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Displaying 1 - 10 of 10.
Project acronym ATOP
Project Atomically-engineered nonlinear photonics with two-dimensional layered material superlattices
Researcher (PI) zhipei SUN
Host Institution (HI) AALTO KORKEAKOULUSAATIO SR
Summary The project aims at introducing a paradigm shift in the development of nonlinear photonics with atomically-engineered two-dimensional (2D) van der Waals superlattices (2DSs). Monolayer 2D materials have large optical nonlinear susceptibilities, a few orders of magnitude larger than typical traditional bulk materials. However, nonlinear frequency conversion efficiency of monolayer 2D materials is typically weak mainly due to their extremely short interaction length (~atomic scale) and relatively large absorption coefficient (e.g.,>5×10^7 m^-1 in the visible range for graphene and MoS2 after thickness normalization). In this context, I will construct atomically-engineered heterojunctions based 2DSs to significantly enhance the nonlinear optical responses of 2D materials by coherently increasing light-matter interaction length and efficiently creating fundamentally new physical properties (e.g., reducing optical loss and increasing nonlinear susceptibilities). The concrete project objectives are to theoretically calculate, experimentally fabricate and study optical nonlinearities of 2DSs for next-generation nonlinear photonics at the nanoscale. More specifically, I will use 2DSs as new building blocks to develop three of the most disruptive nonlinear photonic devices: (1) on-chip optical parametric generation sources; (2) broadband Terahertz sources; (3) high-purity photon-pair emitters. These devices will lead to a breakthrough technology to enable highly-integrated, high-efficient and wideband lab-on-chip photonic systems with unprecedented performance in system size, power consumption, flexibility and reliability, ideally fitting numerous growing and emerging applications, e.g. metrology, portable sensing/imaging, and quantum-communications. Based on my proven track record and my pioneering work on 2D materials based photonics and optoelectronics, I believe I will accomplish this ambitious frontier research program with a strong interdisciplinary nature.
The project aims at introducing a paradigm shift in the development of nonlinear photonics with atomically-engineered two-dimensional (2D) van der Waals superlattices (2DSs). Monolayer 2D materials have large optical nonlinear susceptibilities, a few orders of magnitude larger than typical traditional bulk materials. However, nonlinear frequency conversion efficiency of monolayer 2D materials is typically weak mainly due to their extremely short interaction length (~atomic scale) and relatively large absorption coefficient (e.g.,>5×10^7 m^-1 in the visible range for graphene and MoS2 after thickness normalization). In this context, I will construct atomically-engineered heterojunctions based 2DSs to significantly enhance the nonlinear optical responses of 2D materials by coherently increasing light-matter interaction length and efficiently creating fundamentally new physical properties (e.g., reducing optical loss and increasing nonlinear susceptibilities). The concrete project objectives are to theoretically calculate, experimentally fabricate and study optical nonlinearities of 2DSs for next-generation nonlinear photonics at the nanoscale. More specifically, I will use 2DSs as new building blocks to develop three of the most disruptive nonlinear photonic devices: (1) on-chip optical parametric generation sources; (2) broadband Terahertz sources; (3) high-purity photon-pair emitters. These devices will lead to a breakthrough technology to enable highly-integrated, high-efficient and wideband lab-on-chip photonic systems with unprecedented performance in system size, power consumption, flexibility and reliability, ideally fitting numerous growing and emerging applications, e.g. metrology, portable sensing/imaging, and quantum-communications. Based on my proven track record and my pioneering work on 2D materials based photonics and optoelectronics, I believe I will accomplish this ambitious frontier research program with a strong interdisciplinary nature.
Project acronym CaLA
Project The Capillary Lock Actuator: A novel bistable microfluidic actuator for cost-effective high-density actuator arrays suitable for large-scale graphical tactile displays
Researcher (PI) Bastian Rapp
Host Institution (HI) ALBERT-LUDWIGS-UNIVERSITAET FREIBURG
Summary According to the World Health Organization more than 285 million people worldwide are visually impaired. In a world where graphics and online content (images, webpages) become increasingly important the inability to perceive information visually is the primary inhibitor for inclusion. In contrast to display technology for sighted people, tactile displays which translate text and graphics to touchable pixels (taxels) have seen little progress in recent decades. So-called Braille lines which display only a single line of text are still the norm. The reason why graphical tactile displays do not exist is the lack of a suitable actuator technology which allows generating massively parallelized individually addressable cost-effective taxel arrays. This ERC Consolidator project aims at a revolution in microactuator array technology with a fundamentally new concept termed the Capillary Lock Actuator (CaLA). CaLA is a novel bistable massively parallelizable microfluidic microactuator which overcomes many of the limitations currently associated with microactuators. It can be operated with low-voltage control signals and requires virtually no power for actuation. CaLA harnesses three concepts inherent to microfluidics: positive capillary pressure, segmented flow and controllable locally confined changes in wetting. The project will use CaLA actuator arrays for setting up the very first portable tactile graphic display with 30.000 individually addressable taxels thereby significantly outperforming the state-of-the-art. It will be based on manufacturing techniques for highly complex microstructures in glass invented by my group. CaLA will be a significant breakthrough in actuator technology and enabling for many applications in microsystem technology. Most importantly, it will be a significant step towards making the information technology inclusive for the visually impaired by providing the first robust cost-effective solution to large-scale tactile displays.
According to the World Health Organization more than 285 million people worldwide are visually impaired. In a world where graphics and online content (images, webpages) become increasingly important the inability to perceive information visually is the primary inhibitor for inclusion. In contrast to display technology for sighted people, tactile displays which translate text and graphics to touchable pixels (taxels) have seen little progress in recent decades. So-called Braille lines which display only a single line of text are still the norm. The reason why graphical tactile displays do not exist is the lack of a suitable actuator technology which allows generating massively parallelized individually addressable cost-effective taxel arrays. This ERC Consolidator project aims at a revolution in microactuator array technology with a fundamentally new concept termed the Capillary Lock Actuator (CaLA). CaLA is a novel bistable massively parallelizable microfluidic microactuator which overcomes many of the limitations currently associated with microactuators. It can be operated with low-voltage control signals and requires virtually no power for actuation. CaLA harnesses three concepts inherent to microfluidics: positive capillary pressure, segmented flow and controllable locally confined changes in wetting. The project will use CaLA actuator arrays for setting up the very first portable tactile graphic display with 30.000 individually addressable taxels thereby significantly outperforming the state-of-the-art. It will be based on manufacturing techniques for highly complex microstructures in glass invented by my group. CaLA will be a significant breakthrough in actuator technology and enabling for many applications in microsystem technology. Most importantly, it will be a significant step towards making the information technology inclusive for the visually impaired by providing the first robust cost-effective solution to large-scale tactile displays.
Project acronym IMMUNOTHROMBOSIS
Project Cross-talk between platelets and immunity - implications for host homeostasis and defense
Researcher (PI) Steffen MASSBERG
Call Details Advanced Grant (AdG), LS4, ERC-2018-ADG
Summary The overall aim of the IMMUNOTHROMBOSIS project is to clarify the mechanisms underlying the recently identified synergism between thrombosis and inflammation. Thrombus formation and inflammation are vital host responses that ensure homeostasis, but can also drive cardiovascular disease, including myocardial infarction and stroke, the major causes of death in Europe. My group and others discovered, that thrombosis and inflammation are not to be considered separate processes. They are tightly interrelated and synergize in immune defence, but also in inflammatory and thrombotic diseases in a process we termed immunothrombosis. Targeting this synergism has great potential to identify innovative and unconventional strategies to more specifically prevent undesired activation of thrombotic and inflammatory pathways. However, this requires a deeper mechanistic understanding of immunothrombosis. I recently identified two ground-breaking novel immunothrombotic principles: I discovered that platelets have the ability to migrate autonomously, which assists immune cells in fighting pathogens. Further, I revealed that immune cells play a central role in controlling the production of platelets from their megakaryocyte precursors. The physiological and pathophysiological relevance of both processes is unclear. This is the starting point and focus of the IMMUNOTHROMBOSIS project. My aim is to define how platelets use their ability to migrate to support immune cells in protection of vascular integrity (objective 1) and to identify the contribution of platelet migration to different cardiovascular diseases involving immunothrombotic tissue damage (objective 2). Finally, I will clarify how inflammatory responses feedback to the production of thrombotic effectors and dissect inflammatory mechanisms that control platelet production (objective 3). IMMUNOTHROMBOSIS will identify new options for specific prevention or treatment of thrombotic and inflammatory cardiovascular diseases.
The overall aim of the IMMUNOTHROMBOSIS project is to clarify the mechanisms underlying the recently identified synergism between thrombosis and inflammation. Thrombus formation and inflammation are vital host responses that ensure homeostasis, but can also drive cardiovascular disease, including myocardial infarction and stroke, the major causes of death in Europe. My group and others discovered, that thrombosis and inflammation are not to be considered separate processes. They are tightly interrelated and synergize in immune defence, but also in inflammatory and thrombotic diseases in a process we termed immunothrombosis. Targeting this synergism has great potential to identify innovative and unconventional strategies to more specifically prevent undesired activation of thrombotic and inflammatory pathways. However, this requires a deeper mechanistic understanding of immunothrombosis. I recently identified two ground-breaking novel immunothrombotic principles: I discovered that platelets have the ability to migrate autonomously, which assists immune cells in fighting pathogens. Further, I revealed that immune cells play a central role in controlling the production of platelets from their megakaryocyte precursors. The physiological and pathophysiological relevance of both processes is unclear. This is the starting point and focus of the IMMUNOTHROMBOSIS project. My aim is to define how platelets use their ability to migrate to support immune cells in protection of vascular integrity (objective 1) and to identify the contribution of platelet migration to different cardiovascular diseases involving immunothrombotic tissue damage (objective 2). Finally, I will clarify how inflammatory responses feedback to the production of thrombotic effectors and dissect inflammatory mechanisms that control platelet production (objective 3). IMMUNOTHROMBOSIS will identify new options for specific prevention or treatment of thrombotic and inflammatory cardiovascular diseases.
