Hitting Times and Probabilities for Imprecise Markov Chains

We consider the problem of characterising expected hitting times and hitting probabilities for imprecise Markov chains. To this end, we consider three distinct ways in which imprecise Markov chains have been defined in the literature: as sets of homogeneous Markov chains, as sets of more general stochastic processes, and as game-theoretic probability models. Our first contribution is that all these different types of imprecise Markov chains have the same lower and upper expected hitting times, and similarly the hitting probabilities are the same for these three types. Moreover, we provide a characterisation of these quantities that directly generalises a similar characterisation for precise, homogeneous Markov chains

Efficient computation of updated lower expectations for imprecise continuous-time hidden Markov chains

We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden state of the chain. The prefix `imprecise' refers to the fact that we do not consider a classical continuous-time Markov chain, but replace it with a robust extension that allows us to represent various types of model uncertainty, using the theory of imprecise probabilities. The inference problem amounts to computing lower expectations of functions on the state-space of the chain, given observations of the output variables. We develop and investigate this problem with very few assumptions on the output variables; in particular, they can be chosen to be either discrete or continuous random variables. Our main result is a polynomial runtime algorithm to compute the lower expectation of functions on the state-space at any given time-point, given a collection of observations of the output variables

Imprecise Continuous-Time Markov Chains

Continuous-time Markov chains are mathematical models that are used to describe the state-evolution of dynamical systems under stochastic uncertainty, and have found widespread applications in various fields. In order to make these models computationally tractable, they rely on a number of assumptions that may not be realistic for the domain of application; in particular, the ability to provide exact numerical parameter assessments, and the applicability of time-homogeneity and the eponymous Markov property. In this work, we extend these models to imprecise continuous-time Markov chains (ICTMC's), which are a robust generalisation that relaxes these assumptions while remaining computationally tractable. More technically, an ICTMC is a set of "precise" continuous-time finite-state stochastic processes, and rather than computing expected values of functions, we seek to compute lower expectations, which are tight lower bounds on the expectations that correspond to such a set of "precise" models. Note that, in contrast to e.g. Bayesian methods, all the elements of such a set are treated on equal grounds; we do not consider a distribution over this set. The first part of this paper develops a formalism for describing continuous-time finite-state stochastic processes that does not require the aforementioned simplifying assumptions. Next, this formalism is used to characterise ICTMC's and to investigate their properties. The concept of lower expectation is then given an alternative operator-theoretic characterisation, by means of a lower transition operator, and the properties of this operator are investigated as well. Finally, we use this lower transition operator to derive tractable algorithms (with polynomial runtime complexity w.r.t. the maximum numerical error) for computing the lower expectation of functions that depend on the state at any finite number of time points

Hitting times and probabilities for imprecise Markov chains

We consider the problem of characterising expected hitting times and hitting probabilities for imprecise Markov chains. To this end, we consider three distinct ways in which imprecise Markov chains have been defined in the literature: as sets of homogeneous Markov chains, as sets of more general stochastic processes, and as game-theoretic probability models. Our first contribution is that all these different types of imprecise Markov chains have the same lower and upper expected hitting times, and similarly the hitting probabilities are the same for these three types. Moreover, we provide a characterisation of these quantities that directly generalises a similar characterisation for precise, homogeneous Markov chains

INVESTIGATING THE SALINITY TOLERANCE OF THE SWORDTAIL (Xiphophorus hellerii)

The swordtail, Xiphophorus hellerii, is a freshwater fish species native to Mexico and Central America and is commonly used in the tropical aquarium trade. Swordtails have been shown to have limited survival in 6 ‰ salinity (Nanda et al., 2016), suggesting they may have a greater salinity tolerance than previously expected. Using a gradual acclimation method, we examined the salinity tolerance and swim performance of this species. Freshwater-reared female swordtails were housed in 29-gallon aquaria. A control group was held in freshwater throughout the experiment. For the experimental group, the salinity was increased by 2 ‰ every week until 30 ‰. Critical swimming speed (Ucrit) was determined repeatedly for each individual fish (every second week) for both control and salinity acclimated (at 0, 4, 8, 12, 16, and 28 ‰) fish to assess the impact of increased salinity on swimming performance. The critical swimming speed was stable throughout the study for the control group. An initial increase in swim performance was seen at 4 ‰ salinity from the beginning of the experiment but then decreased to control levels by 8 ‰ and was not different from control rates for the remainder of the experiment. Gill Na+/K-—ATPase (NKA) activity was measured at the end of the experiment. There was a 64% increase in NKA activity for the experimental group over the control. Based on these results, swordtails can tolerate much higher salinity than originally thought, with minimal impact on their swimming performance and are able to increase their NKA activity to adapt to the higher salinity environment

Intra-individual polymorphism in diploid and apomictic polyploid hawkweeds (Hieracium, Lactuceae, Asteraceae): disentangling phylogenetic signal, reticulation, and noise

