National University of Ireland, Maynooth

We present results based on full-mission Planck observations of temperature and polarization anisotropies of the CMB. These data are consistent with the six-parameter inflationary LCDM cosmology. From the Planck temperature and lensing data, for this cosmology we find a Hubble constant, H0= (67.8 +/- 0.9) km/s/Mpc, a matter density parameter Omega_m = 0.308 +/- 0.012 and a scalar spectral index with n_s = 0.968 +/- 0.006. (We quote 68% errors on measured parameters and 95% limits on other parameters.) Combined with Planck temperature and lensing data, Planck LFI polarization measurements lead to a reionization optical depth of tau = 0.066 +/- 0.016. Combining Planck with other astrophysical data we find N_ eff = 3.15 +/- 0.23 for the effective number of relativistic degrees of freedom and the sum of neutrino masses is constrained to < 0.23 eV. Spatial curvature is found to be |Omega_K| < 0.005. For LCDM we find a limit on the tensor-to-scalar ratio of r <0.11 consistent with the B-mode constraints from an analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP data leads to a tighter constraint of r < 0.09. We find no evidence for isocurvature perturbations or cosmic defects. The equation of state of dark energy is constrained to w = -1.006 +/- 0.045. Standard big bang nucleosynthesis predictions for the Planck LCDM cosmology are in excellent agreement with observations. We investigate annihilating dark matter and deviations from standard recombination, finding no evidence for new physics. The Planck results for base LCDM are in agreement with BAO data and with the JLA SNe sample. However the amplitude of the fluctuations is found to be higher than inferred from rich cluster counts and weak gravitational lensing. Apart from these tensions, the base LCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.

This paper presents the first cosmological results based on Planck measurements of the cosmic microwave background (CMB) temperature and lensing-potential power spectra. We find that the Planck spectra at high multipoles ( > 40) are extremely well described by the standard spatiallyflat six-parameter CDM cosmology with a power-law spectrum of adiabatic scalar perturbations. Within the context of this cosmology, the Planck data determine the cosmological parameters to high precision: the angular size of the sound horizon at recombination, the physical densities of baryons and cold dark matter, and the scalar spectral index are estimated to be * = (1.04147 0.00062) 10 -2 , b h 2 = 0.02205 0.00028, c h 2 = 0.1199 0.0027, and n s = 0.9603 0.0073, respectively (note that in this abstract we quote 68% errors on measured parameters and 95% upper limits on other parameters). For this cosmology, we find a low value of the Hubble constant, H 0 = (67.3 1.2) km s -1 Mpc -1 , and a high value of the matter density parameter, m = 0.315 0.017. These values are in tension with recent direct measurements of H 0 and the magnituderedshift relation for Type Ia supernovae, but are in excellent agreement with geometrical constraints from baryon acoustic oscillation (BAO) surveys. Including curvature, we find that the Universe is consistent with spatial flatness to percent level precision using Planck CMB data alone. We use high-resolution CMB data together with Planck to provide greater control on extragalactic foreground components in an investigation of extensions to the six-parameter CDM model. We present selected results from a large grid of cosmological models, using a range of additional astrophysical data sets in addition to Planck and high-resolution CMB data. None of these models are favoured over the standard six-parameter CDM cosmology. The deviation of the scalar spectral index from unity is insensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find an upper limit of r 0.002 < 0.11 on the tensor-to-scalar ratio. There is no evidence for additional neutrino-like relativistic particles beyond the three families of neutrinos in the standard model. Using BAO and CMB data, we find N eff = 3.30 0.27 for the effective number of relativistic degrees of freedom, and an upper limit of 0.23 eV for the sum of neutrino masses. Our results are in excellent agreement with big bang nucleosynthesis and the standard value of N eff = 3.046. We find no evidence for dynamical dark energy; using BAO and CMB data, the dark energy equation of state parameter is constrained to be w = -1.13 +0.13 -0.10 . We also use the Planck data to set limits on a possible variation of the fine-structure constant, dark matter annihilation and primordial magnetic fields. Despite the success of the six-parameter CDM model in describing the Planck data at high multipoles, we note that this cosmology does not provide a good fit to the temperature power spectrum at low multipoles. The unusual shape of the spectrum in the multipole range 20 < < 40 was seen previously in the WMAP data and is a real feature of the primordial CMB anisotropies. The poor fit to the spectrum at low multipoles is not of decisive significance, but is an "anomaly" in an otherwise self-consistent analysis of the Planck temperature data.

