On Recurrent Reachability for Continuous Linear Dynamical Systems

The continuous evolution of a wide variety of systems, including continuous-time Markov chains and linear hybrid automata, can be described in terms of linear differential equations. In this paper we study the decision problem of whether the solution $\boldsymbol{x}(t)$ of a system of linear differential equations $d\boldsymbol{x}/dt=A\boldsymbol{x}$ reaches a target halfspace infinitely often. This recurrent reachability problem can equivalently be formulated as the following Infinite Zeros Problem: does a real-valued function $f:\mathbb{R}_{\geq 0}\rightarrow\mathbb{R}$ satisfying a given linear differential equation have infinitely many zeros? Our main decidability result is that if the differential equation has order at most $7$, then the Infinite Zeros Problem is decidable. On the other hand, we show that a decision procedure for the Infinite Zeros Problem at order $9$ (and above) would entail a major breakthrough in Diophantine Approximation, specifically an algorithm for computing the Lagrange constants of arbitrary real algebraic numbers to arbitrary precision.Comment: Full version of paper at LICS'1

Cloud fragmentation and proplyd-like features in HII regions imaged by HST

We have analyzed HST ACS and WFPC2 new and archival images of eight HII regions to look for new proto-planetary disks (proplyds) similar to those found in the Orion Nebula. We find a wealth of features similar in size (though many are larger) to the bright cusps around the Orion Nebula proplyds. None of them, however, contains a definitive central star. From this, we deduce that the new cusps may not be proplyds, but instead are fragments of molecular cloud material. Out of all the features found in the eight HII regions examined, only one, an apparent edge-on silhouette in M17, may have a central star. This feature might join the small number of bona fide proplyds found outside the Orion Nebula, in M8, M20 and possibly in M16. In line with the results found recently by Smith et al. (2005), the paucity of proplyds outside the Orion Nebula, may be explained by their transient nature as well as by the specific environmental conditions under whichthey can be observed.Comment: 51 pages; 19 figures; 5 tables. Accepted by A

Weak and strong disjunction in possibilistic asp

Abstract. Possibilistic answer set programming (PASP) unites answer set programming (ASP) and possibilistic logic (PL) by associating certainty values with rules. The resulting framework allows to combine both non-monotonic reasoning and reasoning under uncertainty in a single framework. While PASP has been well-studied for possibilistic definite and possibilistic normal programs, we argue that the current semantics of possibilistic disjunctive programs are not entirely satisfactory. The problem is twofold. First, the treatment of negation-as-failure in existing approaches follows an all-or-nothing scheme that is hard to match with the graded notion of proof underlying PASP. Second, we advocate that the notion of disjunction can be interpreted in several ways. In particular, in addition to the view of ordinary ASP where disjunctions are used to induce a non-deterministic choice, the possibilistic setting naturally leads to a more epistemic view of disjunction. In this paper, we propose a semantics for possibilistic disjunctive programs, discussing both views on disjunction. Extending our earlier work, we interpret such programs as sets of constraints on possibility distributions, whose least specific solutions correspond to answer sets.

Holography, Unfolding and Higher-Spin Theory

Holographic duality is argued to relate classes of models that have equivalent unfolded formulation, hence exhibiting different space-time visualizations for the same theory. This general phenomenon is illustrated by the $AdS_4$ higher-spin gauge theory shown to be dual to the theory of 3d conformal currents of all spins interacting with 3d conformal higher-spin fields of Chern-Simons type. Generally, the resulting 3d boundary conformal theory is nonlinear, providing an interacting version of the 3d boundary sigma model conjectured by Klebanov and Polyakov to be dual to the $AdS_4$ HS theory in the large $N$ limit. Being a gauge theory it escapes the conditions of the theorem of Maldacena and Zhiboedov, which force a 3d boundary conformal theory to be free. Two reductions of particular higher-spin gauge theories where boundary higher-spin gauge fields decouple from the currents and which have free boundary duals are identified. Higher-spin holographic duality is also discussed for the cases of $AdS_3/CFT_2$ and duality between higher-spin theories and nonrelativistic quantum mechanics. In the latter case it is shown in particular that ($dS$) $AdS$ geometry in the higher-spin setup is dual to the (inverted) harmonic potential in the quantum-mechanical setup.Comment: 57 pages, V2: Acknowledgements, references, comments, clarifications and new section on reductions of particular HS theories associated with free boundary theories are added. Typos corrected, V3. Minor corrections: clarification in section 9 is added and typos correcte

