Binary Distribution Research Articles

Taking More Society for Academic Emergency Medicine Practice Tests Does Not Lead to Improved National EM-M4 Exam Scores

Emergency medicine (EM) is a required clerkship for third-year medical students, and an elective EM acting internship (AI) is available to fourth-year students at our institution. The Society for Academic Emergency Medicine's (SAEM) National Emergency Medicine M4 Examination (EM-M4) is administered to students at the end of the EM AI experience. To prepare for the exam, students gain access to 23 practice tests available from SAEM. In this study we investigate the correlation between the number of practice tests taken and EM-M4 performance. We collected data for EM-M4 and the US Medical Licensing Exam (USMLE) Step 2 Clinical Knowledge (CK) from students completing a MS4 EM clerkship in consecutive medical school classes from 2014-2017 at a private medical school. In addition, we collected data during the clerkship on the number of practice exams taken and whether a comprehensive practice exam was taken. We analyzed the study population three ways to determine whether the number of practice tests impacted final exam results: a binary distribution (1-11 or 12-23 tests taken); quaternary distribution (1-6, 7-12, 13-18, or 19-23 tests taken); and individual test variability (1,2,3,…22,23 tests taken). Complete data for 147 students was used for data analysis. The EM-M4 showed moderate (r = 0.49) correlations with USMLE Step 2 CK. There was no significant difference in EM-M4 performance in the binary analysis (P ≤ 0.09), the quaternary analysis (P ≤ 0.09), or the continuous variable analysis (P ≤ 0.52). Inclusion of a comprehensive practice test also did not correlate with EM-M4 performance (P ≤ 0.78). Degree of utilization of SAEM practice tests did not seem to correlate with performance on the EM-M4 examination at our institution. This could be due to many factors including that the question bank is composed of items that had poor item discrimination, possible inadequate coverage of EM curriculum, and/or use of alternative study methods. While further investigation is needed, if our conclusions prove generalizable, then using the SAEM practice tests is an extraneous cognitive load from a modality without proven benefit.

Numerical study of heat transfer for gravity-driven binary size particle flow around circular tube

As the primary working medium in moving bed heat exchangers, solid bulk materials are composed of multiple size particles. To clarify the effect of particle size distribution (PSD) on heat transfer, the discrete element method (DEM) is used to study the flow and heat transfer of binary size particle flow around a circular tube. The heat transfer model for multiple size particles is developed and coupled with DEM method. The particle flow characteristics with PSD width are analyzed in detail. The results show that particle size segregation, competitive flow and flow instability are the unique characteristics of binary size particle flow around a tube. Wider PSD will enhance these characteristics and have a positive effect on particle renewal in the stagnation zone, which could decrease the local heat resistance. The total heat transfer coefficient between particle flow and tube wall increases at most by 9.73% as PSD is wider. • Binary size particle flow around a circular tube is studied with DEM method. • Binary size particle flow can form local particle size segregation around tube. • Binary size particles can decrease the stagnation zone above the tube. • A wider binary particle size distribution can increase the flow instability. • A wider binary particle size distribution can enhance heat transfer performance.

State Estimation-Based Hybrid-Triggered Controller Design for Synchronization of Repeated Scalar Nonlinear Complex Dynamical Networks

The goal of this work is to examine the issue of state estimation-based synchronization of nonlinear complex dynamical networks that are prone to external disturbances, repeated scalar nonlinearities and time-varying coupling delays. In a nutshell, hybrid-triggered communication transmission nonfragile control design with respect to the estimated states and extended dissipative theory is designed, which comprises of both the time and event-triggered mechanisms, and a hybrid generator is presented between the sensor and controller. More preciously, a stochastic variable satisfying the Bernoulli random binary distribution is utilized to represent the phenomenon of random transmission between the time and event-triggered mechanism. Furthermore, delay-dependent adequate conditions for ensuring the synchronization of the addressed system are developed in the form of linear matrix inequalities. And, the requisite gain matrices and hybrid-triggered parameters are evaluated with the help of solving these procured conditions. Lastly, a numerical example with an application to memristor-based Chua’s circuit model is demonstrated to ensure the effectiveness of established control technique.