Abstract The monthly global 2° × 2° Extended Reconstructed Sea Surface Temperature (ERSST) has been revised and updated from version 4 to version 5. This update incorporates a new release of ICOADS release 3.0 (R3.0), a decade of near-surface data from Argo floats, and a new estimate of centennial sea ice from HadISST2. A number of choices in aspects of quality control, bias adjustment, and interpolation have been substantively revised. The resulting ERSST estimates have more realistic spatiotemporal variations, better representation of high-latitude SSTs, and ship SST biases are now calculated relative to more accurate buoy measurements, while the global long-term trend remains about the same. Progressive experiments have been undertaken to highlight the effects of each change in data source and analysis technique upon the final product. The reconstructed SST is systematically decreased by 0.077°C, as the reference data source is switched from ship SST in ERSSTv4 to modern buoy SST in ERSSTv5. Furthermore, high-latitude SSTs are decreased by 0.1°–0.2°C by using sea ice concentration from HadISST2 over HadISST1. Changes arising from remaining innovations are mostly important at small space and time scales, primarily having an impact where and when input observations are sparse. Cross validations and verifications with independent modern observations show that the updates incorporated in ERSSTv5 have improved the representation of spatial variability over the global oceans, the magnitude of El Niño and La Niña events, and the decadal nature of SST changes over 1930s–40s when observation instruments changed rapidly. Both long- (1900–2015) and short-term (2000–15) SST trends in ERSSTv5 remain significant as in ERSSTv4.

This article examines how the availability of Big Data, coupled with new data analytics, challenges established epistemologies across the sciences, social sciences and humanities, and assesses the extent to which they are engendering paradigm shifts across multiple disciplines. In particular, it critically explores new forms of empiricism that declare ‘the end of theory’, the creation of data-driven rather than knowledge-driven science, and the development of digital humanities and computational social sciences that propose radically different ways to make sense of culture, history, economy and society. It is argued that: (1) Big Data and new data analytics are disruptive innovations which are reconfiguring in many instances how research is conducted; and (2) there is an urgent need for wider critical reflection within the academy on the epistemological implications of the unfolding data revolution, a task that has barely begun to be tackled despite the rapid changes in research practices presently taking place. After critically reviewing emerging epistemological positions, it is contended that a potentially fruitful approach would be the development of a situated, reflexive and contextually nuanced epistemology.

urban populations. We begin by defining the state of the art, explaining the science of smart cities. We define six scenarios based on new cities badging themselves as smart, older cities regenerating themselves as smart, the development of science parks, tech cities, and technopoles focused on high technologies, the development of urban services using contemporary ICT, the use of ICT to develop new urban intelligence functions, and the development of online and mobile forms of participation. Seven project areas are then proposed: Integrated Databases for the Smart City, Sensing, Networking and the Impact of New Social Media, Modelling Network Performance, Mobility and Travel Behaviour, Modelling Urban Land Use, Transport and Economic Interactions, Modelling Urban Transactional Activities in Labour and Housing Markets, Decision Support as Urban Intelligence, Participatory Governance and Planning Structures for the Smart City. Finally we anticipate the paradigm shifts that will occur in this research and define a series of key demonstrators which we believe are important to progressing a science of smart cities.

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD) is a technique for calculating derivatives of numeric functions expressed as computer programs efficiently and accurately, used in fields such as computational fluid dynamics, nuclear engineering, and atmospheric sciences. Despite its advantages and use in other fields, machine learning practitioners have been little influenced by AD and make scant use of available tools. We survey the intersection of AD and machine learning, cover applications where AD has the potential to make a big impact, and report on some recent developments in the adoption of this technique. We aim to dispel some misconceptions that we contend have impeded the use of AD within the machine learning community.

