Dialectica Interpretation with Marked Counterexamples

Goedel's functional "Dialectica" interpretation can be used to extract functional programs from non-constructive proofs in arithmetic by employing two sorts of higher-order witnessing terms: positive realisers and negative counterexamples. In the original interpretation decidability of atoms is required to compute the correct counterexample from a set of candidates. When combined with recursion, this choice needs to be made for every step in the extracted program, however, in some special cases the decision on negative witnesses can be calculated only once. We present a variant of the interpretation in which the time complexity of extracted programs can be improved by marking the chosen witness and thus avoiding recomputation. The achieved effect is similar to using an abortive control operator to interpret computational content of non-constructive principles.Comment: In Proceedings CL&C 2010, arXiv:1101.520

The European Monetary Union and the Regional Inequalities (?)

In this paper there will be made an attempt for a comparative political and economic evaluation of the European Monetary Union with the criterionof regional inequalities of the European Union. The national and the regional inequalities of the European Union will be analyzed under the framework of the policies of the European Monetary Union. Initially we will examine the regional dimension of the european unification on the basis of the European Union with 15 member-states(EU15).As criteria we select the different levels of economic development of the member-states examining the regional inequalities on a national level.On this basis we observ that the member states converge creating the "hard core of Europe" and the member states diverge from the average level of the development of the European Union determining the countries of "community cohesion". Next we apply the previous criteria to the EU27, in other words it is useful to research the inequalities of the levels of economic development, which result in the European Union, if all the other candidate countries would be able to be taken within the EU of 15 as is today.In the EU of 27 with the basis of per capita GNP exist three groups of countries instead of two as exist today. The first group consists of the present member states of the E15,except for Spain,Greece and Portugal of which the GNP per capita exceeds by 20% the new weighted average of the EU27. the second group consists of the present member states of community cohesion ,i.e. Spain greece and Portugal plus Cyprus,Czechia,and Malta with per capita GNP between 68%(Czechia)and 95%(Spain) of the averege of the EU27. The third group consists of the remaining eight candidate countries with GNP per capita below 40% of the average of the EU27,with the exemption of Slovakia and Hungaria of which the GNP per capita lies between 56%-58% of the average of the EU27. Therefore,the expected expansion with the complex inequalities will result in a big challenge for the European regional policy, and the policy of the economic and social cohesion. First,the expansion will more than double the population of the European Union that lives in regions with GNP per capita below of the 75%of the present average of the EU.This number will raise from 71 million at the present to 174 million of people or different stated from 19% of the total of 15 to 36% of the total of EU27. Second the scale and the size of regional inequalities will be increased. Therefore in 1998 for the less development regions of the EU 15 the per capita GNP was on average 65%of the average of the EU15.With the expansion the GNP per capita of the less development regions of the candidate countries was on the 37% of the average of EU15. Therefore, the co-existence of the poor and rich regions within the eu 27 will make the regional inequalities more complex in this part of the Union which consists of poor countries.We make possibly find ourselves in a new allocation of poverty. Finally,we will attempt to achieve the necessary interventions between the EU15 and the EU27, researching the modern problems of the EU under the expected expansion of the European Union.

The Regional Inequalities in the European Union and the Countries of Community Cohesion (Portugal,Spain,Ireland and Greece)

An attempt will be made, in this article,to analyze the regional inequalities within the European Union emphasizing in the countries of Communty Cohesion and the relationship between North and South.The estimation of regional policy in thi level will be made with the following variables:the deviations from the average community Gross Domestic Product GDP) the annual growth rates og GDP and the level of Unemployment. During the process of European integration it has been observed changes in the classification of the cohesion countries within the European Union.It will be an effort to estimate if these changes have been caused from the policies of the European Union or from the national policies of the member states. The analysis will be made in comparative terms among the supernational policies of the EU and the national policies of countries of community cohesion.