Project acronym inCREASE
Project Coding for Security and DNA Storage
Researcher (PI) Antonia Wachter-Zeh
Host Institution (HI) TECHNISCHE UNIVERSITAET MUENCHEN
Summary Communication and data storage systems are indispensable parts of our every-day life. However, these systems deal with severe challenges in security and reliability. Security is important whenever a user communicates or stores sensitive data, e.g., medical information; reliability has to be guaranteed to be able to transmit or store information while noise occurs. Algebraic codes (ACs) are a powerful means to achieve both. Within inCREASE, I will construct and evaluate special codes for security applications and DNA storage. The tasks are structured into three work packages: (1) post-quantum secure code-based cryptosystems, (2) secure key regeneration based on ACs, (3) ACs for DNA-based storage systems. The focus of inCREASE lies on innovative theoretical concepts. The goal of work package (1) is to investigate and design code-based cryptosystems; one promising idea is to apply insertion/deletion correcting codes. The security of these systems will be analysed from two points of view: structural attacks on the algorithms and hardware implementations with side-channel attacks. Secure cryptographic key regeneration is the goal of (2) and can be achieved by physical unclonable functions (PUFs). Here, ACs are necessary to reproduce the key reliably. This project will study the error patterns that occur in PUFs, model them theoretically, and design suitable coding schemes. The investigation on (3) will start with a study of the data of existing DNA storage systems. The outcome will be an error model that will include insertions, deletions, substitutions, and duplications. Therefore, inCREASE will design ACs for these error types. This will be especially challenging regarding the mathematical concepts. These codes will be evaluated by simulations and using data sets of DNA storage systems. This project is high risk/high gain with impact not only to storage and security, but to the methodology as well as other areas such as communications.
Communication and data storage systems are indispensable parts of our every-day life. However, these systems deal with severe challenges in security and reliability. Security is important whenever a user communicates or stores sensitive data, e.g., medical information; reliability has to be guaranteed to be able to transmit or store information while noise occurs. Algebraic codes (ACs) are a powerful means to achieve both. Within inCREASE, I will construct and evaluate special codes for security applications and DNA storage. The tasks are structured into three work packages: (1) post-quantum secure code-based cryptosystems, (2) secure key regeneration based on ACs, (3) ACs for DNA-based storage systems. The focus of inCREASE lies on innovative theoretical concepts. The goal of work package (1) is to investigate and design code-based cryptosystems; one promising idea is to apply insertion/deletion correcting codes. The security of these systems will be analysed from two points of view: structural attacks on the algorithms and hardware implementations with side-channel attacks. Secure cryptographic key regeneration is the goal of (2) and can be achieved by physical unclonable functions (PUFs). Here, ACs are necessary to reproduce the key reliably. This project will study the error patterns that occur in PUFs, model them theoretically, and design suitable coding schemes. The investigation on (3) will start with a study of the data of existing DNA storage systems. The outcome will be an error model that will include insertions, deletions, substitutions, and duplications. Therefore, inCREASE will design ACs for these error types. This will be especially challenging regarding the mathematical concepts. These codes will be evaluated by simulations and using data sets of DNA storage systems. This project is high risk/high gain with impact not only to storage and security, but to the methodology as well as other areas such as communications.
Project acronym IntegraBrain
Project Integrated Implant Technology for Multi-modal Brain Interfaces
Researcher (PI) Ivan MINEV
Host Institution (HI) TECHNISCHE UNIVERSITAET DRESDEN
Summary Bioelectronic medicine may soon replace systemic drugs for treating some chronic conditions. The clinician will implant a miniature laboratory to deliver and coordinate a multi-modal treatment program directly at the affected tissue. The technology to bring this vision to the clinic is not yet available. The IntegraBrain project will contribute by building an implantable network of sensors and actuators. Actuators will deploy electricity, light, drugs and thermal energy as modalities of the therapeutic program, while sensors will monitor its progress. A key technological advance will be a method for direct writing of the sensor-actuator network. To achieve this, we will develop a palette of functional inks where each ink supports one of the therapeutic modalities. The technology has the potential to be tailored for applications in soft tissue organs, especially in the nervous system, where injury or degeneration can result in chronic disability. We will apply IntegraBrain technology in two niches of the nervous system in rodents. In the central nervous system, we will demonstrate seizure control by multi-modal neuromodulation. In the peripheral nervous system, we will demonstrate reversible block and excitation. For the first time, we will observe if multi-modal neuromodulation leads to synergistic effects on the nervous system. With the IntegraBrain project, we hope to catalyse pre-clinical development of implantable human-machine interfaces for therapeutic applications.
Bioelectronic medicine may soon replace systemic drugs for treating some chronic conditions. The clinician will implant a miniature laboratory to deliver and coordinate a multi-modal treatment program directly at the affected tissue. The technology to bring this vision to the clinic is not yet available. The IntegraBrain project will contribute by building an implantable network of sensors and actuators. Actuators will deploy electricity, light, drugs and thermal energy as modalities of the therapeutic program, while sensors will monitor its progress. A key technological advance will be a method for direct writing of the sensor-actuator network. To achieve this, we will develop a palette of functional inks where each ink supports one of the therapeutic modalities. The technology has the potential to be tailored for applications in soft tissue organs, especially in the nervous system, where injury or degeneration can result in chronic disability. We will apply IntegraBrain technology in two niches of the nervous system in rodents. In the central nervous system, we will demonstrate seizure control by multi-modal neuromodulation. In the peripheral nervous system, we will demonstrate reversible block and excitation. For the first time, we will observe if multi-modal neuromodulation leads to synergistic effects on the nervous system. With the IntegraBrain project, we hope to catalyse pre-clinical development of implantable human-machine interfaces for therapeutic applications.
Project acronym LRC
Project Laser Resonance Chromatography of Superheavy Metals
Researcher (PI) Mustapha Laatiaoui
Host Institution (HI) JOHANNES GUTENBERG-UNIVERSITAT MAINZ
Summary This project aims at developing a novel method of optical spectroscopy to study the wholly unexplored atomic structure of the superheavy transition metals, starting with element 103, lawrencium (Lr). My team will experimentally identify optical spectral lines that will serve as fingerprints in the search for superheavy elements in the universe. The spectral lines are strongly influenced by relativistic and quantum electrodynamic effects and thus will constitute powerful benchmarks for atomic modeling incorporated within this project. Furthermore, since the nuclear charge distribution influences the atomic structure, our experimental data will advance our understanding of the effects of nuclear shells and deformations on the stability of radionuclides at the top of the Segré chart. While I recently opened up the atomic structure of element 102, nobelium, the new challenges faced are the refractory nature of the elements, which lay ahead, coupled with shorter half-lives and decreasing production yields. I propose to overcome these by developing an ultra-sensitive and fast Laser Resonance Chromatography (LRC) to set the new standard in optical spectroscopy. The LRC method combines the element selectivity and spectral precision of laser spectroscopy with cutting-edge technology of ion-mobility mass spectrometry. Based on high-accuracy atomic calculations, my team will optically probe the 1S0-3P1 ground-state transition in singly-charged 255Lr ions and record the distinct arrival times of the ions after passing a drift tube to identify the laser resonance signal. We will perform the experiments at leading in-flight facilities such as the GSI velocity filter SHIP and the new GANIL separator S3. Crucially, the LRC method will be insensitive to physicochemical properties and tolerant of the decreasing yields with increasing atomic number. This paves the way for atomic structure studies of the superheavy elements, in particular, those of refractory nature beyond lawrencium.
This project aims at developing a novel method of optical spectroscopy to study the wholly unexplored atomic structure of the superheavy transition metals, starting with element 103, lawrencium (Lr). My team will experimentally identify optical spectral lines that will serve as fingerprints in the search for superheavy elements in the universe. The spectral lines are strongly influenced by relativistic and quantum electrodynamic effects and thus will constitute powerful benchmarks for atomic modeling incorporated within this project. Furthermore, since the nuclear charge distribution influences the atomic structure, our experimental data will advance our understanding of the effects of nuclear shells and deformations on the stability of radionuclides at the top of the Segré chart. While I recently opened up the atomic structure of element 102, nobelium, the new challenges faced are the refractory nature of the elements, which lay ahead, coupled with shorter half-lives and decreasing production yields. I propose to overcome these by developing an ultra-sensitive and fast Laser Resonance Chromatography (LRC) to set the new standard in optical spectroscopy. The LRC method combines the element selectivity and spectral precision of laser spectroscopy with cutting-edge technology of ion-mobility mass spectrometry. Based on high-accuracy atomic calculations, my team will optically probe the 1S0-3P1 ground-state transition in singly-charged 255Lr ions and record the distinct arrival times of the ions after passing a drift tube to identify the laser resonance signal. We will perform the experiments at leading in-flight facilities such as the GSI velocity filter SHIP and the new GANIL separator S3. Crucially, the LRC method will be insensitive to physicochemical properties and tolerant of the decreasing yields with increasing atomic number. This paves the way for atomic structure studies of the superheavy elements, in particular, those of refractory nature beyond lawrencium.
Project acronym NU-CLEUS
Project Exploring coherent neutrino-nucleus scattering with gram-scale cryogenic calorimeters
Researcher (PI) Raimund STRAUSS