Part I: The Basic Account. 1. Language and Cognition: Constructing an Alternative Approach Within the Behavioral Tradition S.C. Hayes, et al. 2. Derived Relational Responding as Learned Behavior S.C. Hayes, et al. 3. Multiple Stimulus Relations and the Transformation of Stimulus Functions D. Barnes-Holmes, et al. 4. Relations Among Relations: Analogies, Metaphors, and Stories I. Stewart, et al. 5. Thinking, Problem-Solving, and Pragmatic Verbal Analysis S.C. Hayes, et al. 6. Understanding and Verbal Regulation D. Barnes-Holmes, et al. 7. Self and Self-Directed Rules D. Barnes-Holmes, et al. 8. Relational Frame Theory: A Precis S.C. Hayes, et al. Part II: Extensions and Applications. 9. Psychological Development Y. Barnes-Holmes, et al. 10. Education Y. Barnes-Holmes, et al. 11. Social Processes B. Roche, et al. 12. Psychopathology and Psychotherapy K.G. Wilson, et al. 13. Religion, Spirituality, and Transcendence D. Barnes-Holmes, et al. Epilogue. References. Index.

Exit of cytochrome c from mitochondria into the cytosol has been implicated as an important step in apoptosis. In the cytosol, cytochrome c binds to the CED-4 homologue, Apaf-1, thereby triggering Apaf-1-mediated activation of caspase-9. Caspase-9 is thought to propagate the death signal by triggering other caspase activation events, the details of which remain obscure. Here, we report that six additional caspases (caspases-2, -3, -6, -7, -8, and -10) are processed in cell-free extracts in response to cytochrome c, and that three others (caspases-1, -4, and -5) failed to be activated under the same conditions. In vitro association assays confirmed that caspase-9 selectively bound to Apaf-1, whereas caspases-1, -2, -3, -6, -7, -8, and -10 did not. Depletion of caspase-9 from cell extracts abrogated cytochrome c-inducible activation of caspases-2, -3, -6, -7, -8, and -10, suggesting that caspase-9 is required for all of these downstream caspase activation events. Immunodepletion of caspases-3, -6, and -7 from cell extracts enabled us to order the sequence of caspase activation events downstream of caspase-9 and reveal the presence of a branched caspase cascade. Caspase-3 is required for the activation of four other caspases (-2, -6, -8, and -10) in this pathway and also participates in a feedback amplification loop involving caspase-9.

The European Space Agency's Planck satellite, dedicated to studying the early Universe and its subsequent evolution, was launched 14 May 2009 and has been scanning the microwave and submillimetre sky continuously since 12 August 2009. In March 2013, ESA and the Planck Collaboration released the initial cosmology products based on the first 15.5 months of Planck data, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the mission and its performance, the processing, analysis, and characteristics of the data, the scientific results, and the science data products and papers in the release. The science products include maps of the cosmic microwave background (CMB) and diffuse extragalactic foregrounds, a catalogue of compact Galactic and extragalactic sources, and a list of sources detected through the Sunyaev-Zeldovich effect. The likelihood code used to assess cosmological models against the Planck data and a lensing likelihood are described. Scientific results include robust support for the standard six-parameter ΛCDM model of cosmology and improved measurements of its parameters, including a highly significant deviation from scale invariance of the primordial power spectrum. The Planck values for these parameters and others derived from them are significantly different from those previously determined. Several large-scale anomalies in the temperature distribution of the CMB, first detected by WMAP, are confirmed with higher confidence. Planck sets new limits on the number and mass of neutrinos, and has measured gravitational lensing of CMB anisotropies at greater than 25σ. Planck finds no evidence for non-Gaussianity in the CMB. Planck's results agree well with results from the measurements of baryon acoustic oscillations. Planck finds a lower Hubble constant than found in some more local measures. Some tension is also present between the amplitude of matter fluctuations (σ8) derived from CMB data and that derived from Sunyaev-Zeldovich data. The Planck and WMAP power spectra are offset from each other by an average level of about 2% around the first acoustic peak. Analysis of Planck polarization data is not yet mature, therefore polarization results are not released, although the robust detection of E-mode polarization around CMB hot and cold spots is shown graphically. © 2014 ESO.

