processors and threads showing that a single node can perform hundreds of simultaneous analyses at over a million packets/sec (roughly equivalent to a 10 Gigabit link)., Comment: arXiv admin note: text overlap with arXiv:2203.13934, arXiv:2108.06653, arXiv:2008.00307

Modern network sensors continuously produce enormous quantities of raw data that are beyond the capacity of human analysts. Cross-correlation of network sensors increases this challenge by enriching every network event with additional metadata. These large volumes of enriched network data present opportunities to statistically characterize network traffic and quickly answer a key question: "What are the primary cyber characteristics of my network data?" The Python GraphBLAS and PyD4M analysis frameworks enable anonymized statistical analysis to be performed quickly and efficiently on very large network data sets. This approach is tested using billions of anonymized network data samples from the largest Internet observatory (CAIDA Telescope) and tens of millions of anonymized records from the largest commercially available background enrichment capability (GreyNoise). The analysis confirms that most of the enriched variables follow expected heavy-tail distributions and that a large fraction of the network traffic is due to a small number of cyber activities. This information can simplify the cyber analysts' task by enabling prioritization of cyber activities based on statistical prevalence. -- Los sensores de red modernos producen enormes cantidades de datos sin procesar que est\'an m\'as all\'a de la capacidad del an\'alisis humano. Una correlaci\'on cruzada de sensores de red se convierte en un desaf\'io al enriquecer cada evento de red con metadatos adicionales. Estos grandes vol\'umenes de datos de red enriquecidos presentan una oportunidad para caracterizar estad\'isticamente el tr\'afico de red y responder a la pregunta: "?Cu\'ales son las principales caracter\'isticas cibern\'eticas de mis datos de red?" Los esquemas de an\'alisis de Python GraphBLAS y D4M permiten realizar an\'alisis estad\'isticos an\'onimos, r\'apidos y eficientes en conjuntos grandes de datos de red. Este enfoque se prueba utilizando miles de millones de muestras de datos de red an\'onimos del observatorio de Internet m\'as grande (Telescopio CAIDA) y decenas de millones de registros an\'onimos del fondo comercial con la mayor capacidad de enriquecimiento (GreyNoise). El an\'alisis confirma que la mayor\'ia de las variables enriquecidas siguen las distribuciones de cola pesada y que una gran fracci\'on del tr\'afico de red se debe a una peque\`na cantidad de actividades cibern\'eticas. Esta informaci\'on puede simplificar la tarea de los analistas cibern\'eticos al permitir la priorizaci\'on de las actividades cibern\'eticas en funci\'on de la prevalencia estad\'istica., Comment: 17 pages, 16 figures, HPEC, Spanish version

We consider a biased nearest-neighbor random walk on $\Z$ which at each step is trapped for some random time with random, site-dependent mean. We derive a simple formula for the speed function in terms of the model parameters., Comment: 10 pages, 3 figures

New experiments that target the B-mode polarization signals in the Cosmic Microwave Background require more sensitivity, more detectors, and thus larger-aperture millimeter-wavelength telescopes, than previous experiments. These larger apertures require ever larger vacuum windows to house cryogenic optics. Scaling up conventional vacuum windows, such as those made of High Density Polyethylene (HDPE), require a corresponding increase in the thickness of the window material to handle the extra force from the atmospheric pressure. Thicker windows cause more transmission loss at ambient temperatures, increasing optical loading and decreasing sensitivity. We have developed the use of woven High Modulus Polyethylene (HMPE), a material 100 times stronger than HDPE, to manufacture stronger, thinner windows using a pressurized hot lamination process. We discuss the development of a specialty autoclave for generating thin laminate vacuum windows and the optical and mechanical characterization of full scale science grade windows, with the goal of developing a new window suitable for BICEP Array cryostats and for future CMB applications.