Summary ν-cleus will be a new multi-purpose table-top experiment aimed at the first exploration of coherent neutrino-nucleus scattering (CNNS) at a nuclear power reactor. Our novel detector technology will achieve an unprecedentedly high sensitivity to new physics within and beyond the Standard Model of Particle Physics, with an enormous discovery potential. The new method is not only complementary to competing approaches, but superior in terms of performance, cost and size. The ultra-low threshold character of my experiment will allow a determination of the Weinberg angle at MeV-scale momentum transfers and the first direct search for eV-scale sterile neutrinos via CNNS. We will significantly improve the sensitivity for a neutrino magnetic dipole moment, unravel anomalies in the reactor antineutrino spectrum and test new models for exotic neutral currents. My research on gram-scale cryogenic calorimeters (gramCCs) has resulted in a recent breakthrough: we achieved the world-best energy threshold for nuclear-recoils of 19.7eV, one order of magnitude lower than for previous detectors. I propose to operate gramCCs within a fiducial-volume cryogenic detector. This completely new detector concept is suited for an above-ground operation of excellent performance while backgrounds are significantly suppressed. Located at a nuclear power reactor ν-cleus will achieve a signal-to-background ratio of ~10^3 - a unique situation in neutrino physics. This will enable a rapid discovery of CNNS within a few weeks. ν-cleus will have enormous impact on modern physics and future technologies. It will be a prototype for next-generation, high-precision solar neutrino experiments and guarantees a technological spin-off for reactor safeguards and non-proliferation measures. With this ERC grant I will set up a high-class research team with world-leading expertise in cryogenic detectors and low-background techniques, which will ensure Europe's role as a pioneer in this new field.
ν-cleus will be a new multi-purpose table-top experiment aimed at the first exploration of coherent neutrino-nucleus scattering (CNNS) at a nuclear power reactor. Our novel detector technology will achieve an unprecedentedly high sensitivity to new physics within and beyond the Standard Model of Particle Physics, with an enormous discovery potential. The new method is not only complementary to competing approaches, but superior in terms of performance, cost and size. The ultra-low threshold character of my experiment will allow a determination of the Weinberg angle at MeV-scale momentum transfers and the first direct search for eV-scale sterile neutrinos via CNNS. We will significantly improve the sensitivity for a neutrino magnetic dipole moment, unravel anomalies in the reactor antineutrino spectrum and test new models for exotic neutral currents. My research on gram-scale cryogenic calorimeters (gramCCs) has resulted in a recent breakthrough: we achieved the world-best energy threshold for nuclear-recoils of 19.7eV, one order of magnitude lower than for previous detectors. I propose to operate gramCCs within a fiducial-volume cryogenic detector. This completely new detector concept is suited for an above-ground operation of excellent performance while backgrounds are significantly suppressed. Located at a nuclear power reactor ν-cleus will achieve a signal-to-background ratio of ~10^3 - a unique situation in neutrino physics. This will enable a rapid discovery of CNNS within a few weeks. ν-cleus will have enormous impact on modern physics and future technologies. It will be a prototype for next-generation, high-precision solar neutrino experiments and guarantees a technological spin-off for reactor safeguards and non-proliferation measures. With this ERC grant I will set up a high-class research team with world-leading expertise in cryogenic detectors and low-background techniques, which will ensure Europe's role as a pioneer in this new field.
Project acronym NUAGE
Project Nucleolar regulation of longevity
Researcher (PI) Adam Antebi
Summary Research over the last few decades has revealed that animal life span is malleable and regulated by conserved metabolic signaling pathways, including reduced insulin/IGF signaling, mTOR, mitochondrial function, dietary restriction, and signals from the reproductive system. Whether these various pathways converge on common processes, however, has remained elusive. We recently discovered the nucleolus to be a crucial focal point of regulation in all these pathways. The nucleolus is a subnuclear organelle dedicated to rRNA production and ribogenesis, but also controls assembly of other ribonucleoprotein complexes including spliceosomes, signal recognition particle, small RNA processing, stress granules, and responds to growth and stress signaling. Remarkably we found that small nucleoli are a cellular hallmark of longevity in diverse species, and a correlate of metabolic health in humans. At the molecular level, long-lived animals show reduced levels of the nucleolar ribosomal RNA methylase, fibrillarin (FIB-1), and knockdown of C. elegans FIB-1 reduces nucleolar size, extends life span, and enhances innate immunity. Conversely, knockout of NCL-1/TRIM2 expands nucleolar size, suppresses life extension of major longevity pathways, and renders animals pathogen sensitive, revealing key regulators of nucleolargenesis, immunity and longevity. Here I propose to (Aim 1) clarify the mechanism of action of NCL-1, FIB-1 and interacting molecules (2) perform novel genetic screens for nucleolargenesis in C. elegans (3) uncover global transcriptomic and proteomic changes induced by NCL-1 and FIB-1 and survey several candidate nucleolar processes in regulating longevity and immunity (4) probe NCL-1/TRIM2 regulation of longevity in the short-lived killifish, Notobranchius furzeri, and develop nucleolar biomarkers of metabolic health in humans. These groundbreaking studies should illuminate how conserved signaling pathways work through the nucleolus to regulate health and life span.
Research over the last few decades has revealed that animal life span is malleable and regulated by conserved metabolic signaling pathways, including reduced insulin/IGF signaling, mTOR, mitochondrial function, dietary restriction, and signals from the reproductive system. Whether these various pathways converge on common processes, however, has remained elusive. We recently discovered the nucleolus to be a crucial focal point of regulation in all these pathways. The nucleolus is a subnuclear organelle dedicated to rRNA production and ribogenesis, but also controls assembly of other ribonucleoprotein complexes including spliceosomes, signal recognition particle, small RNA processing, stress granules, and responds to growth and stress signaling. Remarkably we found that small nucleoli are a cellular hallmark of longevity in diverse species, and a correlate of metabolic health in humans. At the molecular level, long-lived animals show reduced levels of the nucleolar ribosomal RNA methylase, fibrillarin (FIB-1), and knockdown of C. elegans FIB-1 reduces nucleolar size, extends life span, and enhances innate immunity. Conversely, knockout of NCL-1/TRIM2 expands nucleolar size, suppresses life extension of major longevity pathways, and renders animals pathogen sensitive, revealing key regulators of nucleolargenesis, immunity and longevity. Here I propose to (Aim 1) clarify the mechanism of action of NCL-1, FIB-1 and interacting molecules (2) perform novel genetic screens for nucleolargenesis in C. elegans (3) uncover global transcriptomic and proteomic changes induced by NCL-1 and FIB-1 and survey several candidate nucleolar processes in regulating longevity and immunity (4) probe NCL-1/TRIM2 regulation of longevity in the short-lived killifish, Notobranchius furzeri, and develop nucleolar biomarkers of metabolic health in humans. These groundbreaking studies should illuminate how conserved signaling pathways work through the nucleolus to regulate health and life span.
Project acronym SpreadMRI
Project Ultra-Fast, Spread-Spectrum Magnetic Resonance Imaging
Researcher (PI) Klaus SCHEFFLER
Summary Imaging speed is a key factor to capture rapid changes at high spatial and temporal resolution. A major limitation of magnetic resonance (MR) imaging is its rather low speed compared to other modalities like ultra sound or computerized tomography. We aim to explore two novel concepts to boost MR imaging speed by another order of magnitude compared to existing techniques. SpreadMRI fundamentally steps beyond current concepts of image encoding by exploiting a spectral spin modulation that so far has not been utilized. SpreadMRI is based on the rapid and local modulation of magnetic fields produced by current loops and/or radiofrequency (RF) loops. Applied spectral modulations are in the MHz range bridging the low-frequency band of switched gradients (kHz) and the 100 MHz range of the Larmor frequency. SpreadMRI spreads the bandwidth of gradient-encoded spin frequencies using distinct carrier frequencies originating from a certain region of the object. This spatially unique information will then be used to disentangle parts of the object, and thus to drastically boost imaging speed. Approaching this intermediate frequency band requires to address several basic research questions related to image reconstruction, electromagnetic coupling, spin Physics and possible biological effects. Based on theoretical analysis and exhaustive electromagnetic simulations of dedicated current loop and RF coil arrangements, including variants of different modulation patterns, several types of SpreadMRI coils for human head imaging at 9.4T will be developed and applied for high temporal and spatial functional brain imaging. The specific approach of SpreadMRI will lead to major changes in the hard- and software environment of current MR-scanners. It will not only provide new insight within the areas covered by the proposal, but will definitely benefit conventional MR diagnostic by enabling new applications with a simultaneous reduction of motion artifacts and increased patient throughput.
Imaging speed is a key factor to capture rapid changes at high spatial and temporal resolution. A major limitation of magnetic resonance (MR) imaging is its rather low speed compared to other modalities like ultra sound or computerized tomography. We aim to explore two novel concepts to boost MR imaging speed by another order of magnitude compared to existing techniques. SpreadMRI fundamentally steps beyond current concepts of image encoding by exploiting a spectral spin modulation that so far has not been utilized. SpreadMRI is based on the rapid and local modulation of magnetic fields produced by current loops and/or radiofrequency (RF) loops. Applied spectral modulations are in the MHz range bridging the low-frequency band of switched gradients (kHz) and the 100 MHz range of the Larmor frequency. SpreadMRI spreads the bandwidth of gradient-encoded spin frequencies using distinct carrier frequencies originating from a certain region of the object. This spatially unique information will then be used to disentangle parts of the object, and thus to drastically boost imaging speed. Approaching this intermediate frequency band requires to address several basic research questions related to image reconstruction, electromagnetic coupling, spin Physics and possible biological effects. Based on theoretical analysis and exhaustive electromagnetic simulations of dedicated current loop and RF coil arrangements, including variants of different modulation patterns, several types of SpreadMRI coils for human head imaging at 9.4T will be developed and applied for high temporal and spatial functional brain imaging. The specific approach of SpreadMRI will lead to major changes in the hard- and software environment of current MR-scanners. It will not only provide new insight within the areas covered by the proposal, but will definitely benefit conventional MR diagnostic by enabling new applications with a simultaneous reduction of motion artifacts and increased patient throughput.