Modeling and analysis of networked finite state machine subject to random communication losses

<abstract><p>In networked control systems, channel packet loss is inevitable due to the restricted bandwidth, especially in control (from supervisory controller to some remote actuators), which will lead to the occurrence of failure control. In this paper, the controllability of networked finite state machine (<italic>NFSM</italic>) is investigated within the framework of matrix semi-tensor product (<italic>STP</italic>), where random channel packet losses are considered. Firstly, to capture the transition dynamics under random packet losses in the control channel, we introduce a stochastic variable to estimate the state evolution, and the variable is assumed to obey the Bernoulli binary distribution. Meanwhile, the <italic>NFSM</italic> with random channel packet losses can be expressed as a probabilistic logic representation. Subsequently, by means of the delicate operation of matrix <italic>STP</italic>, some concise validation conditions for the controllability with a probability of one ($ w.p. $ 1), are derived for <italic>NFSM</italic> based on the probabilistic logic representation. Finally, a typical computing instance is used to demonstrate the validity of the proposed method. The conclusions are conducive to study the security issues of the system involving opacity, fault detection, controller design and so on.</p></abstract>

Wave Function Realization of a Thermal Collision Model.

An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling stochastic wave functions converging to a density operator description. The stochastic techniques are based on the quantum collision model. Modeling systems dynamics with wave functions and modeling the interaction with the environment with a collision sequence reduces the scale of the complexity significantly. The algorithm developed can be implemented on quantum computers. We introduce stochastic methods that exploit statistical characteristics of the model such as Markovianity, Brownian motion, and binary distribution. The central limit theorem is employed to study the convergence of distributions of stochastic dynamics of pure quantum states represented by wave vectors. By averaging a sample of functions in the distribution we prove and demonstrate the convergence of the dynamics to the mixed quantum state described by a density operator.

Parameter distributions of binary black hole mergers near supermassive black holes as seen by advanced gravitational wave detectors

ABSTRACT The environment surrounding supermassive black holes (SMBHs) in galactic nuclei (GNs) is expected to harbour stellar-mass binary black hole (BBH) populations. These binaries were suggested to form a hierarchical triple system with the SMBH, and gravitational perturbations from the SMBH can enhance the mergers of BBHs through Lidov–Kozai (LK) oscillations. Previous studies determined the expected binary parameter distribution for this merger channel in single GNs. Here, we account for the different spatial distribution and mass distribution models of BBHs around SMBHs and perform direct high-precision regularized N-body simulations, including Post-Newtonian (PN) terms up to order PN2.5, to model merging BBH populations in single GNs. We use a full inspiral-merger-ringdown waveform model of BBHs with non-zero eccentricities and take into account the observational selection effect to determine the parameter distributions of LK-induced BBHs detected with a single advanced gravitational-wave (GW) detector from all GNs in the Universe. We find that the detected mergers’ total binary mass distribution is tilted towards lower masses, and the mass ratio distribution is roughly uniform. The redshift distribution peaks between ∼0.15 and 0.55, and the vast majority of binaries merge within redshift ∼1.1. The fraction of binaries entering the LIGO/Virgo/KAGRA band with residual eccentricities >0.1 is below $\sim 10 {{\ \rm per\ cent}}$. We identify a negative correlation between residual eccentricity and mass parameters and a negative correlation between residual eccentricity and source distance. Our results for the parameter distributions and correlations among binary parameters may make it possible to disentangle this merger channel from other BBH merger channels statistically.

LibRoadRunner 2.0: a high performance SBML simulation and analysis library.

This article presents libRoadRunner 2.0, an extensible, high-performance, cross-platform, open-source software library for the simulation and analysis of models expressed using the systems biology markup language (SBML). libRoadRunner is a self-contained library, able to run either as a component inside other tools via its C++, C and Python APIs, or interactively through its Python or Julia interface. libRoadRunner uses a custom just-in-time (JIT) compiler built on the widely used LLVM JIT compiler framework. It compiles SBML-specified models directly into native machine code for a large variety of processors, making it fast enough to simulate extremely large models or repeated runs in reasonable timeframes. libRoadRunner is flexible, supporting the bulk of the SBML specification (except for delay and non-linear algebraic equations) as well as several SBML extensions such as hierarchical composition and probability distributions. It offers multiple deterministic and stochastic integrators, as well as tools for steady-state, sensitivity, stability and structural analyses. libRoadRunner binary distributions for Windows, Mac OS and Linux, Julia and Python bindings, source code and documentation are all available at https://github.com/sys-bio/roadrunner, and Python bindings are also available via pip. The source code can be compiled for the supported systems as well as in principle any system supported by LLVM-13, such as ARM-based computers like the Raspberry Pi. The library is licensed under the Apache License Version 2.0.