The regional dimensions of the european integration under the expected expansion of the European Union

In this paper it will be made an attempt for a comparative political and economy evaluation of the European Integration with the criterion of regional inequalities of the european Union. The problem of the European Integration will be analyzed on the basis of national and regional inequalities of the European Union. Initially we will examine the regional dimension of the European unification on the asis of the European Union with 15 member-states (EU15). As criteria we select the different levels of economic development of the member-states examining the regional inequalities at national level. On this basis we obsserve that the member states converge creating the "hard core of Europe" and the member states diverge from the average level of the development of the European Union so that determining the countries of "community cohesion". Next we apply the previous criteria to the EU27,in other words it is useful to research the inequalities of the levels of economic development,which rrresult in the European Union,if all the others candidate countries would be able to be taken within the EI of 15 as is today. In the EU of 27 with the basis of per capita GNP exist three groups of countries instead of two as exist today. The first group it consists of the present member-states of the EU15,except Spain,Greece and Portugal of which the GNP per capita exceeds by 20% the new weighted average of the EU27. The second group it consists of the present member states of community cohesion, i.e. Spain Greece and Portugal plus Cyprus,Czechia, and Malta with percapita GNP between 68%(Czechia) and 95% (Spain) of the average of the EU27. The third group it consists of the remaining eight (8) candidate countries with GNP per capita below of the 40% of the average of the EU27, with the exemption of Slovakia and Hungary og which the GNP per capita lies between 56%-58% of the average of the EU27. Therefore, the expected expansion with the complex inequalities, will result a big challenge for the European regional policy, and the policy of the economic and social cohesion. First, the expansion will make more than double the population of the European Union that lives with GNP per capita below of the 75% of the present average of the EU.This number will raise from 71 million at the present to 174 million of people or different stated from 19% of the total of EU15 to 36% of the total of EU27. Second, the scale and the size of regional inequalities will be increased. Therefore, in the 1998 for the less developed regionsn the EU15 the per capita GNPwas an average of the EU15. With the expansion, the GNP per capita of the less developed regions of the candidata countries was on the 37% of the average of EU15. Therefore the co-existence of the poor and rich regions within the EU27 will make the regional inequalities more complex in this part of the Union which consists of poor countries. We may possibly will find ourselves in a new allocation of poverty. Finally, we will attempt to achieve the necessary interventions between the EU15 and the EU27, researching the modern problems of the EU under the expected expansion of the European Union.

Linking period and cohort life-expectancy linear increases in Gompertz proportional hazards models

In a Gompertz mortality model with constant yearly improvements at all ages, linear increases in period life expectancy correspond to linear increases in the respective cohort life expectancy. The link between the two measures can be given by a simple approximate relationship.cohort life expectancy, Gompertz mortality, Linear Shift Models, period life expectancy

Analysis of methods for extraction of programs from non-constructive proofs

The present thesis compares two computational interpretations of non-constructive proofs: refined A-translation and Gödel's functional "Dialectica" interpretation. The behaviour of the extraction methods is evaluated in the light of several case studies, where the resulting programs are analysed and compared. It is argued that the two interpretations correspond to specific backtracking implementations and that programs obtained via the refined A-translation tend to be simpler, faster and more readable than programs obtained via Gödel's interpretation. Three layers of optimisation are suggested in order to produce faster and more readable programs. First, it is shown that syntactic repetition of subterms can be reduced by using let-constructions instead of meta substitutions abd thus obtaining a near linear size bound of extracted terms. The second improvement allows declaring syntactically computational parts of the proof as irrelevant and that this can be used to remove redundant parameters, possibly improving the efficiency of the program. Finally, a special case of induction is identified, for which a more efficient recursive extracted term can be defined. It is shown the outcome of case distinctions can be memoised, which can result in exponential improvement of the average time complexity of the extracted program

Dynamical analysis of the circumprimary planet in the eccentric binary system HD59686

