Distinguishing Hidden Markov Chains

Hidden Markov Chains (HMCs) are commonly used mathematical models of probabilistic systems. They are employed in various fields such as speech recognition, signal processing, and biological sequence analysis. We consider the problem of distinguishing two given HMCs based on an observation sequence that one of the HMCs generates. More precisely, given two HMCs and an observation sequence, a distinguishing algorithm is expected to identify the HMC that generates the observation sequence. Two HMCs are called distinguishable if for every $\varepsilon > 0$ there is a distinguishing algorithm whose error probability is less than $\varepsilon$. We show that one can decide in polynomial time whether two HMCs are distinguishable. Further, we present and analyze two distinguishing algorithms for distinguishable HMCs. The first algorithm makes a decision after processing a fixed number of observations, and it exhibits two-sided error. The second algorithm processes an unbounded number of observations, but the algorithm has only one-sided error. The error probability, for both algorithms, decays exponentially with the number of processed observations. We also provide an algorithm for distinguishing multiple HMCs. Finally, we discuss an application in stochastic runtime verification.Comment: This is the full version of a LICS'16 pape

Optimal sequential fingerprinting: Wald vs. Tardos

We study sequential collusion-resistant fingerprinting, where the fingerprinting code is generated in advance but accusations may be made between rounds, and show that in this setting both the dynamic Tardos scheme and schemes building upon Wald's sequential probability ratio test (SPRT) are asymptotically optimal. We further compare these two approaches to sequential fingerprinting, highlighting differences between the two schemes. Based on these differences, we argue that Wald's scheme should in general be preferred over the dynamic Tardos scheme, even though both schemes have their merits. As a side result, we derive an optimal sequential group testing method for the classical model, which can easily be generalized to different group testing models.Comment: 12 pages, 10 figure

A perspective from extinct radionuclides on a Young Stellar Object: The Sun and its accretion disk

Meteorites, which are remnants of solar system formation, provide a direct glimpse into the dynamics and evolution of a young stellar object (YSO), namely our Sun. Much of our knowledge about the astrophysical context of the birth of the Sun, the chronology of planetary growth from micrometer-sized dust to terrestrial planets, and the activity of the young Sun comes from the study of extinct radionuclides such as 26Al (t1/2 = 0.717 Myr). Here we review how the signatures of extinct radionuclides (short-lived isotopes that were present when the solar system formed and that have now decayed below detection level) in planetary materials influence the current paradigm of solar system formation. Particular attention is given to tying meteorite measurements to remote astronomical observations of YSOs and modeling efforts. Some extinct radionuclides were inherited from the long-term chemical evolution of the Galaxy, others were injected into the solar system by a nearby supernova, and some were produced by particle irradiation from the T-Tauri Sun. The chronology inferred from extinct radionuclides reveals that dust agglomeration to form centimeter-sized particles in the inner part of the disk was very rapid (<50 kyr), planetesimal formation started early and spanned several million years, planetary embryos (possibly like Mars) were formed in a few million years, and terrestrial planets (like Earth) completed their growths several tens of million years after the birth of the Sun.Comment: 49 pages, 9 figures, 1 table. Uncorrected preprin

POSTNATAL BRAIN DYSMORPHOLOGY INDUCED BY PRENATAL ALCOHOL EXPOSURE: A PRECLINICAL MRI STUDY

poster abstractBrain dysmorphology is one of the most critical features of Fetal Alcohol Spectrum Disorders (FASD). This study was designed to use high resolution preclinical MRI system to compare the brain structures between alcohol exposed C57BL/6 mice with control. The objective is to examine how alcohol affects a dose- and timing-dependent brain dysmorphology during development comparable to that of human FASD. Three treated groups, ALC (pre- and pregnancy alcohol with 4.2 % (v/v) alcohol liquid), PF (pre alcohol and a calorically matched liquid pregnancy diet), and CHOW (ad lib chow/water), were examined. Mouse heads were imaged using 9.4T preclinical MRI system with 3D gradient echo (GRE) sequence to acquire volumetric images with voxel size as low as 40 microns. Whole brain, olfactory bulbs, cortex, hypothalamus, and cerebellum were segmented and the volumes were calculated. Data was examined by ANOVA followed with paired comparison between treatment groups to test the effect of prenatal alcohol exposure. ALC group had shown consistently smaller mean volumes of difference brain regions than the other two groups. Volume of total brain, olfactory bulbs and cerebellum were observed to be significantly different for ALC compared to PF pups. This indicated that prenatal alcohol exposure caused retarded fetal brain development. Comparing PF with CHOW pups, only cerebellum volume was observed to be significantly different. For cortex volume, no significant difference was shown for any pairwise comparison. These results suggest that alcohol effect contribute to brain dysmorphology, and match with our previous craniofacial dysmorphology study. This could be important to assist in the understanding of clinical variants of human FASD patients in brain dysmorphology