Polarization Analysis of Gene Sequence Structures: Mapping of Extreme Local Polarization States

A method for visualization and identification of nucleotide sequences is proposed based on the synthesis of phase screens displaying the structure of the analyzed sequences and reconstruction of binary maps of the extreme values of the local Stokes vector components in the diffraction zone. This diffraction zone is formed due to reading out the phase screen by a coherent collimated beam with two orthogonally polarized (x–y) components. With different phase delays of the x–y components of the readout beam introduced by the phase screen elements, this causes a variety of local polarization states in the diffraction zone. The discrimination level for the local component of the Stokes vector chosen for the binary mapping is established near the extreme value for this component. Computer verification of the proposed method using nucleotide sequences for various strains of the model African swine fewer (ASF) virus as the test objects shows its high efficiency in the detection of differences between two compared sequences corresponding to the same type of infectious agent. Analysis of the model data for the strains under study made it possible to establish a power-law character of correlation coefficients of the synthesized binary distributions of extreme local polarization states depending on the discrimination threshold detuning from the maximum value of the Stokes vector component used for the mapping .

No Peaks without Valleys: The Stable Mass Transfer Channel for Gravitational-wave Sources in Light of the Neutron Star–Black Hole Mass Gap

Gravitational-wave (GW) detections are starting to reveal features in the mass distribution of double compact objects. The lower end of the black hole (BH) mass distribution is especially interesting as few formation channels contribute here and because it is more robust against variations in the cosmic star formation than the high-mass end. In this work we explore the stable mass transfer channel for the formation of GW sources with a focus on the low-mass end of the mass distribution. We conduct an extensive exploration of the uncertain physical processes that impact this channel. We note that, for fiducial assumptions, this channel reproduces the peak at ∼9 M ☉ in the GW-observed binary BH mass distribution remarkably well and predicts a cutoff mass that coincides with the upper edge of the purported neutron star–black hole (NS–BH) mass gap. The peak and cutoff mass are a consequence of the unique properties of this channel; namely (1) the requirement of stability during the mass transfer phases, and (2) the complex way in which the final compact object masses scale with the initial mass. We provide an analytical expression for the cutoff in the primary component mass and show that this adequately matches our numerical results. Our results imply that selection effects resulting from the formation channel alone can provide an explanation for the purported NS–BH mass gap in GW detections. This provides an alternative to the commonly adopted view that the gap emerges during BH formation.

Ring-ExpLWE: A High-Performance and Lightweight Post-Quantum Encryption Scheme for Resource-Constrained IoT Devices

As the Internet of Things (IoT) expands explosively existing network connections, the transmission and processing of private data is facing more serious threats of leakage and theft. Classical public key encryption schemes are difficult to guarantee strong security protection, because the mathematically hard problems they rely on are no longer difficult to solve under the rapid development of quantum computing. Therefore, a more high-performance and quantum-resistant encryption scheme Ring-ExpLWE is proposed, in which the error vector is sampled in the exponential distribution instead of the binary distribution in the previous Ring-BinLWE. We evaluate the Ring-ExpLWE’s security level by analyzing the runtime under quantum hybrid attack and comparing the standard deviation of the noise polynomial coefficients. Compared with Ring-BinLWE, the proposed Ring-ExpLWE requires larger runtime for quantum hybrid attack and has a more discrete noise distribution. Therefore, Ring-ExpLWE can provide a higher security level under the same parameter set. Moreover, the high-performance software and hardware implementations for the Ring-ExpLWE scheme are proposed, respectively. Based on the Cortex-M3 microprocessor platform, encryption, and decryption only require 35.6 and 17.8 ms in our software implementation, respectively. Compared with the previous Ring-BinLWE schemes, while significantly improving the security level, the Area <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> Time (AT) of our high-performance and lightweight hardware implementations is reduced by 49.2% and 49.5%, respectively, when the FPGA platform is Spartan 6.

