Effects of Coulomb Friction on the Performance of a Servomechanism Having Backlash. Part II—Transient Response Considerations

The paper gives results of analysis of the effects of coulomb friction on the transient response of a servo system containing backlash in the output coupling. First, the qualitative aspects of the transient response Characteristics are discussed with the help of frequency response methods; next, a quantitative discussion of the same is provided with the help of a piece-wise linear solution of the characteristic differential equations. Simulator results in support of the theoretical observations are also give

Detection of trend changes in time series using Bayesian inference

Change points in time series are perceived as isolated singularities where two regular trends of a given signal do not match. The detection of such transitions is of fundamental interest for the understanding of the system's internal dynamics. In practice observational noise makes it difficult to detect such change points in time series. In this work we elaborate a Bayesian method to estimate the location of the singularities and to produce some confidence intervals. We validate the ability and sensitivity of our inference method by estimating change points of synthetic data sets. As an application we use our algorithm to analyze the annual flow volume of the Nile River at Aswan from 1871 to 1970, where we confirm a well-established significant transition point within the time series.Comment: 9 pages, 12 figures, submitte

Interest Rates and Information Geometry

The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a Riemannian structure induced by the embedding of the family into the Hilbert space of square-integrable functions, and is characterised by the Fisher-Rao metric. In the nonparametric case the relevant geometry is determined by the spherical distance function of Bhattacharyya. In the context of term structure modelling, we show that minus the derivative of the discount function with respect to the maturity date gives rise to a probability density. This follows as a consequence of the positivity of interest rates. Therefore, by mapping the density functions associated with a given family of term structures to Hilbert space, the resulting metrical geometry can be used to analyse the relationship of yield curves to one another. We show that the general arbitrage-free yield curve dynamics can be represented as a process taking values in the convex space of smooth density functions on the positive real line. It follows that the theory of interest rate dynamics can be represented by a class of processes in Hilbert space. We also derive the dynamics for the central moments associated with the distribution determined by the yield curve.Comment: 20 pages, 3 figure

Statistical mechanics of transcription-factor binding site discovery using Hidden Markov Models

Hidden Markov Models (HMMs) are a commonly used tool for inference of transcription factor (TF) binding sites from DNA sequence data. We exploit the mathematical equivalence between HMMs for TF binding and the "inverse" statistical mechanics of hard rods in a one-dimensional disordered potential to investigate learning in HMMs. We derive analytic expressions for the Fisher information, a commonly employed measure of confidence in learned parameters, in the biologically relevant limit where the density of binding sites is low. We then use techniques from statistical mechanics to derive a scaling principle relating the specificity (binding energy) of a TF to the minimum amount of training data necessary to learn it.Comment: 25 pages, 2 figures, 1 table V2 - typos fixed and new references adde

A New Approach to Time Domain Classification of Broadband Noise in Gravitational Wave Data

Broadband noise in gravitational wave (GW) detectors, also known as triggers, can often be a deterrant to the efficiency with which astrophysical search pipelines detect sources. It is important to understand their instrumental or environmental origin so that they could be eliminated or accounted for in the data. Since the number of triggers is large, data mining approaches such as clustering and classification are useful tools for this task. Classification of triggers based on a handful of discrete properties has been done in the past. A rich information content is available in the waveform or 'shape' of the triggers that has had a rather restricted exploration so far. This paper presents a new way to classify triggers deriving information from both trigger waveforms as well as their discrete physical properties using a sequential combination of the Longest Common Sub-Sequence (LCSS) and LCSS coupled with Fast Time Series Evaluation (FTSE) for waveform classification and the multidimensional hierarchical classification (MHC) analysis for the grouping based on physical properties. A generalized k-means algorithm is used with the LCSS (and LCSS+FTSE) for clustering the triggers using a validity measure to determine the correct number of clusters in absence of any prior knowledge. The results have been demonstrated by simulations and by application to a segment of real LIGO data from the sixth science run.Comment: 16 pages, 16 figure

A distinct peak-flux distribution of the third class of gamma-ray bursts: A possible signature of X-ray flashes?

Gamma-ray bursts are the most luminous events in the Universe. Going beyond the short-long classification scheme we work in the context of three burst populations with the third group of intermediate duration and softest spectrum. We are looking for physical properties which discriminate the intermediate duration bursts from the other two classes. We use maximum likelihood fits to establish group memberships in the duration-hardness plane. To confirm these results we also use k-means and hierarchical clustering. We use Monte-Carlo simulations to test the significance of the existence of the intermediate group and we find it with 99.8% probability. The intermediate duration population has a significantly lower peak-flux (with 99.94% significance). Also, long bursts with measured redshift have higher peak-fluxes (with 98.6% significance) than long bursts without measured redshifts. As the third group is the softest, we argue that we have {related} them with X-ray flashes among the gamma-ray bursts. We give a new, probabilistic definition for this class of events.Comment: accepted for publication in Ap

On finite pp-groups whose automorphisms are all central

An automorphism $\alpha$ of a group $G$ is said to be central if $\alpha$ commutes with every inner automorphism of $G$. We construct a family of non-special finite $p$-groups having abelian automorphism groups. These groups provide counter examples to a conjecture of A. Mahalanobis [Israel J. Math., {\bf 165} (2008), 161 - 187]. We also construct a family of finite $p$-groups having non-abelian automorphism groups and all automorphisms central. This solves a problem of I. Malinowska [Advances in group theory, Aracne Editrice, Rome 2002, 111-127].Comment: 11 pages, Counter examples to a conjecture from [Israel J. Math., {\bf 165} (2008), 161 - 187]; This paper will appear in Israel J. Math. in 201

Temperature effects on zoeal morphometric traits and intraspecific variability in the hairy crab Cancer setosus across latitude

International audiencePhenotypic plasticity is an important but often ignored ability that enables organisms, within species-specific physiological limits, to respond to gradual or sudden extrinsic changes in their environment. In the marine realm, the early ontogeny of decapod crustaceans is among the best known examples to demonstrate a temperature-dependent phenotypic response. Here, we present morphometric results of larvae of the hairy crab , the embryonic development of which took place at different temperatures at two different sites (Antofagasta, 23°45′ S; Puerto Montt, 41°44′ S) along the Chilean Coast. Zoea I larvae from Puerto Montt were significantly larger than those from Antofagasta, when considering embryonic development at the same temperature. Larvae from Puerto Montt reared at 12 and 16°C did not differ morphometrically, but sizes of larvae from Antofagasta kept at 16 and 20°C did, being larger at the colder temperature. Zoea II larvae reared in Antofagasta at three temperatures (16, 20, and 24°C) showed the same pattern, with larger larvae at colder temperatures. Furthermore, larvae reared at 24°C, showed deformations, suggesting that 24°C, which coincides with temperatures found during strong EL Niño events, is indicative of the upper larval thermal tolerance limit.   is exposed to a wide temperature range across its distribution range of about 40° of latitude. Phenotypic plasticity in larval offspring does furthermore enable this species to locally respond to the inter-decadal warming induced by El Niño. Morphological plasticity in this species does support previously reported energetic trade-offs with temperature throughout early ontogeny of this species, indicating that plasticity may be a key to a species' success to occupy a wide distribution range and/or to thrive under highly variable habitat conditions