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Liquid simulation with mesh-based surface tracking
Get PDFAnimating detailed liquid surfaces has always been a challenge for computer graphics researchers and visual effects artists. Over the past few years, researchers in this field have focused on mesh-based surface tracking to synthesize extremely detailed liquid surfaces as efficiently as possible. This course provides a solid understanding of the steps required to create a fluid simulator with a mesh-based liquid surface.
The course begins with an overview of several existing liquid-surface-tracking techniques and the pros and cons of each method. Then it explains how to embed a triangle mesh into a finite-difference-based fluid simulator and describes several methods for allowing the liquid surface to merge together or break apart. The final section showcases the benefits and further applications of a mesh-based liquid surface, highlighting state-of-the-art methods for tracking colors and textures, maintaining liquid volume, preserving small surface features, and simulating realistic surface-tension waves
Modern ionotropic glutamate receptor with a K+ selectivity signature sequence
Get PDFGlutamate is the major excitatory neurotransmitter in the mammalian central nervous system and gates non-selective cation channels. The origins of glutamate receptors are not well understood as they differ structurally and functionally from simple bacterial ligand-gated ion channels. Here we report the discovery of an ionotropic glutamate receptor that combines the typical eukaryotic domain architecture with the 'TXVGYG' signature sequence of the selectivity filter found in K+ channels. This receptor exhibits functional properties intermediate between bacterial and eukaryotic glutamate-gated ion channels, suggesting a link in the evolution of ionotropic glutamate receptors
Temporal specifications with accumulative values
Get PDFThere is recently a significant effort to add quantita- tive objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications.
In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire computation.
We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation asser- tions may be refined with “controlled-accumulation”, allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable
Diffusion runs low on persistence fast
No full textInterpreting an image as a function on a compact sub- set of the Euclidean plane, we get its scale-space by diffu- sion, spreading the image over the entire plane. This gener- ates a 1-parameter family of functions alternatively defined as convolutions with a progressively wider Gaussian ker- nel. We prove that the corresponding 1-parameter family of persistence diagrams have norms that go rapidly to zero as time goes to infinity. This result rationalizes experimental observations about scale-space. We hope this will lead to targeted improvements of related computer vision methods
Approximation of event probabilities in noisy cellular processes
Get PDFMolecular noise, which arises from the randomness of the discrete events in the cell, significantly influences fundamental biological processes. Dis- crete-state continuous-time stochastic models (CTMC) can be used to describe such effects, but the calculation of the probabilities of certain events is computa- tionally expensive.
We present a comparison of two analysis approaches for CTMC. On one hand, we estimate the probabilities of interest using repeated Gillespie simulation and determine the statistical accuracy that we obtain. On the other hand, we apply a numerical reachability analysis that approximates the probability distributions of the system at several time instances. We use examples of cellular processes to demonstrate the superiority of the reachability analysis if accurate results are required
Reconstructing eight decades of genetic variation in an isolated Danish population of the large blue butterfly Maculinea arion
No full textBackground
Fragmentation of terrestrial ecosystems has had detrimental effects on metapopulations of habitat specialists. Maculinea butterflies have been particularly affected because of their specialized lifecycles, requiring both specific food-plants and host-ants. However, the interaction between dispersal, effective population size, and long-term genetic erosion of these endangered butterflies remains unknown. Using non-destructive sampling, we investigated the genetic diversity of the last extant population of M. arion in Denmark, which experienced critically low numbers in the 1980s.
Results
Using nine microsatellite markers, we show that the population is genetically impoverished compared to nearby populations in Sweden, but less so than monitoring programs suggested. Ten additional short repeat microsatellites were used to reconstruct changes in genetic diversity and population structure over the last 77 years from museum specimens. We also tested amplification efficiency in such historical samples as a function of repeat length and sample age. Low population numbers in the 1980s did not affect genetic diversity, but considerable turnover of alleles has characterized this population throughout the time-span of our analysis.
Conclusions
Our results suggest that M. arion is less sensitive to genetic erosion via population bottlenecks than previously thought, and that managing clusters of high quality habitat may be key for long-term conservation
Covering and packing with spheres by diagonal distortion in R^n
No full textWe address the problem of covering ℝ n with congruent balls, while minimizing the number of balls that contain an average point. Considering the 1-parameter family of lattices defined by stretching or compressing the integer grid in diagonal direction, we give a closed formula for the covering density that depends on the distortion parameter. We observe that our family contains the thinnest lattice coverings in dimensions 2 to 5. We also consider the problem of packing congruent balls in ℝ n , for which we give a closed formula for the packing density as well. Again we observe that our family contains optimal configurations, this time densest packings in dimensions 2 and 3
Energy and mean-payoff parity Markov decision processes
Get PDFWe consider Markov Decision Processes (MDPs) with mean-payoff parity and energy parity objectives. In system design, the parity objective is used to encode ω-regular specifications, and the mean-payoff and energy objectives can be used to model quantitative resource constraints. The energy condition re- quires that the resource level never drops below 0, and the mean-payoff condi- tion requires that the limit-average value of the resource consumption is within a threshold. While these two (energy and mean-payoff) classical conditions are equivalent for two-player games, we show that they differ for MDPs. We show that the problem of deciding whether a state is almost-sure winning (i.e., winning with probability 1) in energy parity MDPs is in NP ∩ coNP, while for mean- payoff parity MDPs, the problem is solvable in polynomial time, improving a recent PSPACE bound
Temporal specifications with accumulative values
Get PDFThere is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(ν) ≥ c and Avg(ν) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(ν) and Avg(ν) denote the accumulated sum and average of the values of ν from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimlnfAvg(ν) ≥ c and LimSupAvg(ν) ≥ c, referring to the average value along an entire computation. We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation assertions may be refined with "controlled-accumulation", allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modaliti- - es, and in particular CTL and LTL, makes the problem undecidable
Quantitative evaluation of BFT protocols
Get PDFByzantine Fault Tolerant (BFT) protocols aim to improve the reliability of distributed systems. They enable systems to tolerate arbitrary failures in a bounded number of nodes. BFT protocols are usually proven correct for certain safety and liveness properties. However, recent studies have shown that the performance of state-of-the-art BFT protocols decreases drastically in the presence of even a single malicious node. This motivates a formal quantitative analysis of BFT protocols to investigate their performance characteristics under different scenarios. We present HyPerf, a new hybrid methodology based on model checking and simulation techniques for evaluating the performance of BFT protocols. We build a transition system corresponding to a BFT protocol and systematically explore the set of behaviors allowed by the protocol. We associate certain timing information with different operations in the protocol, like cryptographic operations and message transmission. After an elaborate state exploration, we use the time information to evaluate the performance characteristics of the protocol using simulation techniques. We integrate our framework in Mace, a tool for building and verifying distributed systems. We evaluate the performance of PBFT using our framework. We describe two different use-cases of our methodology. For the benign operation of the protocol, we use the time information as random variables to compute the probability distribution of the execution times. In the presence of faults, we estimate the worst-case performance of the protocol for various attacks that can be employed by malicious nodes. Our results show the importance of hybrid techniques in systematically analyzing the performance of large-scale systems