The role of the turbulence driving mode for the initial mass function

ABSTRACT Turbulence is a critical ingredient for star formation, yet its role for the initial mass function (IMF) is not fully understood. Here we perform magnetohydrodynamical (MHD) simulations of star cluster formation including gravity, turbulence, magnetic fields, stellar heating, and outflow feedback to study the influence of the mode of turbulence driving on IMF. We find that simulations that employ purely compressive turbulence driving (COMP) produce a higher fraction of low-mass stars as compared to simulations that use purely solenoidal driving (SOL). The characteristic (median) mass of the sink particle (protostellar) distribution for COMP is shifted to lower masses by a factor of ∼1.5 compared to SOL. Our simulation IMFs capture the important features of the observed IMF form. We find that turbulence-regulated theories of the IMF match our simulation IMFs reasonably well in the high-mass and low-mass range, but underestimate the number of very low-mass stars, which form towards the later stages of our simulations and stop accreting due to dynamical interactions. Our simulations show that for both COMP and SOL, the multiplicity fraction is an increasing function of the primary mass, although the multiplicity fraction in COMP is higher than that of SOL for any primary mass range. We find that binary mass ratio distribution is independent of the turbulence driving mode. The average specific angular momentum of the sink particles in SOL is a factor of 2 higher than that for COMP. Overall, we conclude that the turbulence driving mode plays a significant role in shaping the IMF.

Feature Borrowing in Language Contact

In this paper, we consider mood selection in embedded clauses by focusing on a German-based minority language, Cimbrian, which is spoken in a northern Italian enclave. Mood selection in Cimbrian relies on the presence of two different complementizers, az and ke (the latter being borrowed from Romance varieties), each of which selectively require a specific mood. Az selects the mood subjunctive in modal sentences introduced by non-factive verbs, whereas ke co-occurs with the indicative in purely declarative clauses introduced by factive and semi-factive verbs. However, this binary distribution is challenged in the two following contexts, and it is precisely at this point that feature borrowing comes into play: (i) with the verb gloam ‘to believe/to think’, the expected binary pattern appears (irrealis az + subjunctive and the realis ke + indicative), but, crucially, a third construction emerges, namely ke + subj.; (ii) surprisingly, az + subj. displays some ‘gaps’ in its paradigm, specifically in the first person, which appeared in the data we collected via translation tasks from Italian into Cimbrian. Both phenomena shed light on how language contact works, not in terms of structural borrowing but rather in terms of the transfer of the specific features of a given lexical item.

The statistical properties of early-type stars from LAMOST DR8

Context. Massive binary stars play a crucial role in many astrophysical fields. Investigating the statistical properties of massive binary stars is essential to trace the formation of massive stars and constrain the evolution of stellar populations. However, no consensus has been achieved on the statistical properties of massive binary stars, mainly due to the lack of a large and homogeneous sample of spectroscopic observations. Aims. We study the intrinsic binary fraction fbin and distributions of mass ratio f(q) and orbital period f(P) of early-type stars (comprised of O-, B-, and A-type stars) and investigate their dependences on effective temperature Teff, stellar metallicity [M/H], and the projection velocity vsini, based on the homogeneous spectroscopic sample from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) Data Release Eight (DR8). Methods. We collected 886 early-type stars, each with more than six observations from the LAMOST DR8, and divided the sample into subgroups based on their derived effective temperature (Teff), metallicity ([M/H]), and projected rotational velocity (vsini). Radial velocity measurements were archived from a prior study. A set of Monte Carlo simulations, following distributions of f(P)∝Pπ and f(q)∝qγ were applied to the observed binary fraction to correct for any observational biases. The uncertainties of the derived results induced by the sample size and observation frequency are examined systematically. Results. We found that fbin increases with increasing Teff. For stars in groups of B8-A, B4-B7, O-B3, the binary fractions are fbin = 48% ± 10%, 60%±10%, and 76%±10%, respectively. The binary fraction is positively correlated with metallicity for spectra in the sample, with derived values of fbin = 44% ± 10%, 60%±10%, and 72%±10% for spectra with metallicity ranges of [M/H] &lt; −0.55, −0.55 ≤ [M/H] &lt; −0.1, to [M/H] ≥ −0.1. Over all the vsini values we considered, the fbin have constant values of ∼50%. It seems that the binary population is relatively evenly distributed over a wide range of vsini values, while the whole sample shows that most of the stars are concentrated at low values of vsini (probably from strong wind and magnetic braking of single massive stars) and at high values of vsini (likely from the merging of binary stars). Stellar evolution and binary interaction may be partly responsible for this. In the case of samples with more than six observations, we derived π = −0.9 ± 0.35, −0.9 ± 0.35, and −0.9 ± 0.35, and γ = −1.9 ± 0.9, −1.1 ± 0.9, and −2 ± 0.9 for stars of types O-B3, B4-B7, and B8-A, respectively. There are no correlations found between π(γ) and Teff, nor for π(γ) and [M/H]. The uncertainties of the distribution decrease toward a larger sample size with higher observational cadence.