We present a detailed orbital and stability analysis of the HD~59686 binary-star planet system. HD~59686 is a single-lined moderately close ($a_{B} = 13.6\,$AU) eccentric ($e_{B} = 0.73$) binary, where the primary is an evolved K giant with mass $M = 1.9 M_{\odot}$ and the secondary is a star with a minimum mass of $m_{B} = 0.53 M_{\odot}$. Additionally, on the basis of precise radial velocity (RV) data a Jovian planet with a minimum mass of $m_p = 7 M_{\mathrm{Jup}}$, orbiting the primary on a nearly circular S-type orbit with $e_p = 0.05$ and $a_p = 1.09\,$AU, has recently been announced. We investigate large sets of orbital fits consistent with HD 59686's radial velocity data by applying bootstrap and systematic grid-search techniques coupled with self-consistent dynamical fitting. We perform long-term dynamical integrations of these fits to constrain the permitted orbital configurations. We find that if the binary and the planet in this system have prograde and aligned coplanar orbits, there are narrow regions of stable orbital solutions locked in a secular apsidal alignment with the angle between the periapses, $\Delta \omega$, librating about $0^\circ$. We also test a large number of mutually inclined dynamical models in an attempt to constrain the three-dimensional orbital architecture. We find that for nearly coplanar and retrograde orbits with mutual inclination $145^\circ \lesssim \Delta i \leq 180^\circ$, the system is fully stable for a large range of orbital solutions.Comment: 17 pages, 11 figures, accepted for publication by A

Precise radial velocities of giant stars VIII. Testing for the presence of planets with CRIRES Infrared Radial Velocities

We have been monitoring 373 very bright (V < 6 mag) G and K giants with high precision optical Doppler spectroscopy for more than a decade at Lick Observatory. Our goal was to discover planetary companions around those stars and to better understand planet formation and evolution around intermediate-mass stars. However, in principle, long-term, g-mode nonradial stellar pulsations or rotating stellar features, such as spots, could effectively mimic a planetary signal in the radial velocity data. Our goal is to compare optical and infrared radial velocities for those stars with periodic radial velocity patterns and to test for consistency of their fitted radial velocity semiamplitudes. Thereby, we distinguish processes intrinsic to the star from orbiting companions as reason for the radial velocity periodicity observed in the optical. Stellar spectra with high spectral resolution have been taken in the H-band with the CRIRES near-infrared spectrograph at ESO's VLT for 20 stars of our Lick survey. Radial velocities are derived using many deep and stable telluric CO2 lines for precise wavelength calibration. We find that the optical and near-infrared radial velocities of the giant stars in our sample are consistent. We present detailed results for eight stars in our sample previously reported to have planets or brown dwarf companions. All eight stars passed the infrared test. We conclude that the planet hypothesis provides the best explanation for the periodic radial velocity patterns observed for these giant stars.Comment: 14 pages, 6 figures, 3 tables, accepted by Astronomy & Astrophysic

Precise radial velocities of giant stars. XI. Two brown dwarfs in 6:1 mean motion resonance around the K giant star ν\nu Ophiuchi

We present radial-velocity (RV) measurements for the K giant $\nu$ Oph (= HIP88048, HD163917, HR6698), which reveal two brown dwarf companions with a period ratio close to 6:1. For our orbital analysis we use 150 precise RV measurements taken at Lick Observatory between 2000 and 2011, and we combine them with RV data for this star available in the literature. Using a stellar mass of $M = 2.7\,M_\odot$ for $\nu$ Oph and applying a self-consistent N-body model we estimate the minimum dynamical companion masses to be $m_1\sin i \approx 22.2\,M_{\mathrm{Jup}}$ and $m_2\sin i \approx 24.7\,M_{\mathrm{Jup}}$, with orbital periods $P_1 \approx 530$ d and $P_2 \approx 3185$ d. We study a large set of potential orbital configurations for this system, employing a bootstrap analysis and a systematic $\chi_{\nu}^2$ grid-search coupled with our dynamical fitting model, and we examine their long-term stability. We find that the system is indeed locked in a 6:1 mean motion resonance (MMR), with $\Delta \omega$ and all six resonance angles $\theta_{1}, \ldots, \theta_{6}$ librating around 0$^\circ$. We also test a large set of coplanar inclined configurations, and we find that the system will remain in a stable resonance for most of these configurations. The $\nu$ Oph system is important for probing planetary formation and evolution scenarios. It seems very likely that the two brown dwarf companions of $\nu$ Oph formed like planets in a circumstellar disk around the star and have been trapped in a MMR by smooth migration capture.Comment: 17 pages, 9 figures. New version with corrected number in title. No other change

Photonic Bandgap Analysis and Fabrication of Macroporous Silicon by Electrochemical Etching