Long range detection is a cornerstone of defense in many operating domains (land, sea, undersea, air, space, ..,). In the cyber domain, long range detection requires the analysis of significant network traffic from a variety of observatories and outposts. Construction of anonymized hypersparse traffic matrices on edge network devices can be a key enabler by providing significant data compression in a rapidly analyzable format that protects privacy. GraphBLAS is ideally suited for both constructing and analyzing anonymized hypersparse traffic matrices. The performance of GraphBLAS on an Accolade Technologies edge network device is demonstrated on a near worse case traffic scenario using a continuous stream of CAIDA Telescope darknet packets. The performance for varying numbers of traffic buffers, threads, and processor cores is explored. Anonymized hypersparse traffic matrices can be constructed at a rate of over 50,000,000 packets per second; exceeding a typical 400 Gigabit network link. This performance demonstrates that anonymized hypersparse traffic matrices are readily computable on edge network devices with minimal compute resources and can be a viable data product for such devices., Comment: Accepted to IEEE HPEC, Outstanding Paper Award, 8 pages, 8 figures, 1 table, 70 references. arXiv admin note: text overlap with arXiv:2108.06653, arXiv:2008.00307, arXiv:2203.10230

The Internet has become a critical component of modern civilization requiring scientific exploration akin to endeavors to understand the land, sea, air, and space environments. Understanding the baseline statistical distributions of traffic are essential to the scientific understanding of the Internet. Correlating data from different Internet observatories and outposts can be a useful tool for gaining insights into these distributions. This work compares observed sources from the largest Internet telescope (the CAIDA darknet telescope) with those from a commercial outpost (the GreyNoise honeyfarm). Neither of these locations actively emit Internet traffic and provide distinct observations of unsolicited Internet traffic (primarily botnets and scanners). Newly developed GraphBLAS hyperspace matrices and D4M associative array technologies enable the efficient analysis of these data on significant scales. The CAIDA sources are well approximated by a Zipf-Mandelbrot distribution. Over a 6-month period 70\% of the brightest (highest frequency) sources in the CAIDA telescope are consistently detected by coeval observations in the GreyNoise honeyfarm. This overlap drops as the sources dim (reduce frequency) and as the time difference between the observations grows. The probability of seeing a CAIDA source is proportional to the logarithm of the brightness. The temporal correlations are well described by a modified Cauchy distribution. These observations are consistent with a correlated high frequency beam of sources that drifts on a time scale of a month., Comment: 8 pages, 8 figures, 2 tables, 59 references; accepted to GrAPL 2022. arXiv admin note: substantial text overlap with arXiv:2108.06653

We consider the combinatorial Laplacian on a sequence of discrete tori which approximate the m-dimensional torus. In the special case m=1, Friedli and Karlsson derived an asymptotic expansion of the corresponding spectral zeta function in the critical strip, as the approximation parameter goes to infinity. There, the authors have also formulated a conjecture on this asymptotics, that is equivalent to the Riemann conjecture. In this paper, inspired by the work of Friedli and Karlsson, we prove that a similar asymptotic expansion holds for m=2. Similar argument applies to higher dimensions as well. A conjecture on this asymptotics gives an equivalent formulation of the Epstein-Riemann conjecture, if we replace the standard discrete Laplacian with the $9$-point star discrete Laplacian., Comment: 37 pages, 2 figures

Adversarial Internet robots (botnets) represent a growing threat to the safe use and stability of the Internet. Botnets can play a role in launching adversary reconnaissance (scanning and phishing), influence operations (upvoting), and financing operations (ransomware, market manipulation, denial of service, spamming, and ad click fraud) while obfuscating tailored tactical operations. Reducing the presence of botnets on the Internet, with the aspirational target of zero, is a powerful vision for galvanizing policy action. Setting a global goal, encouraging international cooperation, creating incentives for improving networks, and supporting entities for botnet takedowns are among several policies that could advance this goal. These policies raise significant questions regarding proper authorities/access that cannot be answered in the abstract. Systems analysis has been widely used in other domains to achieve sufficient detail to enable these questions to be dealt with in concrete terms. Defeating botnets using an observe-pursue-counter architecture is analyzed, the technical feasibility is affirmed, and the authorities/access questions are significantly narrowed. Recommended next steps include: supporting the international botnet takedown community, expanding network observatories, enhancing the underlying network science at scale, conducting detailed systems analysis, and developing appropriate policy frameworks., Comment: 26 pages, 13 figures, 2 tables, 72 references, submitted to PlosOne