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Saint-Laurent-de-Jourdes è un comune francese di 168 abitanti situato nel dipartimento della Vienne nella regione della Nuova Aquitania.

Società

Evoluzione demografica

Note

Altri progetti

Saint-Laurent-de-Jourdes

redpajama_set_name: RedPajamaWikipedia


The ViewSonic VG2719-2K is a 27' WQHD full ergonomic monitor with rich and accurate colour performance for graphic design, for office work and for home entertainment. Featuring a WQHD resolution panel (2560 x 1440) and SuperClear IPS-Type technology, content is displayed in refined detail from virtually any viewing angle. WQHD resolution displays more content on the screen than FHD resolution, reduces scrolling and boosts productivity. The 10-bit colour depth, which produces 1.07 billion colours, and the 99% sRGB colour coverage ensures vivid colour reproduction for web content editing, graphic design or photo editing. VG2719-2K's ergonomic design offers a wide range of tilt, swivel, pivot, and height adjustments, while narrow bezel gives the monitor a clean aesthetic and is convenient for setting up multiple monitors side-by-side to improve workflow management. In addition, with optional ViewSplit software, users can divide, organize, and customize the screen layout for better workflow efficiency. This 27' WQHD 2560 x 1440 panel gives users the benefit of greater image detail, fitting more content onto the screen, with up to 70% more on-screen desktop space than a standard Full HD (1920 x 1080) display. Enjoy rich, vivid colours with consistent brightness, no matter your vantage point. With SuperClear IPS-Type panel technology, VG2719-2K monitors deliver the same image quality whether you are looking at the screen from above, below, the front, or the side.


Celebrate the end of the school year with a special family campout at Stone Barn Farm at Allens Pond Wildlife Sanctuary! We'll enjoy some camping fun, games and fireside s'mores. A special evening hike will bring us around the grounds in search of local wildlife and seasonal phenomena.
All you need to bring is your camping gear (tarp highly recommended as a ground barrier underneath), refillable water bottles and beach gear – there is free time that can be spent at one of our local beaches each afternoon. Insect repellant and sunscreen are also recommended.
We will provide a BBQ dinner, fireside s'mores and breakfast. If you have any dietary restrictions, please let us know. Feel free to pack any nut-free snacks.
Registration required by June 26th.


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Hearthstone Rise of Shadows release time and what to expect
9-4-2019 Games Online Metro Uk News 95 Print
(Picture: Blizzard Entertainment)
Hearthstone's newest expansion pack comes out today with plenty of new cards for players to try out.
The theme of the new collection is being evil, as it brings together many of the game's biggest villains.
It will be Hearthstone's first-ever year-long story-line which will allow players to join the League of E.V.I.L by being villains in the game.
The new cards will include new mechanics and abilities including schemes, lackeys and twinspells.
Here is everything that you need to know about the Rise of Shadows and when you can get it.
When is the Heartstone Rise of Shadows release time?
The new Hearthstone expansion arrives on Tuesday 9 April at around 6pm in the UK.
These are the full estimated release times –
North America: 9 April 10:00 PDT / 13.00 EST
Europe: 9 April 17:00 GMT / 18:00 BST
Asia: 10 April 02:00 KS / 01:00 CST
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What to expect in the Rise of Shadows expansion?
Rise of Shadows will provide a year-long story line for players to progress through with new quests and cards to use.
Some of the villains spotlighted in the new expansion include Dr. Boom, Madam Lazul and King Togwaggle.
New cards will include 1/1 minions known as Lackeys who have special battlecry abilities that can help strengthen the rest of your deck.
The collection will also include new spell cards known as Schemes that can build up in strength over time when they are in your hand, as well as twinspells that create copies of themselves after they are used.
The standard bundle of 50 packs will cost £44.99, while the mega bundle of 80 packs is available to buy for £69.99.
Players who pre-purchase a standard bundle will receive the Jewel of Lazul card back as well as a random Legendary card, but if you get a mega bundle then you will also receive the Madam Lazul Priest Hero.
Players who log into the game during the launch of the new expansion will also receive the Archmage Vargoth Legendary card.
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redpajama_set_name: RedPajamaCommonCrawl


After we were finished with Assisi, our next mission was to relax for a few days on the beautiful Amalfi Coast – specifically in Sorrento. Our Airbnb accommodation was a large apartment with an even larger view!
There were so many things to see. This walled village with Naples in the background. Beneath the village is the main road into Sorrento with amazing views as you drive along the coast line.
There were small castles and watch towers set up to watch over the shores – and we worked out that if you actually sat in one for a day you could watch the sunset and sunrise from the one location!
Atop another hill is a massive cross that looks over the whole of Sorrento.
The houses and shops that were actually right on the beach were in the shadow of a giant cliff, but right on the water. You could see cruise ships go past from time to time.
In between the gap of two mountains, you can see the shadowy top of Mount Vesuvius – the volcano that buried Pompeii. There was also a small village nestled in the crook of the mountains with their view Vesuvio on one side, the Sorrento valley on the other.
That night we watched a storm roll in and play with the colours of the clouds out above the water.
We also watched the sun set over the valley and the colours change dramatically.
And then at night, the lights came on and showed us the beautiful buildings in the valley.
And the coolest thing is that we didn't leave the apartment all day. All the above photos (no filter) were taken from the terrace of the apartment we stayed in. It really is the most amazing place.
Tomorrow we will be venturing out to see the sights – more photos then!


3 beds | 2 baths | 1,357 sqft | $232 per sq. ft.
Step into this one of a kind halfplex that feels like a single family home! Lot's of privacy in this low maintenance backyard with a beautiful deck surrounded by many trees. This home is renovated from the flooring, dual pane windows, paint, appliances, plugs, switches, baseboards, granite counter tops, sinks, cabinets, back splash, light fixtures, baseboards, plumbing fixtures and many more! Plus the front and garage door have a custom paint job to give a rustic look to it. Come view this property soon, it will go fast!
EX: I found this listing on PMZ.com. Please send me more information about 8812 Kelsey Dr, Elk Grove, CA 95624-1867. Thank you.