Los cristales fotónicos son materiales creados artificialmente, que pueden hacer con los fotones lo que los semiconductores ordinarios hacen con los electrones: es decir, pueden mostrar una banda fotónica prohibida (PBG), situación en la cual fotones con determinadas energías no pueden propagarse dentro del cristal independientemente de la polarización y la dirección de propagación. Por lo tanto, la banda prohibida para los fotones puede ser el verdadero análogo óptico de la banda prohibida fundamental en los semiconductores. Desde su invento en 1987, los cristales fotónicos han atraído un interés considerable debido a sus propiedades ópticas inusuales. Las propiedades únicas de los cristales fotónicos también han llevado al reconocimiento de su estudio como un nuevo y principal campo de la optoelectrónica.El silicio macroporoso con su elevada constante dieléctrica, sus altas relaciones de aspecto y su total compatibilidad con la industria microelectrónica es un modelo excelente para estudiar las propiedades ópticas de cristales fotónicos bidimensionales y asimismo tridimensionales. Adicionalmente, se ha demostrado que el silicio macroporoso tiene varias aplicaciones únicas en muchos otros campos, como la electrónica, el micromecanizado, la detección de gases y la biotecnología. La investigación del silicio macroporoso crece continuamente debido a su enorme potencial de aplicaciones.El trabajo presentado en esta tesis trata dos temas: simulación de la estructura de bandas fotónicas y análisis de cristales fotónicos bidimensionales, y la fabricación de estructuras bidimensionales basadas en silicio macroporoso para aplicaciones como cristales fotónicos en el espectro infrarrojo. Debido a que muchas posibles aplicaciones de los cristales fotónicos están basadasen sus bandas fotónicas prohibidas, es interesante diseñar cristales fotónicos con una bandaprohibida absoluta, que sea tan grande como es posible. En esta tesis describimos el método para alargar la banda fotónica absoluta, mostrando el papel de la simetría en el diseño de estructuras fotónicas óptimas. Hemos estudiado como reduciendo la simetría mediante incorporación de elementos adicionales en la celda unitaria o mediante cambio de la forma de los "átomos" afecta la relación de dispersión de los dos modos de polarización (TM y TE) en cristales fotónicos bidimensionales. Nuestro objetivo ha sido optimizar la magnitud de la banda fotónica absoluta, reduciendo la simetría de las celdas cuadrada y triangular y construir de este modo estructuras nuevas, llamadas celdas híbridas. Usando el método de las deferencias finitas en el dominio de tiempo (FDTD) hemos realizado un detallado análisis numérico de la relación de dispersión en celdas híbridas bidimensionales que consisten en columnas de aire en silicio.En el caso de celda cuadrada, la reducción de la simetría ha sido aplicada con éxito para maximizar la magnitud de la banda prohibida. Para la celda cuadrada que consiste en columnas cilíndricas de aire, la incorporación de una columna adicional aumenta tres veces la magnitud de la PBG absoluta. En el caso de celda cuadrada de columnas cuadradas de aire, la rotación de las columnas juega un papel crítico en la creación de la PBG absoluta.Si las columnas cuadradas no están rotadas no existe una PBG absoluta. La magnitud de la PBG absoluta se ha mejorado considerablemente a través de la combinación de incorporación de una columna adicional y rotación de las columnas cuadradas. Además, se genera una nueva PBG absoluta que se encuentra para un amplio rango de ángulos de rotación y dimensiones de las columnas, que están lejos de la condición de empaquetamiento (cuando las columnas se tocan). Esto favorece la fabricación de los cristales fotónicos.La PBG absoluta es de mayor magnitud para la celda triangular formada por columnas cilíndricas de aire. Los resultados de las simulaciones demuestran que modificando la estructura triangular mediante incorporación de columnas adicionales o mediante columnas cuadradas (aunque las columnas estén rotadas) no mejora la PBG absoluta, por lo menos en el caso estudiado de estructura aire/silicio. La adición de columnas adicionales en la celda triangular reduce la magnitud de la PBG absoluta.Hemos realizado un detallado análisis cuantitativo de las PBG absolutas para 2D celdas triangulares y hexagonales, considerando que entre las columnas y la matriz dieléctrica hay una capa superficial de otro material dieléctrico. Esta capa superficial puede ser indeseada (resultado del proceso de fabricación) o puede ser creada intencionadamente.Las propiedades de las bandas fotónicas se ven afectadas del grosor y también de la constante dieléctrica de la capa superficial. Los resultados de las simulaciones demuestran que para estructuras que están formadas por columnas de aire en un material dieléctrico