We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey, which includes more than twice the integration time of the nominal survey used for the 2013 release papers. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be n s = 0.968 0.006 and tightly constrain its scale dependence to dn s /dln k = -0.003 0.007 when combined with the Planck lensing likelihood. When the Planck high-polarization data are included, the results are consistent and uncertainties are further reduced. The upper bound on the tensor-to-scalar ratio is r 0.002 < 0.11 (95% CL). This upper limit is consistent with the B-mode polarization constraint r < 0.12 (95% CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data. These results imply that V() 2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R 2 inflation. We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis. Three independent methods reconstructing the primordial power spectrum consistently recover a featureless and smooth P R (k) over the range of scales 0.008 Mpc -1 < k < 0.1 Mpc -1 . At large scales, each method finds deviations from a power law, connected to a deficit at multipoles 20-40 in the temperature power spectrum, but at an uncompelling statistical significance owing to the large cosmic variance present at these multipoles. By combining power spectrum and non-Gaussianity bounds, we constrain models with generalized Lagrangians, including Galileon models and axion monodromy models. The Planck data are consistent with adiabatic primordial perturbations, and the estimated values for the parameters of the base cold dark matter (CDM) model are not significantly altered when more general initial conditions are admitted. In correlated mixed adiabatic and isocurvature models, the 95% CL upper bound for the non-adiabatic contribution to the observed CMB temperature variance is | non-adi | < 1.9%, 4.0%, and 2.9% for CDM, neutrino density, and neutrino velocity isocurvature modes, respectively. We have tested inflationary models producing an anisotropic modulation of the primordial curvature power spectrum finding that the dipolar modulation in the CMB temperature field induced by a CDM isocurvature perturbation is not preferred at a statistically significant level. We also establish tight constraints on a possible quadrupolar modulation of the curvature perturbation. These results are consistent with the Planck 2013 analysis based on the nominal mission data and further constrain slow-roll single-field inflationary models, as expected from the increased precision of Planck data using the full set of observations.

Abstract Identifying and understanding COVID-19 vaccine hesitancy within distinct populations may aid future public health messaging. Using nationally representative data from the general adult populations of Ireland ( N = 1041) and the United Kingdom (UK; N = 2025), we found that vaccine hesitancy/resistance was evident for 35% and 31% of these populations respectively. Vaccine hesitant/resistant respondents in Ireland and the UK differed on a number of sociodemographic and health-related variables but were similar across a broad array of psychological constructs. In both populations, those resistant to a COVID-19 vaccine were less likely to obtain information about the pandemic from traditional and authoritative sources and had similar levels of mistrust in these sources compared to vaccine accepting respondents. Given the geographical proximity and socio-economic similarity of the populations studied, it is not possible to generalize findings to other populations, however, the methodology employed here may be useful to those wishing to understand COVID-19 vaccine hesitancy elsewhere.

Diverse bilaterian clades emerged apparently within a few million years during the early Cambrian, and various environmental, developmental, and ecological causes have been proposed to explain this abrupt appearance. A compilation of the patterns of fossil and molecular diversification, comparative developmental data, and information on ecological feeding strategies indicate that the major animal clades diverged many tens of millions of years before their first appearance in the fossil record, demonstrating a macroevolutionary lag between the establishment of their developmental toolkits during the Cryogenian [(850 to 635 million years ago (Ma)], and the later ecological success of metazoans during the Ediacaran (635 to 541 Ma) and Cambrian (541 to 488 Ma) periods. We argue that this diversification involved new forms of developmental regulation, as well as innovations in networks of ecological interaction within the context of permissive environmental circumstances.