Formation of Kuiper Belt Binaries

It appears that at least several percent of large Kuiper belt objects are members of wide binaries. Physical collisions are too infrequent to account for their formation. Collisionless gravitational interactions are more promising. These provide two channels for binary formation. In each, the initial step is the formation of a transient binary when two large bodies penetrate each other's Hill spheres. Stabilization of a transient binary requires that it lose energy. Either dynamical friction due to small bodies or the scattering of a third large body can be responsible. Our estimates favor the former, albeit by a small margin. We predict that most objects of size comparable to those currently observed in the Kuiper belt are members of multiple systems. More specifically, we derive the probability that a large body is a member of a binary with semi-major axis of order a. The probability depends upon sigma, the total surface density, Sigma, the surface density of large bodies having radius R, and theta=10^-4, the angle subtended by the solar radius as seen from the Kuiper belt. For (sigma/Sigma)R<a< R/theta, the probability is just (Sigma/rho R)theta^-2, the optical depth of the large bodies divided by the solid angle subtended by the Sun. For R<a<r_u=(sigma/Sigma)R, it varies inversely with semimajor axis and reaches (sigma/rho R)theta^-2 at a=R. Based on current surveys of the Kuiper belt, we estimate Sigma/rho=3 10^-4cm and R=100km. We obtain sigma/rho=0.3cm by extrapolating the surface density deduced for the minimum mass solar nebula. Rough predictions are: outside of the critical separation r_u/a_odot=3'', the binary probability is 0.3%; at separations of 0.2'', comparable to current resolving capabilities, it reaches 5%, in agreement with results from the HST binary survey by Brown

Sibling comparisons elucidate the associations between educational attainment polygenic scores and alcohol, nicotine and cannabis.

Background and aimsThe associations between low educational attainment and substance use disorders (SUDs) may be related to a common genetic vulnerability. We aimed to elucidate the associations between polygenic scores for educational attainment and clinical criterion counts for three SUDs (alcohol, nicotine and cannabis).DesignPolygenic association and sibling comparison methods. The latter strengthens inferences in observational research by controlling for confounding factors that differ between families.SettingSix sites in the United States.ParticipantsEuropean ancestry participants aged 25 years and older from the Collaborative Study on the Genetics of Alcoholism (COGA). Polygenic association analyses included 5582 (54% female) participants. Sibling comparisons included 3098 (52% female) participants from 1226 sibling groups nested within the overall sample.MeasurementsOutcomes included criterion counts for DSM-5 alcohol use disorder (AUDSX), Fagerström nicotine dependence (NDSX) and DSM-5 cannabis use disorder (CUDSX). We derived polygenic scores for educational attainment (EduYears-GPS) using summary statistics from a large (&gt; 1 million) genome-wide association study of educational attainment.FindingsIn polygenic association analyses, higher EduYears-GPS predicted lower AUDSX, NDSX and CUDSX [P &lt; 0.01, effect sizes (R2 ) ranging from 0.30 to 1.84%]. These effects were robust in sibling comparisons, where sibling differences in EduYears-GPS predicted all three SUDs (P &lt; 0.05, R2 0.13-0.20%).ConclusionsIndividuals who carry more alleles associated with educational attainment tend to meet fewer clinical criteria for alcohol, nicotine and cannabis use disorders, and these effects are robust to rigorous controls for potentially confounding factors that differ between families (e.g. socio-economic status, urban-rural residency and parental education)

On the Migration of Jupiter and Saturn: Constraints from Linear Models of Secular Resonant Coupling with the Terrestrial Planets

We examine how the late divergent migration of Jupiter and Saturn may have perturbed the terrestrial planets. We identify six secular resonances between the nu_5 apsidal eigenfrequency of Jupiter and Saturn and the four eigenfrequencies of the terrestrial planets (g_{1-4}). We derive analytic upper limits on the eccentricity and orbital migration timescale of Jupiter and Saturn when these resonances were encountered to avoid perturbing the eccentricities of the terrestrial planets to values larger than the observed ones. If Jupiter and Saturn migrated with eccentricities comparable to their present day values, smooth migration with exponential timescales characteristic of planetesimal-driven migration (\tau~5-10 Myr) would have perturbed the eccentricities of the terrestrial planets to values greatly exceeding the observed ones. This excitation may be mitigated if the eccentricity of Jupiter was small during the migration epoch, migration was very rapid (e.g. \tau<~ 0.5 Myr perhaps via planet-planet scattering or instability-driven migration) or the observed small eccentricity amplitudes of the j=2,3 terrestrial modes result from low probability cancellation of several large amplitude contributions. Further, results of orbital integrations show that very short migration timescales (\tau<0.5 Myr), characteristic of instability-driven migration, may also perturb the terrestrial planets' eccentricities by amounts comparable to their observed values. We discuss the implications of these constraints for the relative timing of terrestrial planet formation, giant planet migration, and the origin of the so-called Late Heavy Bombardment of the Moon 3.9+/-0.1 Ga ago. We suggest that the simplest way to satisfy these dynamical constraints may be for the bulk of any giant planet migration to be complete in the first 30-100 Myr of solar system history.Comment: Accepted for publication in The Astrophysical Journa

Genetic correlates of the development of theta event related oscillations in adolescents and young adults

The developmental trajectories of theta band (4–7 Hz) event-related oscillations (EROs), a key neurophysiological constituent of the P3 response, were assessed in 2170 adolescents and young adults ages 12 to 25. The theta EROs occurring in the P3 response, important indicators of neurocognitive function, were elicited during the evaluation of task-relevant target stimuli in visual and auditory oddball tasks. Associations between the theta EROs and genotypic variants of 4 KCNJ6 single nucleotide polymorphisms (SNPs) were found to vary with age, sex, scalp location, and task modality. Three of the four KCNJ6 SNPs studied here were found to be significantly associated with the same theta EROs in adults in a previous family genome wide association study. Since measures of the P3 response have been found to be a useful endophenotypes for the study of a number of clinical and behavioral disorders, studies of genetic effects on its development in adolescents and young adults may illuminate neurophysiological factors contributing to the onset of these conditions