Statistical Degree Distribution Design for Using Fountain Codes to Control the Peak-To-Average Power Ratio in an OFDM System.

Utilizing fountain codes to control the peak-to-average power ratio (PAPR) is a classic scheme in Orthogonal Frequency Division Multiplexing (OFDM) wireless communication systems. However, because the robust soliton distribution (RSD) produces large-degree values, the decoding performance is severely reduced. In this paper, we design statistical degree distribution (SD) under a scenario that utilizes fountain codes to control the PAPR. The probability of the PAPR produced is combined with RSD to design PRSD, which enhances the smaller degree value produced. Subsequently, a particle swarm optimization (PSO) algorithm is used to search the optimal degree value between the binary exponential distribution (BED) and PRSD distribution according to the minimum average degree principle. Simulation results demonstrate that the proposed method outperforms other relevant degree distributions in the same controlled PAPR threshold, and the average degree value and decoding efficiency are remarkably improved.

The thermodynamics of stellar multiplicity: an analytic model for the dynamical evolution of binary star populations in dense stellar environments due to single–binary interactions

ABSTRACT We recently derived, using the density-of-states approximation, analytic distribution functions for the outcomes of direct single-binary scatterings. Using these outcome distribution functions, we present in this paper a self-consistent statistical mechanics-based analytic model obtained using the Fokker–Planck limit of the Boltzmann equation. Our model quantifies the dominant gravitational physics, combining both strong and weak single–binary interactions, which drives the time evolution of binary orbital parameter distributions in dense stellar environments. We focus in particular the distributions of binary orbital energies and eccentricities. We find a novel steady-state distribution of binary eccentricities, featuring strong depletions of both the highest and the lowest eccentricity binaries. In energy space, we compare the predictions of our analytic model to the results of numerical N-body simulations, and find that the agreement is good for the initial conditions considered here. This work is a first step towards the development of a fully self-consistent semi-analytic model for dynamically evolving binary star populations in dense stellar environments due to direct few-body interactions.

Constraints on the merging binary neutron star mass distribution and equation of state based on the incidence of jets in the population

A relativistic jet has been produced in the single well-localised binary neutron star (BNS) merger detected to date in gravitational waves (GWs), and the local rates of BNS mergers and short gamma-ray bursts are of the same order of magnitude. This suggests that jet formation is not a rare outcome for BNS mergers, and we show that this intuition can be turned into a quantitative constraint: at least about one-third of GW-detected BNS mergers and at least about one-fifth of all BNS mergers should produce a successful jet (90% credible level). Whether a jet is launched depends on the properties of the merger remnant and of the surrounding accretion disc, which in turn are a function of the progenitor binary masses and equation of state (EoS). The incidence of jets in the population therefore carries information about the binary component mass distribution and EoS. Under the assumption that a jet can only be produced by a black hole remnant surrounded by a non-negligible accretion disc, we show how the jet incidence can be used to place a joint constraint on the space of BNS component mass distributions and EoS. The result points to a broad mass distribution, with particularly strong support for masses in the 1.3 − 1.6 M⊙ range. The constraints on the EoS are shallow, but we show how they will tighten as the knowledge on the jet incidence improves. We also discuss how to extend the method to include future BNS mergers, with possibly uncertain jet associations.

Learning-accelerated asynchronous decentralized optimization for integrated transmission and distribution systems over lossy networks