With the recognition of cyberspace as an operating domain, concerted effort is now being placed on addressing it in the whole-of-domain manner found in land, sea, undersea, air, and space domains. Among the first steps in this effort is applying the standard supporting concepts of security, defense, and deterrence to the cyber domain. This paper presents an architecture that helps realize forward defense in cyberspace, wherein adversarial actions are repulsed as close to the origin as possible. However, substantial work remains in making the architecture an operational reality including furthering fundamental research cyber science, conducting design trade-off analysis, and developing appropriate public policy frameworks.

Consider a supercritical Crump--Mode--Jagers process $(\mathcal Z_t^{\varphi})_{t \geq 0}$ counted with a random characteristic $\varphi$. Nerman's celebrated law of large numbers [Z. Wahrsch. Verw. Gebiete 57, 365--395, 1981] states that, under some mild assumptions, $e^{-\alpha t} \mathcal Z_t^\varphi$ converges almost surely as $t \to \infty$ to $aW$. Here, $\alpha>0$ is the Malthusian parameter, $a$ is a constant and $W$ is the limit of Nerman's martingale, which is positive on the survival event. In this general situation, under additional (second moment) assumptions, we prove a central limit theorem for $(\mathcal Z_t^{\varphi})_{t \geq 0}$. More precisely, we show that there exist a constant $k \in \mathbb N_0$ and a function $H(t)$, a finite random linear combination of functions of the form $t^j e^{\lambda t}$ with $\alpha/2 \leq \mathrm{Re}(\lambda)<\alpha$, such that $(\mathcal Z_t^\varphi - a e^{\alpha t}W -H(t))/\sqrt{t^k e^{\alpha t}}$ converges in distribution to a normal random variable with random variance. This result unifies and extends various central limit theorem-type results for specific branching processes., Comment: 67 pages, 3 figures; This is the revised version, incorporating suggestions from the referees reports. Accepted for publication in the Annals of Probability

The Internet has never been more important to our society, and understanding the behavior of the Internet is essential. The Center for Applied Internet Data Analysis (CAIDA) Telescope observes a continuous stream of packets from an unsolicited darkspace representing 1/256 of the Internet. During 2019 and 2020 over 40,000,000,000,000 unique packets were collected representing the largest ever assembled public corpus of Internet traffic. Using the combined resources of the Supercomputing Centers at UC San Diego, Lawrence Berkeley National Laboratory, and MIT, the spatial temporal structure of anonymized source-destination pairs from the CAIDA Telescope data has been analyzed with GraphBLAS hierarchical hypersparse matrices. These analyses provide unique insight on this unsolicited Internet darkspace traffic with the discovery of many previously unseen scaling relations. The data show a significant sustained increase in unsolicited traffic corresponding to the start of the COVID19 pandemic, but relatively little change in the underlying scaling relations associated with unique sources, source fan-outs, unique links, destination fan-ins, and unique destinations. This work provides a demonstration of the practical feasibility and benefit of the safe collection and analysis of significant quantities of anonymized Internet traffic., Comment: 8 pages, 9 figures, 2 tables, 43 references, accepted to IEEE HPEC 2021. arXiv admin note: substantial text overlap with arXiv:2008.00307

We discuss laser-based and quantum logic inspired cooling and detection methods amenable to single (anti-)protons. These would be applicable e.g. in a g-factor based test of CPT invariance as currently pursued within the BASE collaboration. Towards this end, we explore sympathetic cooling of single (anti-)protons with atomic ions as suggested by Heinzen and Wineland (1990)., Comment: Presented at LEAP 2016 in Kanazawa, Japan