Higher Spin Fields in Siegel Space, Currents and Theta Functions

Dynamics of four-dimensional massless fields of all spins is formulated in the Siegel space of complex $4\times 4$ symmetric matrices. It is shown that the unfolded equations of free massless fields, that have a form of multidimensional Schrodinger equations, naturally distinguish between positive- and negative-frequency solutions of relativistic field equations, i.e. particles and antiparticles. Multidimensional Riemann theta functions are shown to solve massless field equations in the Siegel space. We establish the correspondence between conserved higher-spin currents in four-dimensional Minkowski space and those in the ten-dimensional matrix space. It is shown that global symmetry parameters of the current in the matrix space should be singular to reproduce a nonzero current in Minkowski space. The \D-function integral evolution formulae for 4d massless fields in the Fock-Siegel space are obtained. The generalization of the proposed scheme to higher dimensions and systems of higher ranks is considered.Comment: LaTeX, 38 pages, v.3: clarifications, acknowledgements and references added, typos corrected, v.4: more comments and references added, typos corrected, the version to appear in JHE

Higher Spin Conformal Currents in Minkowski Space

Using unfolded formulation of free equations for massless fields of all spins we obtain explicit form of higher-spin conformal conserved charges bilinear in 4d massless fields of arbitrary spins.Comment: LaTeX, 10 pages. Corrected typo

The DLV System for Knowledge Representation and Reasoning

This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to $\Delta^P_3$-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of DLV, and by deriving new complexity results we chart a complete picture of the complexity of this language and important fragments thereof. Furthermore, we illustrate the general architecture of the DLV system which has been influenced by these results. As for applications, we overview application front-ends which have been developed on top of DLV to solve specific knowledge representation tasks, and we briefly describe the main international projects investigating the potential of the system for industrial exploitation. Finally, we report about thorough experimentation and benchmarking, which has been carried out to assess the efficiency of the system. The experimental results confirm the solidity of DLV and highlight its potential for emerging application areas like knowledge management and information integration.Comment: 56 pages, 9 figures, 6 table

The development of a specific pathogen free (SPF) barrier colony of marmosets (Callithrix jacchus) for aging research

A specific pathogen free (SPF) barrier colony of breeding marmosets (Callithrix jacchus) was established at the Barshop Institute for Longevity and Aging Studies. Rodent and other animal models maintained as SPF barrier colonies have demonstrated improved health and lengthened lifespans enhancing the quality and repeatability of aging research. The marmosets were screened for two viruses and several bacterial pathogens prior to establishing the new SPF colony. Twelve founding animals successfully established a breeding colony with increased reproductive success, improved health parameters, and increased median lifespan when compared to a conventionally housed, open colony. The improved health and longevity of marmosets from the SPF barrier colony suggests that such management can be used to produce a unique resource for future studies of aging processes in a nonhuman primate model

Differential expression analysis with global network adjustment

<p>Background: Large-scale chromosomal deletions or other non-specific perturbations of the transcriptome can alter the expression of hundreds or thousands of genes, and it is of biological interest to understand which genes are most profoundly affected. We present a method for predicting a gene’s expression as a function of other genes thereby accounting for the effect of transcriptional regulation that confounds the identification of genes differentially expressed relative to a regulatory network. The challenge in constructing such models is that the number of possible regulator transcripts within a global network is on the order of thousands, and the number of biological samples is typically on the order of 10. Nevertheless, there are large gene expression databases that can be used to construct networks that could be helpful in modeling transcriptional regulation in smaller experiments.</p> <p>Results: We demonstrate a type of penalized regression model that can be estimated from large gene expression databases, and then applied to smaller experiments. The ridge parameter is selected by minimizing the cross-validation error of the predictions in the independent out-sample. This tends to increase the model stability and leads to a much greater degree of parameter shrinkage, but the resulting biased estimation is mitigated by a second round of regression. Nevertheless, the proposed computationally efficient “over-shrinkage” method outperforms previously used LASSO-based techniques. In two independent datasets, we find that the median proportion of explained variability in expression is approximately 25%, and this results in a substantial increase in the signal-to-noise ratio allowing more powerful inferences on differential gene expression leading to biologically intuitive findings. We also show that a large proportion of gene dependencies are conditional on the biological state, which would be impossible with standard differential expression methods.</p> <p>Conclusions: By adjusting for the effects of the global network on individual genes, both the sensitivity and reliability of differential expression measures are greatly improved.</p&gt

Master Higher-Spin Particle

We propose a "master" higher-spin (HS) particle system. The particle model relevant to the unfolded formulation of HS theory, as well as the HS particle model with a bosonic counterpart of supersymmetry, follow from the master model as its two different gauges. Quantization of the master system gives rise to a new form of the massless HS equations in an extended space involving, besides extra spinorial coordinates, also a complex scalar one. As solutions to these equations we recover the massless HS multiplet with fields of all integer and half-integer helicities, and obtain new multiplets with a non-zero minimal helicity. The HS multiplets are described by complex wave functions which are holomorphic in the scalar coordinate and carry an extra U(1) charge q. The latter fully characterizes the given multiplet by fixing the minimal helicity as q/2. We construct a twistorial formulation of the master system and present the general solution of the associate HS equations through an unconstrained twistor "prepotential".Comment: 21 pages, minor corrections, version to appear in Class. Quantum Gra