la existencia de una capa superficial reduce la magnitud de la PBG absoluta. Por otro lado, para estructuras formadas de columnas dieléctricas en aire la capa superficial puede mejorar la PBG cuando la constante dieléctrica de la capa es mayor que la de las columnas.Esto proporciona mayor flexibilidad en la realización práctica de estos 2D cristales fotónicos. Por ejemplo, en ciertas ocasiones es imposible obtener pilares dieléctricos con un diámetro determinado o de un material concreto por limitaciones tecnológicas. Sin embargo, los pilares se pueden fabricar de un material con menor constante dieléctrica para el cual existe una técnica bien desarrollada. Después los pilares se pueden cubrir con el material deseado mediante deposición, obteniendo las mismas propiedades como en el caso de la estructura sin capa superficial.Hemos desarrollado un equipo de ataque electroquímico para fabricación de 2D estructuras periódicas basadas en la formación de silicio macroporoso. Asimismo, hemos realizado un estudio de la influencia de los parámetros del ataque electroquímico sobre la morfología de los poros. Crecimiento estable de macroporos se puede obtener sólo si todos los parámetros del proceso de ataque (resistividad del substrato, concentración de HF, corriente de ataque, potencial anódico, temperatura, etc.) están ajustados apropiadamente.Las condiciones óptimas ocupan una pequeña parte de todos los posibles parámetros del proceso. Por ejemplo, concentraciones de HF mayores de 10 wt.%, que se usan generalmente para crecer películas micro- y mesoporosas, no son apropiadas para crecer macroporos con una profundidad grande y una forma cilíndrica. Potenciales relativamente altos (para nuestras muestras mayores de 2 V) aumentan inevitablemente la formación de "breakdown-type" poros. Por otro lado, potenciales relativamente bajos (menores de 1 V) generalmente producen un crecimiento inestable de los poros que están parcial o totalmente recubiertos de silicio microporoso.La corriente aplicada es el parámetro más crítico del proceso. Densidades de la corriente mayors de la densidad crítica Jps, que depende de la temperatura y de la concentración de HF, situaría el proceso en la región de electropulido. El control de la corriente durante el proceso es una tarea clave. Mantener la corriente de ataque constante durante todo el proceso es insuficiente para el crecimiento estable de macroporos cilíndricos. Se han identificado dos efectos que influyen la forma de los poros en profundidad. Primero, la concentración de HF disminuye cerca de la punta de los poros debido a las limitaciones por difusión en poros estrechos y hondos. Este efecto produce un incremento del diámetro del poro cerca de la punta. Segundo, la superficie interna de los poros aumenta para prolongados tiempos de ataque, provocando un incremento de la corriente de oscuridad y por lo tanto la formación de poros cónicos. Su diámetro decrece en profundidad. El incremento de la corriente de ataque de manera adecuada, tal que se produzca crecimiento de poros con forma cónica inversa, es un método para compensar la conicidad inicial de los poros. Si el ataque se realiza a temperaturas más bajas y burbujeando el electrolito con nitrógeno se puede reducir la corriente de oscuridad, formando poros menos cónicos. Otro método efectivo es el uso de un surfactante apropiado. Los surfactantes se usan por lo general para prevenir degradación causada por las burbujas de hidrógeno que se pegan en la superficie de la muestra. Hemos probado dos diferentes tipos de surfactants (TritonX-100 no iónico y SDS aniónico). Hemos observado que la adición de surfactantes no iónicos aumenta la corriente de oscuridad y la formación de poros cónicos. Por otro lado, el uso de surfactantes aniónicos reduce considerablemente la corriente de oscuridad y poros cilíndricos se pueden producir casi sin dificultad.Aplicando las reglas explicadas arriba se han obtenido matrices altamente uniformes de macroporos con diferente distribución y dimensiones.Por último, también se presentan algunos resultados preliminares sobre aplicaciones novedosas de silicio macroporoso. Las características estructurales de las matrices de macroporos se han utilizado para fabricar pilares de óxido de silicio que podrían encontrar aplicaciones en la biotecnología como plataformas tridimensionales para detección de reconocimiento de moléculas o como matrices de microjeringas. También se ha fabricado un filtro que consiste en membranas de silicio macroporoso y se han medido sus características ópticas. Este filtro se comporta como pasabajas cuando la luz incidente es paralela a los poros. Los resultados obtenidos son solamente cuantitativos y sugieren una futura optimización del proceso de ataque para fabricar muestras de alta calidad.Asimismo se ha introducido modulación periódica del