We present methods to manipulate and detect the motional state and the spin state of a single antiproton or proton which are currently under development within the BASE (Baryon Antibaryon Symmetry Experiment) collaboration. These methods include sympathetic laser cooling of a single (anti-)proton using a co-trapped atomic ion as well as quantum logic spectroscopy with the two particles and could be implemented within the collaboration for state preparation and state readout in the antiproton $g$-factor measurement experiment at CERN. In our project, these techniques shall be applied using a single $^9\text{Be}^+$ ion as the atomic ion in a Penning trap system at a magnetic field of 5 T. As an intermediate step, a controlled interaction of two beryllium ions in a double-well potential as well as sympathetic cooling of one ion by the other shall be demonstrated., Comment: Proceedings of the 13th International Conference on Low Energy Antiproton Physics (LEAP 2018) Paris, France, 12-16 March 2018

Current experimental efforts to test the fundamental CPT symmetry with single (anti-)protons are progressing at a rapid pace but are hurt by the nonzero temperature of particles and the difficulty of spin state detection. We describe a laser-based and quantum logic inspired approach to single (anti-)proton cooling and state detection., Comment: Presented at the Seventh Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 20-24, 2016

Current precision experiments with single (anti)protons to test CPT symmetry progress at a rapid pace, but are complicated by the need to cool particles to sub-thermal energies. We describe a cryogenic Penning-trap setup for $^9$Be$^+$ ions designed to allow coupling of single (anti)protons to laser-cooled atomic ions for sympathetic cooling and quantum logic spectroscopy. We report on trapping and laser cooling of clouds and single $^9$Be$^+$ ions. We discuss prospects for a microfabricated trap to allow coupling of single (anti)protons to laser-cooled $^9$Be$^+$ ions for sympathetic laser cooling to sub-mK temperatures on ms time scales., Comment: Presented at the Eighth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, May 12-16, 2019

We demonstrate phase locking of two ultraviolet laser sources by modulating a fundamental infrared laser with 4th-order sidebands using an electro-optic modulator and phase locking of one sideband to a second fundamental infrared laser. Subsequent sum frequency generation and second harmonic generation successfully translates the frequency offset to the ultraviolet domain. The phase lock at 139 GHz is confirmed through stimulated Raman transitions for thermometry of $^9$Be$^+$ ions confined in a cryogenic Penning trap. This technique might be used for sideband cooling of single $^9$Be$^+$ ions as well as sympathetic cooling schemes and quantum logic based measurements in Penning traps in the future., Comment: 7 figures, accepted for publication in J. Phys. B

Cosmological observations as well as theoretical approaches to physics beyond the Standard Model provide strong motivations for experimental tests of fundamental symmetries, such as CPT invariance. In this context, the availability of cold baryonic antimatter at CERN has opened an avenue for ultrahigh-precision comparisons of protons and antiprotons in Penning traps. This work discusses an experimental method inspired by quantum logic techniques that will improve particle localization and readout speed in such experiments. The method allows for sympathetic cooling of the (anti-)proton to its quantum-mechanical ground state as well as the readout of its spin alignment, replacing the commonly used continuous Stern-Gerlach effect. Both of these features are achieved through coupling to a laser-cooled `logic' ion co-trapped in a double-well potential. This technique will boost the measurement sampling rate and will thus provide results with lower statistical uncertainty, contributing to stringent searches for time dependent variations in the data. Such measurements ultimately yield extremely high sensitivities to CPT violating coefficients acting on baryons in the Standard-Model Extension, will allow the exploration of previously unmeasured types of symmetry violations, and will enable antimatter-based axion-like dark matter searches with improved mass resolution., Comment: Accepted for publication in New Journal of Physics