I just formated my disk, and had a new computer but I had my old hard drives installed in the new system. What I have is 2 back ups that I would schedule a backup every 2 weeks for my outlook mail program. Now that I have a fresh install, I can't figure out how to get my old mail on my new outlook 2003. How do I do this?
If you have backups then you would want to restore the files from your backups to then import into Outlook 2003 on your current PC. What backup software are you using?


A dandy or how Player's Cigarettes described him - a young gallant of mid-17th century is more of a collective image rather than a certain figure. Two love-locks, in other words curls of hair worn on the temple of forehead, are considered to be a distinctive feature of dandies of the 1640-1650's, the time when Charles I was still owning the throne of England. It's worth mentioning that such, as we call it these days, beauty trend brought along a lot of controversy regarding the fact that once masculine dress of the Cavalier was turned into effeminate one. Debates over this topic can still be continued these days, but we all know that real dandies care more about their looks rather than what others may say, aren't they?


Intel has released more information regarding the availability of Skylake, their successor to Broadwell. The first surprise is that Skylake is still on track for an end of year release in 2015. After the delays with Broadwell, many thought that the Skylake roll-out would be similarly pushed back. Because of the lack of delay, the first Skylake chips will ship to manufacturers only a few months after the general availability of desktop Broadwell models.
Another surprise is that the Intel Gen 9 graphics completely do away with VGA connector support. That's right, the 15 pin analog "D" shaped connector is finally getting nixed - at least from the built-in Intel graphics.
Unlike Broadwell, which only supports DDR4 memory on the server and the extreme versions, Skylake will finally support DDR4 on consumer rated models.
I haven't posted a progress report in a while, and I wouldn't expect everyone to follow the mailing list, so here's a short list of the latest features of the site.
Journals are now enabled for all user accounts! Similar to the venerable Slashcode journal, the Pipedot version allows you to write your extended thoughts and post them in the familiar story-like form – complete with comments and community moderation. An example journal story can be found here.
If you where previously using the root of your user page (e.g. http://bryan.pipedot.org/) to display your feed page, you will need to instead append "/feed/" to the end of your shortcuts (i.e. http://bryan.pipedot.org/feed/) Sorry for the inconvenience.
Originally, I adopted a similar system as Slashcode, where each object gets an auto-incrementing integer. However, this global increment is just not usable in terms of a distributed system. And so, after rewriting a large chunk of the site, objects are now given a unique ID that looks more like a Message-ID from Email and Usenet messages.
All items (stories, comments, polls, etc...) on this site are now assigned a short code similar to those seen on Twitter (t.co), Google (goo.gl), bit.ly, and others - except that it's built into the site and automatic.
These links are useful for character limited services, such as Twitter posts, as well as any other scenario where a shorter link would be appreciated. Also, like other link shortener services, you can tack a "+" on to the end of the short link to get statistics on who has clicked it.
I thought the SoylentNews federation would be a cool mini-project. Combine the efforts of two nearly identical sites while improving the resiliency of both. If you missed it (the feature was online for less than a day) the idea was to combine all stories and posts from both sites into one feed. However, I seem to have greatly underestimated the disdain for such a function. Because I'm not overly fond of receiving that many threats and hate mails in a single day, I've simply turned it off and removed all references to SoylentNews in the code.
Pipecode has long supported a profile picture. This feature allows you to show off your mugshot on your user page and various other places. Of course, thus far, only 4 people had managed to find and update their picture. To help prevent a missing image when viewing a profile, I've added Gravatar support to automatically populate profile images. If you do not have a Gravatar, you can still manually update your profile image with the old method. You can also disable Gravatar updates to your picture by unchecking the Gravatar option on your profile settings page.
Nearly all images, icons, and logos on the site now support "retina" displays. So if you are blessed by a device with an incredibly high DPI screen, the graphics here should all look especially crisp.
Truecrypt is dead. Long Live DoxBox.
tdk (of s'qute) has announced a project that he has been working on the last couple of months that is of interest to those still using Windows.
Easy to use, with a 'wizard' for creating new 'DoxBoxes'.
Full transparent encryption, DoxBoxes appear as removable disks in Windows Explorer.
Explorer mode lets you access DoxBoxes when you don't have admin permissions.
Compatible with Linux encryption, Cryptoloop "losetup", dm-crypt, and LUKS. Linux shell scripts support deniable encryption on Linux.
Supports smartcards and security tokens.
Encrypted DoxBoxes can be a file, a partition, or a whole disk.
Runs on Windows Vista onwards (see note below for 64 bit versions).
Supports numerous hash (including SHA-512, RIPEMD-320, Tiger) and encryption algorithms (Including AES, Twofish, and Serpent) in several modes (CBC, LRW, and XTS), giving more options than any other disk encryption software.
Optional 'key files' let you use a thumb-drive as a key.
Portable mode doesn't need to be installed and leaves little trace on 3rd party PCs (administrator rights needed).
Deniable encryption protects you from 'rubber hose cryptography'.
The newest specification for the USB 3.1 Type-C connector is now finalized, finally bringing improvements found in other cables (such as Apple's Lightning cable) to the USB standard.
Although I know some people will undoubtedly whine about yet another USB connector, these changes are long overdue and very welcome in my opinion. Previous USB connectors have ranged from problematic (Mini-B) to unwieldy (USB 3.0 Micro-B) and badly needed replacement.
AMD will start selling a range of SSD products under the Radeon brand later this year. However, with the flash chips sources from Toshiba (19nm) and controller sourced from Indilinx (Barefoot 3) AMD isn't exactly bringing anything new to the table.
Today, Digia announced that they will spin off the QT project into its own dedicated company. In 2012, Digia acquired Qt from Nokia and has been maintaining the enterprise and open source versions at qt.digia.com and qt-project.org, respectively. Merging the two branches and forming a dedicated company will allow the developers to focus 100% on Qt while separating development costs from Digia.
Version 14 of XBMC, the popular HTPC software, is changing its name to "Kodi" to further distance itself from its Xbox origins.
Six years have passed since the Xbox Media Center became XBMC, and simply put, "XBMC" fits less now than it did even in 2008. The software only barely runs on the original Xbox, and then only because some clever developers are still hacking on that platform. It has never run on the Xbox 360 or Xbox One.
Beyond the nonsensical nature of the software's name, there is a secondary issue. Because "XBMC" was originally based on the name Xbox, the developers of the software (that's us) have never had any sort of legal control over the use of its name, which has resulted in a whole slew of problems.
Have you seen ASUS's new $150 x86 tablet and thought to yourself: how can it possibly be so cheap?
Well here's your answer. It just may be because Intel is paying manufacturers to use its chips. That's bad news for Intel. Turns out, because Intel's Bay Trail Atom processors don't have as much functionality integrated onto the chip as the more common ARM SOCs (system on a chip), it creates a higher "bill of materials" for tablet makers. Cash-rich Intel is covering the difference in cost by simply reimbursing the manufacturers for the extra components needed. That might be a stop-gap measure to ensure Intel stays "in the game" where tablets manufacturers are concerned, but a long range strategy it is not.
In the meantime, this is a good time to scoop up a cheapo tablet!
Tesla founder and CEO Elon Musk has revealed plans for a new electric BMW 3 Series rival, including its name – Tesla Model 3. There were rumours that a new smaller Tesla Gen III model was to be called Model E, but in one of his most candid interviews yet, Musk revealed why he had to have a rethink on the name.
Gizmodo thinks this model will be a game changer. Why? For starters: it's a consumer model, priced at $35,000 (a third the price of previous models), and the range is double previous models at 200 miles. Lastly, now that they're opening up the battery tech there is an overt effort to make sure you can charge one of these things anywhere, anytime. Check out the Gizmodo article for some breathless comparisons to Henry Ford's Model T. But it does look like getting a Tesla is about to become a much more obvious option for the casual consumer.
Once hailed as the most free and widest used X toolkit, the future of GTK+ now looks dire. The gnome developers have essentially highjacked the latest version, GTK3, and are actively destroying all ability of non-gnome users from using this once popular toolkit. I find this very unsettling, as I have developed a number of my own desktop applications using GTK+ through all three of its major versions. I've always preferred GTK over QT, but with some of the recent changes, I'm starting to change my mind.
Of course, I'm hardly alone in this opinion as many other projects have abandoned GTK in the recent months. Take Audacious, for example. This GTK music player has had increasing troubles with the gnome developers screwing things up. So many troubles that they are now planning on switching toolkits rather than further deal with the upstream management. Although they had a functional GTK3 port, they've officially reverted back to GTK2 until they can properly refactor their entire program into QT.
I've been a happy user of the XFCE desktop environment for the last few years. This light and easy to use UI gets out of the way and just plain works. However, the interface toolkit of XFCE is tied to GTK2 and its authors have no clear upgrade path. A similar project, LXDE, has also seen the writing on the wall and are well into a rewrite project that switches their preferred toolkit from GTK to QT.


text:
\section{Introduction}

\subsection{Firing Squad Synchronization Problem and the Less-State Race}

\label{intro}
The Firing Squad Synchronization Problem (FSSP) was proposed by John Myhill in 1957.
The goal is to find a single cellular automaton that synchronizes any one-dimensional horizontal array of an arbitrary number of cells.
More precisely, one consider that at initial time, all cells are inactive (i.e. in the \emph{quiescent state}) except for the leftmost cell which is in the general (i.e. in the \emph{general state}).
One wants the evolution of the cellular automaton to lead all cells to transition to a special state (i.e. the \emph{synchronization} or \emph{firing state}) \emph{for} the first time \emph{at} the same time.
This time $t_s$ is called the synchronization time and it is known that its minimal possible value is $2n - 2$ where $n$ is the number of cells.