<p>Abstract</p> <p>Background</p> <p><it>Hieracium </it>s.str. is a complex species-rich group of perennial herbs composed of few sexual diploids and numerous apomictic polyploids. The existence of reticulation and the near-continuity of morphological characters across taxa seriously affect species determination, making <it>Hieracium </it>one of the best examples of a 'botanist's nightmare'. Consequently, its species relationships have not previously been addressed by molecular methods. Concentrating on the supposed major evolutionary units, we used nuclear ribosomal (<it>ETS</it>) and chloroplast (<it>trnT</it>-<it>trnL</it>) sequences in order to disentangle the phylogenetic relationships and to infer the origins of the polyploids.</p> <p>Results</p> <p>Despite relatively low interspecific variation, the nuclear data revealed the existence of two major groups roughly corresponding to species with a Western or Eastern European origin. Extensive reticulation was mainly inferred from the character additivity of parental <it>ETS </it>variants. Surprisingly, many diploid species were of hybrid origin whilst several polyploid taxa showed no evidence of reticulation. Intra-individual <it>ETS </it>sequence polymorphism generally exceeded interspecific variation and was either independent of, or additional to, additive patterns accounted for by hybrid origin. Several <it>ETS </it>ribotypes occurred in different hybrid taxa, but never as the only variant in any species analyzed.</p> <p>Conclusion</p> <p>The high level of intra-individual <it>ETS </it>polymorphism prevented straightforward phylogenetic analysis. Characterization of this variation as additive, shared informative, homoplasious, or unique made it possible to uncover the phylogenetic signal and to reveal the hybrid origin of 29 out of 60 accessions. Contrary to expectation, diploid sexuals and polyploid apomicts did not differ in their molecular patterns. The basic division of the genus into two major clades had not previously been intimated on morphological grounds. Both major groups are thought to have survived in different glacial refugia and to have hybridized as a result of secondary contact. Several lines of evidence suggest the data is best explained by the presence of an extinct range of variation and a larger diversity of ancestral diploids in former times rather than by unsampled variation. Extinct diversity and extensive reticulation are thought to have largely obscured the species relationships. Our study illustrates how multigene sequences can be used to disentangle the evolutionary history of agamic complexes or similarly difficult datasets.</p

СROSS-PLATFORMOWE NARZĘDZIA DO MODELOWANIA I ROZPOZNAWANIA ALFABETU PALCOWEGO JĘZYKA GESTÓW

A solution for the problems of the finger spelling alphabet of gesture language modelling and recognition based on cross-platform technologies is proposed. Modelling and recognition performance can be flexible and adjusted, based on the hardware it operates or based on the availability of an internet connection. The proposed approach tunes the complexity of the 3D hand model based on the CPU type, amount of available memory and internet connection speed. Sign recognition is also performed using cross-platform technologies and the tradeoff in model size and performance can be adjusted.&nbsp; the methods of convolutional neural networks are used as tools for gestures of alphabet recognition. For the gesture recognition experiment, a dataset of 50,000 images was collected, with 50 different hands recorded, with almost 1,000 images per each person. The experimental researches demonstrated the effectiveness of proposed approaches.Zaproponowano rozwiązanie problemów z alfabetem daktylograficznym w modelowaniu języka gestów i rozpoznawaniu znaków w oparciu o technologie wieloplatformowe. Wydajność modelowania i rozpoznawania może być elastyczna i dostosowana, w zależności od wykorzystywanego sprzętu lub dostępności łącza internetowego. Proponowane podejście dostosowuje złożoność modelu 3D dłoni w zależności od typu procesora, ilości dostępnej pamięci i szybkości połączenia internetowego. Rozpoznawanie znaków odbywa się również z wykorzystaniem technologii międzyplatformowych, a kompromis w zakresie wielkości modelu i wydajności może być dostosowany. Jako narzędzia do rozpoznawania gestów alfabetu wykorzystywane są metody konwolucyjnych sieci neuronowych. Na potrzeby eksperymentu rozpoznawania gestów zebrano zbiór danych obejmujący 50 000 obrazów, przy czym zarejestrowano 50 różnych rąk, a na każdą osobę przypadało prawie 1000 obrazów. Badania eksperymentalne wykazały skuteczność proponowanego podejścia

Knowledge-based bias correction : a case study in veterinary decision support

In collaboration with experts from veterinary research institutes throughout Europe, we developed a decision-support system for the early detection of Classical Swine Fever in pigs. For evaluating our system's diagnostic performance, practitioners and researchers collected data from the real-world field and from laboratory experiments. Originating from different sources, these data could not be viewed as constituting an unbiased sample from a single probability distribution. In this paper, we present a knowledge-based method for correcting the biases in estimates from such divergent data. We demonstrate the use of our method for estimating the sensitivity and specificity characteristics of our veterinary decision-support system