Fungal secondary metabolism has become an important research topic with great biomedical and biotechnological value. In the postgenomic era, understanding the diversity and the molecular control of secondary metabolites (SMs) are two challenging tasks addressed by the research community. Discovery of the LaeA methyltransferase 10 years ago opened up a new horizon on the control of SM research when it was found that expression of many SM gene clusters is controlled by LaeA. While the molecular function of LaeA remains an enigma, discovery of the velvet family proteins as interaction partners further extended the role of the LaeA beyond secondary metabolism. The heterotrimeric VelB-VeA-LaeA complex plays important roles in development, sporulation, secondary metabolism, and pathogenicity. Recently, three other methyltransferases have been found to associate with the velvet complex, the LaeA-like methyltransferase F and the methyltransferase heterodimers VipC-VapB. Interaction of VeA with at least four methyltransferase proteins indicates a molecular hub function for VeA that questions: Is there a VeA supercomplex or is VeA part of a highly dynamic cellular control network with many different partners?

We present the all-sky Planck catalogue of Sunyaev-Zeldovich (SZ) sources detected from the 29 month full-mission data. The catalogue (PSZ2) is the largest SZ-selected sample of galaxy clusters yet produced and the deepest systematic all-sky surveyof galaxy clusters. It contains 1653 detections, of which 1203 are confirmed clusters with identified counterparts in external data sets, and is the first SZ-selected cluster survey containing >103 confirmed clusters. We present a detailed analysis of the survey selection function in terms of its completeness and statistical reliability, placing a lower limit of 83% on the purity. Using simulations, we find that the estimates of the SZ strength parameter Y5R500are robust to pressure-profile variation and beam systematics, but accurate conversion to Y500 requires the use of prior information on the cluster extent. We describe the multi-wavelength search for counterparts in ancillary data, which makes use of radio, microwave, infra-red, optical, and X-ray data sets, and which places emphasis on the robustness of the counterpart match. We discuss the physical properties of the new sample and identify a population of low-redshift X-ray under-luminous clusters revealed by SZ selection. These objects appear in optical and SZ surveys with consistent properties for their mass, but are almost absent from ROSAT X-ray selected samples.

We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to be ns = 0.9603 ± 0.0073, ruling out exact scale invariance at over 5 s. Planck establishes an upper bound on the tensor-to-scalar ratio of r&lt; 0.11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V&gt;&lt; 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n = 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining dns/dlnk =-0.0134 ± 0.0090. We verify these conclusions through a numerical analysis, which makes no slow-roll approximation, and carry out a Bayesian parameter estimation and model-selection analysis for a number of inflationary models including monomial, natural, and hilltop potentials. For each model, we present the Planck constraints on the parameters of the potential and explore several possibilities for the post-inflationary entropy generation epoch, thus obtaining nontrivial data-driven constraints. We also present a direct reconstruction of the observable range of the inflaton potential. Unless a quartic term is allowed in the potential, we find results consistent with second-order slow-roll predictions. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit by 2eff 10 ; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with Planck bounds on fNL. Planck constrains with unprecedented accuracy the amplitude and possible correlation (with the adiabatic mode) of non-decaying isocurvature fluctuations. The fractional primordial contributions of cold dark matter (CDM) isocurvature modes of the types expected in the curvaton and axion scenarios have upper bounds of 0.25% and 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelated isocurvature component can improve the 2eff by approximately 4 as a result of slightly lowering the theoretical prediction for the l40 multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions.

BACKGROUND: In recent years, model based approaches such as maximum likelihood have become the methods of choice for constructing phylogenies. A number of authors have shown the importance of using adequate substitution models in order to produce accurate phylogenies. In the past, many empirical models of amino acid substitution have been derived using a variety of different methods and protein datasets. These matrices are normally used as surrogates, rather than deriving the maximum likelihood model from the dataset being examined. With few exceptions, selection between alternative matrices has been carried out in an ad hoc manner. RESULTS: We start by highlighting the potential dangers of arbitrarily choosing protein models by demonstrating an empirical example where a single alignment can produce two topologically different and strongly supported phylogenies using two different arbitrarily-chosen amino acid substitution models. We demonstrate that in simple simulations, statistical methods of model selection are indeed robust and likely to be useful for protein model selection. We have investigated patterns of amino acid substitution among homologous sequences from the three Domains of life and our results show that no single amino acid matrix is optimal for any of the datasets. Perhaps most interestingly, we demonstrate that for two large datasets derived from the proteobacteria and archaea, one of the most favored models in both datasets is a model that was originally derived from retroviral Pol proteins. CONCLUSION: This demonstrates that choosing protein models based on their source or method of construction may not be appropriate.