For this problem, many minimum-time solutions were proposed using different approaches.
As indicated in~\cite{DBLP:journals/amc/UmeoHNIS18}, the first one was proposed by Goto in 1962~\cite{DBLP:journals/amc/UmeoHNIS18} with many thousands of states, followed by Waksman in 1966~\cite{DBLP:journals/iandc/Waksman66}, Balzer in 1967~\cite{DBLP:journals/iandc/Balzer67}, Gerken in 1987~\cite{10012108193}, and finally Mazoyer in 1987~\cite{DBLP:journals/tcs/Mazoyer87} who presented respectively a 16-state, 8-state, 7-state and 6-state minimum-time solution, with no further improvements since 1987.
Indeed, Balzer~\cite{DBLP:journals/iandc/Balzer67} already shows that there are no 4-state minimal-time solutions, latter confirmed by Sanders~\cite{DBLP:conf/parcella/Sanders94} through an exhaustive search and some corrections to Balzer's work.
Whether there exist any 5-state minimumal-time solution or not is still an open question.

Note that all these solutions use a ``divide and conquer'' strategy.
Goto's solution were pretty complex with two types of divisions.
The following ones used a ``mid-way'' division but Mazoyer's 6-state solution uses for the first time a ``two-third'' type of division\footnote{See Figure~\ref{fig:half} for a mid-way division, and Figure~\ref{fig:two-third} for a two-third division}.
In 2018, Clergue, Verel and Formenti~\cite{DBLP:journals/asc/ClergueVF18} generated 718 new 6-state solutions using an Iterated Local Search algorithm to explore the space of 6-state solutions on a cluster of heterogeneous machines:
717 of these solutions use a ``mid-way'' division, and only one use a ``two-third'' division.

\subsection{Context of the Initial Motivations}

In 2012, Maignan and Yunes proposed the methodology of \emph{cellular fields} to described formally the high-level implementation of a CA, and also formally the generation of the ``low-level'' transition table.
One of the expected benefits was to have an infinite CA cleanly modularized into many cellular fields with clear semantical proof of correctness together with a correctness-preserving reduction procedure into a finite state CA \cite{DBLP:conf/acri/MaignanY12} using a particular kind of cellular field, ``reductions''.
This is very similar to what happen in usual computer programming where one writes in a high-level language then transform the code into assembly using a semantic-preserving transformation, \emph{i.e.}~ a compiler.
In 2014, they made precise a particular reduction of the infinite CA into 21 states~\cite{DBLP:conf/acri/MaignanY14,DBLP:journals/jca/MaignanY16}.

From theses works and concepts, two intertwined research directions emerge.
One direction is to ask whether a reduction to fewer states is firstly possible, and secondly automatically generable, in the same spirit as compiler optimization, with the possible application of reducing further the 21 states.
The second direction is to build a map of as many FSSP solutions as possible and study how they relate through the notion of ``reduction'' introduced, with application the discovery of techniques used in hand-made transition table and also the factorisation of correctness proofs.
In 2018, Maignan and Nguyen~\cite{DBLP:journals/jca/NguyenM20} exhibited a few of these relations and in particular the fact the infinite Maignan-Yunes CA could be reduced to the 8-state solutions of Noguchi~\cite{DBLP:journals/tcs/Noguchi04}.

\subsection{From the Initial Motivations to a Surprise}

The initial motivations whose to complete the ``map of reductions'' by including the 718 solutions into the picture.
In particular, a quick look at the 718 solutions gave to the authors the feeling that they could be grouped into equivalence classes using the notion of ``reduction''.
Also, inspired by the idea of \emph{local search} and exploration through small modifications used in~\cite{DBLP:journals/asc/ClergueVF18} to generate the 718 solutions,
the first author tried such search algorithms to generate ``reductions'' of existing solutions rather than transition tables directly.
Although the idea of local search is to navigate randomly in a landscape with few actual solutions, the discovered landscape of reductions has so many solutions that a ``best-effort-exhaustive'' exploration have been tried, leading to \emph{many millions} of 6-states solutions.
Also, this space is much more easily explored because of its nice computational properties.

\subsection{Organization of the Content}

In Section~\ref{background}, we define formally cellular automata, local simulations, FSSP solutions and related objects.
In Section~\ref{sec:prop}, we present nice properties relating these objects and allowing the search algorithm to save a huge amount of time.
In Section~\ref{optim-problem}, we describe the exploration algorithm and continue in Section~\ref{result} with some experimental results and a small analysis of the 718 solutions.
We conclude in Section~\ref{conclusion} with some formal and experimental futur work.

\section{Background}
\label{background}

In this section, we define formally cellular automata, local mappings and FSSP solutions in a way suitable to the current study.
Some objects have ``incomplete'' counterpart manipulated during the exploration algorithm.
The material here is a considerable re-organization of the material found in~\cite{DBLP:journals/jca/NguyenM20}.

\subsection{Cellular Automata}

\begin{definition}\label{def:ca}\label{def:std}
    A \emph{cellular automaton} $\alpha$ consists of a finite set of \emph{states} ${\rm \Sigma}_\alpha$, a set of \emph{initial configurations} ${\rm I}_\alpha \subseteq {{\rm \Sigma}_\alpha}^\mathbb{Z}$ and a partial function ${\rm \delta}_\alpha : {{\rm \Sigma}_\alpha}^3 \pfun {\rm \Sigma}_\alpha$ called the \emph{local transition function} or \emph{local transition table}.
    The elements of ${{\rm \Sigma}_\alpha}^\mathbb{Z}$ are called \emph{(global) configurations} and those of ${{\rm \Sigma}_\alpha}^3$ are called \emph{local configurations}.
    For any $c \in {\rm I}_\alpha$, its \emph{space-time diagram} ${\rm D}_\alpha(c) : \mathbb{N} \times \mathbb{Z} \to {\rm \Sigma}_\alpha$ is defined as:
    \begin{equation*}
        \diagram{\alpha}{c}{t}{p} =
        \begin{cases}
            c(p) & \text{ if } t = 0,\\
            {\rm \delta}_\alpha(l_{-1}, l_0, l_1) & \text{ if } t > 0 \text{ with } l_i = \diagram{\alpha}{c}{t-1}{p+i}.
        \end{cases}
    \end{equation*}
    The partial function ${\rm \delta}_\alpha$ is required to be such that all space-time diagrams have to be totally defined.
    When ${\rm D}_\alpha(c)(t,p) = s$, we say that, for the cellular automaton $\alpha$ and initial configuration $c$, the cell at position $p$ has state $s$ at time $t$.
\end{definition}

\begin{definition}\label{family-std}
    A \emph{family of space-time diagrams $D$} consists of a set of states ${\rm \Sigma}_D$ and an arbitrary set $D \subseteq {{\rm \Sigma}_D}^{\mathbb{N} \times \mathbb{Z}}$ of space-time diagram.
    The \emph{local transition relation $\delta_D \subseteq {{\rm \Sigma}_D}^3 \times {\rm \Sigma}_D$ of $D$} is defined as:
    $$((l^0_{-1}, l^0_0, l^0_1), l^1_0) \in \delta_D :\iff \exists(d,t,p) \in D \times \mathbb{N} \times \mathbb{Z} \text{ s.t. } l^j_i = d(t+j,p+i).$$
    We call $D$ a \emph{deterministic family} if its local transition relation is functional.
\end{definition}

\begin{definition}\label{def:family-to-ca}
    Given a deterministic family $D$, its \emph{associated cellular automaton} ${\rm \Gamma}_D$ is defined as having the set of states ${\rm \Sigma}_{{\rm \Gamma}_D} = {\rm \Sigma}_D$, the set of initial configurations ${\rm I}_{{\rm \Gamma}_D} = \{ d(0,\--) \mid d \in D \}$\footnote{Here, $d(0,\--)$ is the function from $\mathbb{Z}$ to $S$ defined as $d(0,\--)(p) = d(0,p)$.}, and the local transition function ${\rm \delta}_{{\rm \Gamma}_D} = \delta_{D}$.
\end{definition}
\begin{definition}
    Given a cellular automaton $\alpha$, its \emph{associated family of space-time diagram} (abusively denoted) $\family{\alpha}$ is defined as having the set of states ${\rm \Sigma}_{\family{\alpha}} = {\rm \Sigma}_\alpha$, and the set of space-time diagram $\family{\alpha} := \{\,{\rm D}_\alpha(c) \mid c \in {\rm I}_\alpha \,\}$ and is clearly deterministic.
\end{definition}

These inverse constructions shows that deterministic families and cellular automata are two presentations of the same object.
For practical purposes, it is also useful to note that, since ${\rm \delta}_D$ has a finite domain, there are finite subsets of $D$ that are enough to specify it completely.