diámetro de los poros en profundidad y se han fabricado matrices de "ratchet-type" macroporos, los cuales podrían tener aplicaciones como dispositivos para separación de partículas. Se ha demostrado que mediante unos pocos pasos adicionales las matrices de macroporos modulados se pueden convertir en microestructuras tridimensionales de huecos interconectados. Esta técnica se puede aplicar para la fabricación de cristales fotónicos tridimensionales.Photonic crystals are artificially created materials that can do to photons what an ordinary semiconductor does to electrons: that is to say, they can exhibit a photonic band gap, a situation in which photons with certain energies cannot propagate inside the crystal, regardless of polarization and propagation direction. The photonic band gap is therefore likely to be the true optical analog of the fundamental gap of a semiconductor. Since their invention in 1987, photonic crystals have triggered considerable interest because of their unusual optical properties. The unique properties of photonic crystals also led to their study being recognized as a new and major field of optoelectronics.Macroporous silicon, with its high dielectric contrast, very high aspect ratios and full compatibility with the silicon microelectronic industry is an excellent model system for studying the optical properties of two-dimensional and even three-dimensional photonic crystals. Besides, macroporous silicon has been shown to have several unique uses in many other fields, like electronics, micromachining, gas sensing and biotechnology. Research into macroporous silicon is continuously growing, prompted by its enormous potential for applications.The work presented in this thesis deals with two subjects: photonic band structure simulations and analysis of 2D photonic crystals, and the fabrication of macroporous silicon structures suitable for application as 2D infrared photonic crystals.Since many potential applications of photonic crystals are based on their photonic band gaps, it is of interest to design photonic crystals with an absolute band gap that is as large as possible. In this thesis we describe a way to enlarge the absolute photonic band gap, showing the role that symmetry plays in designing optimal photonic structures. We have examined how reducing symmetry by inserting additional elements into the lattice unit cell or by changing the shape of the scatterers alters the dispersion behavior of the TMand TE-polarization modes in 2D photonic crystals. Our goal was to maximize the absolute PBG width by breaking the symmetry of the simple square and triangular lattices and thus to construct new structures, the so-called hybrid lattices. Using the FDTD method for photonic band structure calculations, we performed a detailed numerical analysis of the photonic dispersion relation in 2D hybrid lattices that consist of air holes drilled in silicon.For square lattices, the symmetry reduction approach has been successfully applied to maximize the absolute PBG width. In the case of square lattices of circular air rods, the inclusion of an additional rod increases the absolute PBG threefold. For the case of square lattices of square air rods, the rotation of the rods plays a critical role in the opening of an absolute PBG. No absolute PBG was found if the square rods were not rotated. The size of the absolute PBG is improved most significantly by a combination of the inclusion of an additional rod and the rotation of square rods. Moreover, a new absolute PBG is generated that persists over a wide range of rotation angles and filling fractions, which are far from the closed-packed condition. This greatly favors the fabrication of photonic crystals.The largest absolute PBG is the one for the triangular lattice of circular air rods.Our results have shown that modifying the triangular structure by adding interstitial rods or using square rods (even though the rods are rotated) is not a good way of achieving a larger absolute PBG, at least for the special case of air/silicon structures. Adding more rods to the lattice unit cell cannot further enlarge the absolute PBG width.We have made a detailed quantitative analysis of the absolute PBGs in 2D triangular and honeycomb lattices considering that there is an interfacial (shell) layer between the rods and the background dielectric matrix. This interfacial layer may be the unwanted result of the fabrication process itself or created intentionally. The properties of the photonic gaps are strongly affected by the thickness and the dielectric constant of the shell layer. The results of band structure simulations show that for structures consisting of air rods embedded in a dielectric background this layer reduces the absolute photonic gap.For structures consisting of dielectric rods in air, however, an interfacial layer