Software testing can be regarded as an art, a craft, and a science. The practical, step-by-step approach presented in this book provides a bridge between these different viewpoints. A single worked example runs throughout, with consistent use of test automation. Each testing technique is introduced in the context of this example, helping students see its strengths and weaknesses. The technique is then explained in more detail, providing a deeper understanding of underlying principles. Finally the limitations of each technique are demonstrated by inserting faults, giving learners concrete examples of when each technique succeeds or fails in finding faults. Coverage includes black-box testing, white-box testing, random testing, unit testing, object-oriented testing, and application testing. The authors also emphasise the process of applying the techniques, covering the steps of analysis, test design, test implementation, and interpretation of results. The book's web site has programming exercises and Java source code for all examples.

-glycans at sites N165 and N234 in modulating the conformational dynamics of the spike's receptor binding domain (RBD), which is responsible for ACE2 recognition. This finding is corroborated by biolayer interferometry experiments, which show that deletion of these glycans through N165A and N234A mutations significantly reduces binding to ACE2 as a result of the RBD conformational shift toward the "down" state. Additionally, end-to-end accessibility analyses outline a complete overview of the vulnerabilities of the glycan shield of the SARS-CoV-2 S protein, which may be exploited in the therapeutic efforts targeting this molecular machine. Overall, this work presents hitherto unseen functional and structural insights into the SARS-CoV-2 S protein and its glycan coat, providing a strategy to control the conformational plasticity of the RBD that could be harnessed for vaccine development.

More and more aspects of our everyday lives are being mediated, augmented, produced and regulated by software-enabled technologies. Software is fundamentally composed of algorithms: sets of defined steps structured to process instructions/data to produce an output. This paper synthesises and extends emerging critical thinking about algorithms and considers how best to research them in practice. Four main arguments are developed. First, there is a pressing need to focus critical and empirical attention on algorithms and the work that they do given their increasing importance in shaping social and economic life. Second, algorithms can be conceived in a number of ways – technically, computationally, mathematically, politically, culturally, economically, contextually, materially, philosophically, ethically – but are best understood as being contingent, ontogenetic and performative in nature, and embedded in wider socio-technical assemblages. Third, there are three main challenges that hinder research about algorithms (gaining access to their formulation; they are heterogeneous and embedded in wider systems; their work unfolds contextually and contingently), which require practical and epistemological attention. Fourth, the constitution and work of algorithms can be empirically studied in a number of ways, each of which has strengths and weaknesses that need to be systematically evaluated. Six methodological approaches designed to produce insights into the nature and work of algorithms are critically appraised. It is contended that these methods are best used in combination in order to help overcome epistemological and practical challenges.

The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving them in a number of diverse&#13;\ncommunities, and to review some problems that remain open. An important contribution of our work is to bring together material from several areas of research and to present results in a unified manner. We begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions. Closely related to the concept of stability are the notions of exponential growth rates and converse Lyapunov theorems, both of which are discussed in detail. In particular, results on common quadratic Lyapunov functions and piecewise linear Lyapunov functions are presented, as they represent constructive methods for proving stability and also represent problems in which significant progress has&#13;\nbeen made. We also comment on the inherent difficulty in determining stability of switched systems in general, which is exemplified by NP-hardness and undecidability results. We&#13;\nthen proceed by considering the stability of switched systems in which there are constraints on the switching rules, through both dwell-time requirements and state-dependent switching laws. Also in this case the theory of Lyapunov functions and the existence of converse theorems are reviewed. We briefly comment on the classical Lur’e problem and on the theory of stability radii, both of which contain many of the features of switched systems and are rich sources of practical results on the topic. Finally we present a list of questions and open problems which provide motivation for continued research in this area.