With the rapid growth of distributed renewable energy in distribution networks, the synergistic operation between transmission and distribution networks is increasingly important. Decentralized optimization is employed in the coordination of integrated transmission and distribution networks to reduce the communication burden and protect regional information privacy. Existing works on decentralized optimization algorithms for integrated transmission and distribution networks have seldom addressed packet losses. Moreover, the synchronous operation requirement is difficult to achieve for many decentralized optimization algorithms to solve problems with computationally heterogeneous subproblems and during the occurrence of communication failure. In order to tackle these problems, this paper proposes a decentralized scheme based on the relaxed alternating direction method of multipliers for coordinating the operation of integrated transmission and distribution networks considering communication failures and asynchronous updates. A momentum–extrapolation prediction–correction method is designed to allow operators to forecast their neighbors’ missing boundary variable values and to be solved continuously. Simulation results show that compared with the classical alternating direction method of multipliers, the relaxed alternating direction method of multipliers can obtain the nearly same operation costs with fewer iterations. In addition, the proposed algorithm shows robustness against packet losses and asynchronous computations. It is also found that the prediction–correction technique makes the proposed algorithm converge faster compared with no prediction. • Step size can change the performance of proposed algorithms. • Packet losses are represented by a binary probabilistic distribution model. • Convergence rates are affected by packet losses and asynchronous updates. • A prediction-correction approach is used to forecast the missing information.

Sensitivity Analysis for Binary Sampling Systems via Quantitative Fisher Information Lower Bounds

Determining the quality of sensing devices exhibiting minimal digitization complexity is addressed. Measurements of such sensor systems are characterized by multivariate binary distributions and assessing sensitivity via the Cramér-Rao lower bound turns out to be intractable. In this context, the Fisher matrix of the exponential family and a lower bound for arbitrary probabilistic models are discussed. The conservative approximation for Fisher’s information matrix rests on a surrogate exponential family distribution connected to the actual data-generating system by two compact equivalences. Without characterizing the likelihood and its support, this probabilistic notion enables designing estimators that consistently achieve the sensitivity level defined by the inverse of the conservative information matrix. For hard-limited multivariate Gaussian signal models, a quadratic exponential surrogate distribution tames statistical complexity such that a quantitative and conservative assessment of Fisher information becomes possible. This result is exploited for the Fisherian quantization loss analysis of an array with low-complexity binary sensors in comparison to an ideal system featuring infinite amplitude resolution. Additionally, data-driven assessment by estimating a conservative approximation for the Fisher matrix under recursive binary sampling as implemented in ΣΔ-modulating analog-to-digital converters is demonstrated.

Fuzzy Strategy Grey Wolf Optimizer for Complex Multimodal Optimization Problems.

Traditional grey wolf optimizers (GWOs) have difficulty balancing convergence and diversity when used for multimodal optimization problems (MMOPs), resulting in low-quality solutions and slow convergence. To address these drawbacks of GWOs, a fuzzy strategy grey wolf optimizer (FSGWO) is proposed in this paper. Binary joint normal distribution is used as a fuzzy method to realize the adaptive adjustment of the control parameters of the FSGWO. Next, the fuzzy mutation operator and the fuzzy crossover operator are designed to generate new individuals based on the fuzzy control parameters. Moreover, a noninferior selection strategy is employed to update the grey wolf population, which makes the entire population available for estimating the location of the optimal solution. Finally, the FSGWO is verified on 30 test functions of IEEE CEC2014 and five engineering application problems. Comparing FSGWO with state-of-the-art competitive algorithms, the results show that FSGWO is superior. Specifically, for the 50D test functions of CEC2014, the average calculation accuracy of FSGWO is 33.63%, 46.45%, 62.94%, 64.99%, and 59.82% higher than those of the equilibrium optimizer algorithm, modified particle swarm optimization, original GWO, hybrid particle swarm optimization and GWO, and selective opposition-based GWO, respectively. For the 30D and 50D test functions of CEC2014, the results of the Wilcoxon signed-rank test show that FSGWO is better than the competitive algorithms.

Relative Robustness of CDMs and (M)IRT in Measuring Growth in Latent Skills.

Previous studies have demonstrated evidence of latent skill continuity even in tests intentionally designed for measurement of binary skills. In addition, the assumption of binary skills when continuity is present has been shown to potentially create a lack of invariance in item and latent ability parameters that may undermine applications. In this article, we examine measurement of growth as one such application, and consider multidimensional item response theory (MIRT) as a competing alternative. Motivated by prior findings concerning the effects of skill continuity, we study the relative robustness of cognitive diagnostic models (CDMs) and (M)IRT models in the measurement of growth under both binary and continuous latent skill distributions. We find CDMs to be a less robust way of quantifying growth under misspecification, and subsequently provide a real-data example suggesting underestimation of growth as a likely consequence. It is suggested that researchers should regularly attend to the assumptions associated with the use of latent binary skills and consider (M)IRT as a potentially more robust alternative if unsure of their discrete nature.