Evolution PDEs and augmented eigenfunctions. I finite interval

The so-called unified method expresses the solution of an initial-boundary value problem for an evolution PDE in the finite interval in terms of an integral in the complex Fourier (spectral) plane. Simple initial-boundary value problems, which will be referred to as problems of type~I, can be solved via a classical transform pair. For example, the Dirichlet problem of the heat equation can be solved in terms of the transform pair associated with the Fourier sine series. Such transform pairs can be constructed via the spectral analysis of the associated spatial operator. For more complicated initial-boundary value problems, which will be referred to as problems of type~II, there does \emph{not} exist a classical transform pair and the solution \emph{cannot} be expressed in terms of an infinite series. Here we pose and answer two related questions: first, does there exist a (non-classical) transform pair capable of solving a type~II problem, and second, can this transform pair be constructed via spectral analysis? The answer to both of these questions is positive and this motivates the introduction of a novel class of spectral entities. We call these spectral entities augmented eigenfunctions, to distinguish them from the generalised eigenfunctions introduced in the sixties by Gel'fand and his co-authors

Performance comparison of heating control strategies combining simulation and experimental results

Different heating system controllers for passive solar buildings are compared on two different buildings.The performance criterion combines energy performance and thermal comfort using the "costfunction" paradigm. The experimental facilities did not allow a direct experimental comparison by using two identical buildings. The controllers were implemented alternatively in one building and a performance comparison was obtained in two ways: first by identifying short periods that have similar driving variables (weather conditions and building occupancy) and comparing the experimental results obtained in both cases. The second method mixes experiments and simulation using a well-tuned model of the building and its occupants. This paper discusses the results obtained using the above methods and shows that both methods give consistent estimates of the difference between controllers, while the second method allows to extrapolate useful information from the limited data available

Phase diagrams in the lattice RPM model: from order-disorder to gas-liquid phase transition

The phase behavior of the lattice restricted primitive model (RPM) for ionic systems with additional short-range nearest neighbor (nn) repulsive interactions has been studied by grand canonical Monte Carlo simulations. We obtain a rich phase behavior as the nn strength is varied. In particular, the phase diagram is very similar to the continuum RPM model for high nn strength. Specifically, we have found both gas-liquid phase separation, with associated Ising critical point, and first-order liquid-solid transition. We discuss how the line of continuous order-disorder transitions present for the low nn strength changes into the continuum-space behavior as one increases the nn strength and compare our findings with recent theoretical results by Ciach and Stell [Phys. Rev. Lett. {\bf 91}, 060601 (2003)].Comment: 7 pages, 10 figure

HOMOGENIZATION OF THE HELLENIC CLOUD COVER TIME SERIES - PRELIMINARY RESULTS

Cloud cover is an important meteorological parameter because it affects the ra- diative energy balance of the Earth and precipitation and plays a major role in the hydrological cycle. Impact of clouds on the radiative balance is twofold: cloud cover modifies the albedo of the Earth and the atmospheric long wave radiative exchange. Long records of cloud cover data are the result of human estimations made during the synoptic observation hours at each meteorological station. Currently the quantification of cloud cover has been automated due to the advent of modern remote sensing space (e.g. satellites) and ground sky monitoring techniques (e.g. sky cameras). All weather time series records may suffer from inhomogeneities; their use in climatology requires homogenization. In this work we attempt a preliminary homogenization of the cloud cover time series of the Hellenic National Weather Service (HNMS) network. Data come from 36 meteorological stations, and cover the period from 1975 to 2004. Raw data comprise (synoptic) hourly cloud cover observations which we subjected to quality control before producing daily and then monthly average cloud cover time series. For this homogenization exercise we used the HOMER software tool

HOMOGENIZATION OF THE HELLENIC CLOUD COVER TIME SERIES - PRELIMINARY RESULTS

Cloud cover is an important meteorological parameter because it affects the ra- diative energy balance of the Earth and precipitation and plays a major role in the hydrological cycle. Impact of clouds on the radiative balance is twofold: cloud cover modifies the albedo of the Earth and the atmospheric long wave radiative exchange. Long records of cloud cover data are the result of human estimations made during the synoptic observation hours at each meteorological station. Currently the quantification of cloud cover has been automated due to the advent of modern remote sensing space (e.g. satellites) and ground sky monitoring techniques (e.g. sky cameras). All weather time series records may suffer from inhomogeneities; their use in climatology requires homogenization. In this work we attempt a preliminary homogenization of the cloud cover time series of the Hellenic National Weather Service (HNMS) network. Data come from 36 meteorological stations, and cover the period from 1975 to 2004. Raw data comprise (synoptic) hourly cloud cover observations which we subjected to quality control before producing daily and then monthly average cloud cover time series. For this homogenization exercise we used the HOMER software tool

Covid-19: predictive mathematical formulae for the number of deaths during lockdown and possible scenarios for the post-lockdown period.

In a recent article, we introduced two novel mathematical expressions and a deep learning algorithm for characterizing the dynamics of the number of reported infected cases with SARS-CoV-2. Here, we show that such formulae can also be used for determining the time evolution of the associated number of deaths: for the epidemics in Spain, Germany, Italy and the UK, the parameters defining these formulae were computed using data up to 1 May 2020, a period of lockdown for these countries; then, the predictions of the formulae were compared with the data for the following 122 days, namely until 1 September. These comparisons, in addition to demonstrating the remarkable predictive capacity of our simple formulae, also show that for a rather long time the easing of the lockdown measures did not affect the number of deaths. The importance of these results regarding predictions of the number of Covid-19 deaths during the post-lockdown period is discussed

Structured Variability in Purkinje Cell Activity during Locomotion

The cerebellum is a prominent vertebrate brain structure that is critically involved in sensorimotor function. During locomotion, cerebellar Purkinje cells are rhythmically active, shaping descending signals and coordinating commands from higher brain areas with the step cycle. However, the variation in this activity across steps has not been studied, and its statistical structure, afferent mechanisms, and relationship to behavior remain unknown. Here, using multi-electrode recordings in freely moving rats, we show that behavioral variables systematically influence the shape of the step-locked firing rate. This effect depends strongly on the phase of the step cycle and reveals a functional clustering of Purkinje cells. Furthermore, we find a pronounced disassociation between patterns of variability driven by the parallel and climbing fibers. These results suggest that Purkinje cell activity not only represents step phase within each cycle but also is shaped by behavior across steps, facilitating control of movement under dynamic conditions