\subsection{Local Mappings and Local Simulations}

Theses two concepts are more easily pictured with space-time diagrams.
Given a space-time diagram $d \in S^{\mathbb{N} \times \mathbb{Z}}$, we build a new one $d'$ by determining each state $d'(t,p)$ from a little cone $\langle d(t-dt,p+dp) \mid dt \in \{0,1\}, dp \in \itv{-dt}{+dt} \rangle$ in $d$.
This cone is simply a state for $t = 0$, and when $d$ is generated by a cellular automaton,  this cone is entirely determined by $\langle d(t-1,p+dp) \mid dp \in \itv{-1}{1} \rangle$ for $t \ge 1$.
Since the set of all these triplets is exactly $\dom({\rm \delta}_\alpha)$, the following definitions suffice for the current study.
We call this a local mapping, because the new diagram is determined locally by the original one.
When transforming a deterministic family, the result might not be deterministic, but if it is, we speak of a local simulation between two CA.

\begin{definition}\label{local-mapping}
A \emph{local mapping $h$ from a CA $\alpha$ to a finite set $S$} consists of two functions $h_{\mathtt{z}}: \{ d(0,x) \mid (d, x) \in \family{\alpha} \times \mathbb{Z} \} \to S$ and $h_{\mathtt{s}}: \dom({\rm \delta}_\alpha) \to S$.
\end{definition}

\begin{definition}\label{def:generated-family}
    Given a local mapping $h$ from a CA $\alpha$ to a finite set $S$, we define its \emph{associated family of diagrams} $\Phi_h = \{ h(d) \mid d \in \family{\alpha} \}$ where:
    \begin{equation*}
        h(d)(t,p) =
        \begin{cases}
            h_\mathtt{z}(d(0,p)) & \text{ if } t = 0,\\
            h_\mathtt{s}(l_{-1}, l_0, l_1) & \text{ if } t > 0 \text{ with } l_i = d(t-1)(p+i).
        \end{cases}
    \end{equation*}
\end{definition}

\begin{definition}\label{def:local-simulation}
    A local mapping $h$ from a CA $\alpha$ to a finite set $S$ whose associated family of diagrams $\Phi_h$ is deterministic is called a \emph{local simulation from $\alpha$ to ${\rm \Gamma}_{\Phi_h}$}.
\end{definition}

\begin{proposition}
    Equivalently, a \emph{local simulation $h$ from a CA $\alpha$ to a CA $\beta$} is a local mapping from $\alpha$ to the set ${\rm \Sigma}_\beta$ such that $\{ h_{\mathtt{z}}(c) \mid c \in {\rm I}_\alpha \} = {\rm I}_\beta$ and for all $(c, t, p) \in {\rm I}_\alpha \times \mathbb{N} \times \mathbb{Z}$, we have $h_{\mathtt{s}}(l_{-1}, l_0, l_1) = l'_0$ with $l_i = \diagram{\alpha}{c}{t}{p + i}$ and $l'_0 = \diagram{\beta}{h_{\mathtt{z}}(c)}{t + 1}{p}$.
    The details of these formula are more easily seen graphically.
\end{proposition}
\begin{center}
    \def.6{.6}
    \input{tex/local_mapping.tex}
\end{center}

\subsection{The Firing Squad Synchronization Problem}
\label{fssp}

\begin{definition}\label{fssp_ready}
    A cellular automaton is \emph{FSSP-candidate} if there are four special states ${\tt \star}_\alpha, {\tt G}_\alpha, {\tt Q}_\alpha, {\tt F}_\alpha \in {\rm \Sigma}_\alpha$, if ${\rm I}_\alpha = \{ \initConfigFSSP{n}_\alpha \mid n \ge 2 \}$ with $\initConfigFSSP{n}_\alpha$ being the \emph{FSSP initial configuration} of size $n$, i.e. $\initConfigFSSP{n}(p) = {\tt \star}_\alpha$, ${\tt G}_\alpha$, ${\tt Q}_\alpha$, ${\tt \star}_\alpha$ if $p$ is respectively $p \le 0$, $p = 1$, $p \in \itv{2}{n}$, and $p \ge n + 1$.
    Moreover, ${\tt \star}_\alpha$ must be the \emph{outside state}, \emph{i.e.} for any $(l_{-1},l_0,l_1) \in \dom({\rm \delta}_\alpha)$, we must have ${\rm \delta}(l_{-1},l_0,l_1) = {\tt \star}_\alpha$ if and only if $l_0 = {\tt \star}_\alpha$.
    Also, ${\tt Q}_\alpha$ must be a \emph{quiescent state} so ${\rm \delta}_\alpha({\tt Q}_\alpha,{\tt Q}_\alpha,{\tt Q}_\alpha) = {\rm \delta}_\alpha({\tt Q}_\alpha,{\tt Q}_\alpha,{\tt \star}_\alpha) = {\tt Q}_\alpha$.
\end{definition}

The ${\tt \star}_\alpha$ state is not really counted as a state since it represents cells that should be considered as non-existing.
Therefore, a FSSP-candidate cellular automaton $\alpha$ will be said to have $s$ states when $|{\rm \Sigma}_\alpha \setminus \{{\tt \star}_\alpha\}|\; = s$, and $m$ transitions when $|\dom({\rm \delta}_\alpha) \setminus{\rm \Sigma}_\alpha\times\{{\tt \star}_\alpha\}\times{\rm \Sigma}_\alpha| = m$.

\begin{definition}\label{min_fssp_solution}
A FSSP-candidate cellular automaton $\alpha$ is a \emph{minimal-time FSSP solution} if for any size $n$, ${\rm D}_\alpha(\initConfigFSSP{n})(t,p) = {\tt F}_\alpha$ if and only if $t \ge 2n - 2$ and $p \in \itv{1}{n}$.
We are only concerned with minimal-time solutions but sometimes simply write \emph{FSSP solution}, or \emph{solution} for short.
\end{definition}

\section{Some Useful Algorithmic Properties}
\label{sec:prop}

Our global strategy to find new FSSP solutions is to build them from local simulations of already existing FSSP solution $\alpha$.
Taking the previous definitions litteraly could lead to the following procedure for a given local mapping $h$.
First, generates as many space-time diagrams of $\family{\alpha}$.
Secondly, use $h$ to transform each diagram $d \in \family{\alpha}$ into a new one $h(d)$, thus producing a sub-family of $\Phi_h$.
At the same time, build ${\rm \delta}_{\Phi_h}$ by collecting all local transitions appearing in each $h(d)$ and check for determinism and correct synchronization.
If every thing goes fine, we have a new FSSP solution $\beta = {\rm \Gamma}_{\Phi_h}$.

Such a procedure is time-consuming.
We show here useful properties that reduces drastically this procedure to a few steps.
In fact, the space-time diagrams of $\Phi_h$ never needs to be computed, neither to build the local transition relation $\delta_{\Phi_h}$ (Section~\ref{sltt}), nor to check that ${\rm \Gamma}_{\Phi_h}$ is an FSSP solution as showed in this section (Section~\ref{sec:correctness-preserving}).