The development of language courses designed specifically for Spanish heritage learners has recently gained much attention at all levels of education in the US. Since heritage learners started to acquire the language since childhood at home, their needs are different from those of students in the traditional foreign language classroom. To fulfill these needs, Spanish heritage teachers at all levels are creating programs and materials to serve this student population. The Heritage Spanish web-based community (https://heritagespanish.coerll.utexas. edu), hosted by the Center for Open Educational Resources and Language Learning (COERLL), was created as a space for Spanish teachers to collaborate, share, and communicate about the teaching and learning of Spanish as a heritage language (https://www.coerll. utexas.edu/coerll/about-coerll). A specific example of the design and implementation of Open Educational Resources (OERs) in a Spanish as a heritage language course is found at Lehman College from the City University of New York (CUNY), which serves a significant student population of Hispanic origin. [For the complete volume, "New Case Studies of Openness in and beyond the Language Classroom," see ED596829.]

We present a high-flux source of cold ytterbium atoms that is robust, lightweight and low-maintenance. Our apparatus delivers $10^9$ atoms/s into a 3D magneto-optical trap without requiring water-cooling or high current power supplies. We achieve this by employing a Zeeman slower and a 2D magneto-optical trap fully based on permanent magnets in Halbach configurations. This strategy minimizes mechanical complexity, stray magnetic fields, and heat production while requiring little to no maintenance, making it applicable to both embedded systems that seek to minimize electrical power consumption, and large scale experiments to reduce the complexity of their subsystems., Comment: 12 pages, 8 figures

Our society has never been more dependent on computer networks. Effective utilization of networks requires a detailed understanding of the normal background behaviors of network traffic. Large-scale measurements of networks are computationally challenging. Building on prior work in interactive supercomputing and GraphBLAS hypersparse hierarchical traffic matrices, we have developed an efficient method for computing a wide variety of streaming network quantities on diverse time scales. Applying these methods to 100,000,000,000 anonymized source-destination pairs collected at a network gateway reveals many previously unobserved scaling relationships. These observations provide new insights into normal network background traffic that could be used for anomaly detection, AI feature engineering, and testing theoretical models of streaming networks., Comment: 6 pages, 6 figures,3 tables, 49 references, accepted to IEEE HPEC 2020

In this paper, we draw attention to a problem that is often overlooked or ignored by companies practicing hypothesis testing (A/B testing) in online environments. We show that conducting experiments on limited inventory that is shared between variants in the experiment can lead to high false positive rates since the core assumption of independence between the groups is violated. We provide a detailed analysis of the problem in a simplified setting whose parameters are informed by realistic scenarios. The setting we consider is a $2$-dimensional random walk in a semi-infinite strip. It is rich enough to take a finite inventory into account, but is at the same time simple enough to allow for a closed form of the false-positive probability. We prove that high false-positive rates can occur, and develop tools that are suitable to help design adequate tests in follow-up work. Our results also show that high false-negative rates may occur. The proofs rely on a functional limit theorem for the $2$-dimensional random walk in a semi-infinite strip., Comment: 23 pages, 8 figures

In his, by now, classical work from 1981, Nerman made extensive use of a crucial martingale $(W_t)_{t \geq 0}$ to prove convergence in probability, in mean and almost surely, of supercritical general branching processes (a.k.a. Crump-Mode-Jagers branching processes) counted with a general characteristic. The martingale terminal value $W$ figures in the limits of his results. We investigate the rate at which the martingale, now called Nerman's martingale, converges to its limit $W$. More precisely, assuming the existence of a Malthusian parameter $\alpha > 0$ and $W_0\in L^2$, we prove a functional central limit theorem for $(W-W_{t+s})_{s\in\mathbb{R}}$, properly normalized, as $t\to\infty$. The weak limit is a randomly scaled time-changed Brownian motion. Under an additional technical assumption, we prove a law of the iterated logarithm for $W-W_t$., Comment: submitted for publication, 23 pages