can yield larger photonic gaps if the dielectric constant of the layer is greater than that of the rods.This provides further flexibility in the practical realization of such 2D photonic crystals.For example, in certain cases we may not be able to obtain dielectric rods of the required diameter or of the particular material we need because of technological limitations.However, we are enabled to grow the rods of materials with lower dielectric constants, for which a well-developed technology exists. The rods can then be covered with the required dielectric by deposition, thus achieving almost the same gap properties as those of the ideal shell-less structure.We have developed an electrochemical etching set-up for fabricating 2D periodic structures based on macroporous silicon formation. We have also made a detailed study of how the electrochemical etching parameters influence the pore morphology. Straight and stable macropores can only be etched if all parameters of the etching process (doping level, HF concentration, etching current, anodic potential, temperature, etc.) are properly adjusted. The optimal conditions are only a very tiny part of the total parametric space, which requires a fine control of the process. For example, HF concentrations higher than 10 wt.%, which are commonly used for growing micro- and mesoporous films, are not suitable for growing deep, straight macropores. Relatively high anodic potentials (e.g. even higher than 2 V for our samples) inevitably enhance the formation of spiking breakdowntype pores on macropore walls. On the other hand, low anodic potentials (less than 1 V) usually lead to unstable pore growth with macropores that are partially or fully filled with microporous silicon.Of all etching parameters the applied etching current is the most critical. Current densities greater than the critical current density Jps, which depends on the temperature and electrolyte concentration, will move the system into the electropolishing regime.Controlling the etching current during the process is a key issue. Keeping the etching current constant was found not to be sufficient to grow deep, straight macropores. Two effects that influence the pore shape in depth were identified. First, the decrease in HF concentration towards the pore tips because of diffusional limitations leads to an increase of the pore diameter close to the tip. Second, the pore surface area increases for long anodization times, which leads to an increase in the dark current density and yields conical pores, the diameter of which decreases with depth. Increasing the etching current accordingly, which means to etch pores with the reverse conical shape is one of the methods to reduce the pore conicity. Performing the etching at lower temperatures and bubbling the electrolyte with nitrogen can reduce the dark current and produce less conical pores. Another effective way is to use appropriate surfactants. Surfactants are commonly used to prevent degeneration caused by bubbles sticking to the sample surface. Two surfactants of different types (nonionic TritonX-100 and anionic SDS) were tested. We found that the addition of nonionic surfactants increases the dark current contribution and thus enhances the formation of conical pores. On the other hand, the use of anionic surfactants considerably reduces the dark current and straight pores can be formed almost without difficulty. Highly uniform macropore arrays with different arrangements and dimensions were obtained by applying these "compensation" rules.Finally, we have also presented some preliminary results of our work on novel applications of macroporous silicon. The structural features of the etched macropore arrays have been exploited to fabricate high-aspect-ratio silicon dioxide pillars, which may have applications in biotechnology as a 3D sensor platform for molecular recognition detections or as dense arrays of microsyringes for fluid delivery or precise chemical reaction stimulation. We have also fabricated a macroporous filter consisting of through-wafer pores and measured its optical characteristics. For light incidence parallel to the pores, a shortpass spectral behavior has been observed. The obtained results are only qualitative and suggest that further optimization of the etching process is needed in order to produce higher quality samples. We were also able to introduce periodic modulations of the pore diameter in depth and to fabricate ratchet-type macropore arrays, which have been envisioned for applications as ratchet devices for large-scale particle separation. We have shown that by a few post-etching steps the modulated macropore arrays can be converted into microstructures consisting of interconnected voids in all three dimensions. The technique used can be exploited for the fabrication of fully 3D photonic crystals