TY - JOUR AB - We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds. AU - Dello Schiavo, Lorenzo AU - Suzuki, Kohei ID - 10588 JF - Mathematische Annalen KW - quasi curvature-dimension condition KW - sub-riemannian geometry KW - Sobolev-to-Lipschitz property KW - Varadhan short-time asymptotics SN - 0025-5831 TI - Sobolev-to-Lipschitz property on QCD- spaces and applications VL - 384 ER - TY - JOUR AB - We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities, while at the same time ensuring thermodynamic consistency. A key difficulty of the non-isothermal case lies in the intrinsic presence of cross-diffusion type phenomena like the Soret and the Dufour effect: due to the temperature/energy dependence of the thermodynamic equilibria, a nonvanishing temperature gradient may drive a concentration flux even in a situation with constant concentrations; likewise, a nonvanishing concentration gradient may drive a heat flux even in a case of spatially constant temperature. We use time discretisation and regularisation techniques and derive a priori estimates based on a suitable entropy and the associated entropy production. Renormalised solutions are used in cases where non-integrable diffusion fluxes or reaction terms appear. AU - Fischer, Julian L AU - Hopf, Katharina AU - Kniely, Michael AU - Mielke, Alexander ID - 10547 IS - 1 JF - SIAM Journal on Mathematical Analysis KW - Energy-Reaction-Diffusion Systems KW - Cross Diffusion KW - Global-In-Time Existence of Weak/Renormalised Solutions KW - Entropy Method KW - Onsager System KW - Soret/Dufour Effect SN - 0036-1410 TI - Global existence analysis of energy-reaction-diffusion systems VL - 54 ER - TY - JOUR AB - We study the temporal dissipation of variance and relative entropy for ergodic Markov Chains in continuous time, and compute explicitly the corresponding dissipation rates. These are identified, as is well known, in the case of the variance in terms of an appropriate Hilbertian norm; and in the case of the relative entropy, in terms of a Dirichlet form which morphs into a version of the familiar Fisher information under conditions of detailed balance. Here we obtain trajectorial versions of these results, valid along almost every path of the random motion and most transparent in the backwards direction of time. Martingale arguments and time reversal play crucial roles, as in the recent work of Karatzas, Schachermayer and Tschiderer for conservative diffusions. Extensions are developed to general “convex divergences” and to countable state-spaces. The steepest descent and gradient flow properties for the variance, the relative entropy, and appropriate generalizations, are studied along with their respective geometries under conditions of detailed balance, leading to a very direct proof for the HWI inequality of Otto and Villani in the present context. AU - Karatzas, Ioannis AU - Maas, Jan AU - Schachermayer, Walter ID - 10023 IS - 4 JF - Communications in Information and Systems KW - Markov Chain KW - relative entropy KW - time reversal KW - steepest descent KW - gradient flow SN - 1526-7555 TI - Trajectorial dissipation and gradient flow for the relative entropy in Markov chains VL - 21 ER - TY - CONF AB - We argue that the time is ripe to investigate differential monitoring, in which the specification of a program's behavior is implicitly given by a second program implementing the same informal specification. Similar ideas have been proposed before, and are currently implemented in restricted form for testing and specialized run-time analyses, aspects of which we combine. We discuss the challenges of implementing differential monitoring as a general-purpose, black-box run-time monitoring framework, and present promising results of a preliminary implementation, showing low monitoring overheads for diverse programs. AU - Mühlböck, Fabian AU - Henzinger, Thomas A ID - 10108 KW - run-time verification KW - software engineering KW - implicit specification SN - 0302-9743 T2 - International Conference on Runtime Verification TI - Differential monitoring VL - 12974 ER - TY - GEN AB - We argue that the time is ripe to investigate differential monitoring, in which the specification of a program's behavior is implicitly given by a second program implementing the same informal specification. Similar ideas have been proposed before, and are currently implemented in restricted form for testing and specialized run-time analyses, aspects of which we combine. We discuss the challenges of implementing differential monitoring as a general-purpose, black-box run-time monitoring framework, and present promising results of a preliminary implementation, showing low monitoring overheads for diverse programs. AU - Mühlböck, Fabian AU - Henzinger, Thomas A ID - 9946 KW - run-time verification KW - software engineering KW - implicit specification SN - 2664-1690 TI - Differential monitoring ER - TY - JOUR AB - Neuronal responses to complex stimuli and tasks can encompass a wide range of time scales. Understanding these responses requires measures that characterize how the information on these response patterns are represented across multiple temporal resolutions. In this paper we propose a metric – which we call multiscale relevance (MSR) – to capture the dynamical variability of the activity of single neurons across different time scales. The MSR is a non-parametric, fully featureless indicator in that it uses only the time stamps of the firing activity without resorting to any a priori covariate or invoking any specific structure in the tuning curve for neural activity. When applied to neural data from the mEC and from the ADn and PoS regions of freely-behaving rodents, we found that neurons having low MSR tend to have low mutual information and low firing sparsity across the correlates that are believed to be encoded by the region of the brain where the recordings were made. In addition, neurons with high MSR contain significant information on spatial navigation and allow to decode spatial position or head direction as efficiently as those neurons whose firing activity has high mutual information with the covariate to be decoded and significantly better than the set of neurons with high local variations in their interspike intervals. Given these results, we propose that the MSR can be used as a measure to rank and select neurons for their information content without the need to appeal to any a priori covariate. AU - Cubero, Ryan J AU - Marsili, Matteo AU - Roudi, Yasser ID - 7369 JF - Journal of Computational Neuroscience KW - Time series analysis KW - Multiple time scale analysis KW - Spike train data KW - Information theory KW - Bayesian decoding SN - 0929-5313 TI - Multiscale relevance and informative encoding in neuronal spike trains VL - 48 ER - TY - THES AB - Single cells are constantly interacting with their environment and each other, more importantly, the accurate perception of environmental cues is crucial for growth, survival, and reproduction. This communication between cells and their environment can be formalized in mathematical terms and be quantified as the information flow between them, as prescribed by information theory. The recent availability of real–time dynamical patterns of signaling molecules in single cells has allowed us to identify encoding about the identity of the environment in the time–series. However, efficient estimation of the information transmitted by these signals has been a data–analysis challenge due to the high dimensionality of the trajectories and the limited number of samples. In the first part of this thesis, we develop and evaluate decoding–based estimation methods to lower bound the mutual information and derive model–based precise information estimates for biological reaction networks governed by the chemical master equation. This is followed by applying the decoding-based methods to study the intracellular representation of extracellular changes in budding yeast, by observing the transient dynamics of nuclear translocation of 10 transcription factors in response to 3 stress conditions. Additionally, we apply these estimators to previously published data on ERK and Ca2+ signaling and yeast stress response. We argue that this single cell decoding-based measure of information provides an unbiased, quantitative and interpretable measure for the fidelity of biological signaling processes. Finally, in the last section, we deal with gene regulation which is primarily controlled by transcription factors (TFs) that bind to the DNA to activate gene expression. The possibility that non-cognate TFs activate transcription diminishes the accuracy of regulation with potentially disastrous effects for the cell. This ’crosstalk’ acts as a previously unexplored source of noise in biochemical networks and puts a strong constraint on their performance. To mitigate erroneous initiation we propose an out of equilibrium scheme that implements kinetic proofreading. We show that such architectures are favored over their equilibrium counterparts for complex organisms despite introducing noise in gene expression. AU - Cepeda Humerez, Sarah A ID - 6473 KW - Information estimation KW - Time-series KW - data analysis SN - 2663-337X TI - Estimating information flow in single cells ER - TY - CONF AB - In this paper we consider the online ftp problem. The goal is to service a sequence of file transfer requests given bandwidth constraints of the underlying communication network. The main result of the paper is a technique that leads to algorithms that optimize several natural metrics, such as max-stretch, total flow time, max flow time, and total completion time. In particular, we show how to achieve optimum total flow time and optimum max-stretch if we increase the capacity of the underlying network by a logarithmic factor. We show that the resource augmentation is necessary by proving polynomial lower bounds on the max-stretch and total flow time for the case where online and offline algorithms are using same-capacity edges. Moreover, we also give polylogarithmic lower bounds on the resource augmentation factor necessary in order to keep the total flow time and max-stretch within a constant factor of optimum. AU - Goel, Ashish AU - Henzinger, Monika H AU - Plotkin, Serge AU - Tardos, Eva ID - 11691 KW - Scheduling KW - Flow time SN - 0196-6774 T2 - Proceedings of the 31st annual ACM symposium on Theory of computing TI - Scheduling data transfers in a network and the set scheduling problem ER - TY - CHAP AB - We introduce a temporal logic for the specification of real-time systems. Our logic, TPTL, employs a novel quantifier construct for referencing time: the "freeze" quantifier binds a variable to the time of the local temporal context. TPTL is both a natural language for specification and a suitable formalism for verification. We present a tableau-based decision procedure and a model-checking algorithm for TPTL. Several generalizations of TPTL are shown to be highly undecidable. AU - Alur, Rajeev AU - Henzinger, Thomas A ED - Rus, Teodor ED - Rattray, Charles ID - 4590 KW - real-time systems KW - clock variables SN - 9789810219239 T2 - Theories and Experiences for Real-Time System Development TI - Real-time system = discrete system + clock variables VL - 2 ER -