\subsection{Summarizing Families into Super Local Transition Tables}
\label{sltt}

When trying to construct a CA $\beta$ from a CA $\alpha$ and a local mapping $h$ from the families of space-time diagrams as suggested by the formal definitions, there is huge amount of redundancy.
All entries of the local transition relation ${\rm \delta}_{\Phi_h}$ appear many times in $\Phi_h$, each of them being produced from the same recurring patterns in the space-time diagrams of $\alpha$.
In fact, it is more efficient to simply collect these recurring patterns that we may call \emph{super local transitions}, and work from them without constructing $\Phi_h$ at all.
It is specially useful because we consider a huge number of local mappings from a single CA $\alpha$.

\begin{definition}
    For a given CA $\alpha$, the \emph{super local transition table} $\Delta_\alpha$ consists of two sets $(\Delta_\alpha)_\mathtt{z} \subseteq {{\rm \Sigma}_\alpha}^{3}$ and $(\Delta_\alpha)_\mathtt{s} \subseteq {{\rm \Sigma}_\alpha}^{5} \times {{\rm \Sigma}_\alpha}^{3}$ defined as:
    \begin{align*}
        (s_{-1},s_0,s_1)\phantom{)} \in (\Delta_\alpha)_\mathtt{z} :\iff \exists
        & (d, p) \in \family{\alpha} \times \mathbb{Z} \\
        & \text{ s.t. } s_i = d(0, p+i), \\
        ((s^0_{-2},s^0_{-1},s^0_0,s^0_1,s^0_2), (s^1_{-1},s^1_0,s^1_1)) \in (\Delta_\alpha)_\mathtt{s} :\iff \exists
        & (d, t, p) \in \family{\alpha} \times \mathbb{N} \times\mathbb{Z} \\
        & \text{ s.t. } s^j_i = d(t+j, p+i)
    \end{align*}
\end{definition}

Once all these patterns collected, it is possible to construct the local transition relation ${\rm \delta}_{\Phi_h}$ as specified in the following proposition.

\begin{proposition}
Let $h$ be a local mapping from a CA $\alpha$ to a set $S$.
The local transition relation ${\rm \delta}_{\Phi_h}$ of the family of space-time diagram $\Phi_h$ generated by $h$ and the super local transition function $\Delta_\alpha$ of $\alpha$ obey:
\begin{eqnarray*}
((l^0_{-1},l^0_0,l^0_1), l^1_0) \in {\rm \delta}_{\Phi_h}
& \iff & \exists (s_{-1},s_0,s_1)\phantom{)} \in (\Delta_\alpha)_\mathtt{z} \\
& & \text{ s.t. } l^0_i = h_\mathtt{z}(s_{i}) \text{ and } l^1_0 = h_\mathtt{s}(s_{i-1},s_{i},s_{i+1}) \\
& \vee & \exists ((s^0_{-2},s^0_{-1},s^0_0,s^0_1,s^0_2), (s^1_{-1},s^1_0,s^1_1)) \in (\Delta_\alpha)_\mathtt{s}\\
& & \text{ s.t. } l^j_i = h_\mathtt{s}(s^j_{i-1},s^j_{i},s^j_{i+1})
\end{eqnarray*}
\end{proposition}

We know have an efficient way to build the local transition relation ${\rm \delta}_{\Phi_h}$.
When it is functional, it determines a cellular automaton $\beta = {\rm \Gamma}_{\Phi_h}$.
For our purpose, we need to test or ensure in some way that $\beta$ is an FSSP solution.

\subsection{Local Mappings and FSSP}
\label{sec:correctness-preserving}

We first note that the constraints put by the FSSP on space-time diagrams induces constraints on local simulations between FSSP solutions.
So we can restrict our attention to local mappings respecting these constraints as formalized by the following definition and proposition.

\begin{definition}\label{fssp_compliant}
   A local mapping $h$ from a FSSP solution $\alpha$ to the states ${\rm \Sigma}_\beta$ of a FSSP-candidate CA $\beta$ is said to be \emph{FSSP-compliant} if it is such that
   (0) $h_\mathtt{z}$ maps ${\tt \star}_\alpha$, ${\tt G}_\alpha$, and ${\tt Q}_\alpha$ respectively to ${\tt \star}_\beta$, ${\tt G}_\beta$, and ${\tt Q}_\beta$,
   (1) $h_\mathtt{s}\lConfig{l_{-1}}{l_0}{l_1} = {\tt \star}_\beta$ if and only if $\delta_\alpha\lConfig{l_{-1}}{l_0}{l_1} = {\tt \star}_\alpha$ (meaning simply $l_0 = {\tt \star}_\alpha$),
   (2) $h_\mathtt{s}\lConfig{l_{-1}}{l_0}{l_1} = {\tt F}_\beta$ if and only if $\delta_\alpha\lConfig{l_{-1}}{l_0}{l_1} = {\tt F}_\alpha$, and
   (3) $h_\mathtt{s}\lConfig{{\tt Q}_\alpha}{{\tt Q}_\alpha}{{\tt Q}_\alpha} = h_\mathtt{s}\lConfig{{\tt Q}_\alpha}{{\tt Q}_\alpha}{{\tt \star}} = {\tt Q}_\beta$.
\end{definition}

\begin{proposition}
   Let $\alpha$ be a FSSP solution CA, $\beta$ a FSSP-candidate CA and $h$ a local simulation from $\alpha$ to $\beta$.
   If $\beta$ is a FSSP solution, then $h$ is FSSP-compliant.
\end{proposition}

The following proposition is at the same time not difficult once noted, but extremely surprising and useful: the simple constraints above are also ``totally characterizing'' and the previous implication is in fact an equivalence.
This means in particular that it is not necessary to generate space-time diagrams to check if a constructed CA is an FSSP solution, which saves lot of computations.

\begin{proposition}
   Let $\alpha$ be an FSSP solution, $\beta$ a FSSP-candidate CA and $h$ be local simulation from $\alpha$ to $\beta$.
   If $h$ is FSSP-compliant, then $\beta$ is a FSSP solution.
\end{proposition}

\section{Exploring The Graph of Local Mappings}
\label{optim-problem}

\subsection{The Graph of FSSP-compliant Local Mappings}

In our actual algorithm, we take as input an existing FSSP solution $\alpha$ and fix a set of state $S$ of size $|{\rm \Sigma}_\alpha|$.
The search space consists of all FSSP-compliant local mappings from $\alpha$ to $S$, the neighbors ${N}(h)$ of a local mapping $h$ being all $h'$ that differs from $h$ on exactly one entry, \emph{i.e.}~ $\exists!(l_{-1},l_0,l_1) \in \dom({\rm \delta}_\alpha) \text{ s.t. } h_\mathtt{s}(l_{-1},l_0,l_1) \neq h'_\mathtt{s}(l_{-1},l_0,l_1)$.
More precisely, the mappings are considered modulo bijections of $S$.
Indeed, two mappings $h$ and $h'$ are considered equivalent if there is some bijection $r: S \to S$ such that $h_\mathtt{z} = r \circ h'_\mathtt{z}$ and $h_\mathtt{s} = r \circ h'_\mathtt{s}$.
So the search space is, in a sense, made of equivalence classes, each class being represented by a particular element.
This element is chosen to be the only mapping $h$ in the class such that $h_\mathtt{s}$ is monotonic according to arbitrary total orders on $\dom({\rm \delta}_\alpha)$ and $S$ fixed for the entire run of the algorithm.

Considering 6-states solutions, let us denote ${\rm \Sigma}_\alpha = \{{\tt \star}_\alpha, {\tt G}_\alpha, {\tt Q}_\alpha, {\tt F}_\alpha, {\tt A}_\alpha, {\tt B}_\alpha, {\tt C}_\alpha\}$ and $S = \{{\tt \star}, {\tt G}, {\tt Q}, {\tt F}, {\tt A}, {\tt B}, {\tt C}\}$\footnote{Recall that we do not count the $\star$ states.}.
In each of these sets, four of the states are the special FSSP solution states (Def.~\ref{fssp_ready} and Def.~\ref{min_fssp_solution}).
Only the three states ${\tt A}$, ${\tt B}$, ${\tt C}$ come with no constraints.
We can thus evaluate the size of the search space by looking at the degrees of freedom of FSSP-compliant local mappings (Def~\ref{fssp_compliant}).

Indeed, all FSSP-compliant local mappings $h$ from $\alpha$ to $S$ have the same partial function $h_\mathtt{z}$, and the same value $h_\mathtt{s}(l_{-1},l_0,l_1)$ for those entries $(l_{-1},l_0,l_1) \in \dom(\delta_\alpha)$ forced to $\star$, ${\tt Q}$ or ${\tt F}$.
For all other entries $(l_{-1},l_0,l_1)$, $h_\mathtt{s}(l_{-1},l_0,l_1)$ cannot take the values $\star$ nor ${\tt F}$, leaving 5 values available.
So given an initial solution $\alpha$, the number of local mappings is $5^x$ where $x$ is the size of $\dom({\rm \delta}_\alpha)$ without those entries constrained in Def.~\ref{fssp_compliant}.
To give an idea, for the solution 668 of the 718 solutions, $x = 86$ to the size of the search has 61 digits, and for Mazoyer's solution, $x = 112$ leading to a number with 79 digits.

\subsection{Preparation Before the Algorithm}

As described in Section~\ref{sltt}, the local mappings are evaluated from the super local transition table.
To build this table, we generate, for each size $n$ from 2 to 5000, the space-time diagram ${\rm D}_\alpha(\bar{n})$ and collect all super local transitions occurring from time $0$ to $2n-4$ and from position $1$ to $n$.
Note that for all known minimum-time 6-state solutions, no additional super local transitions appear after $n = 250$.

The starting point of the exploration is the local mapping $h_\alpha$ corresponding to the local transition function ${\rm \delta}_\alpha$ itself, \emph{i.e.}~ $(h_\alpha)_\mathtt{z} = q \restriction \{ {\tt \star}_\alpha, {\tt G}_\alpha, {\tt Q}_\alpha \}$ and $(h_\alpha)_\mathtt{s} = q \circ {\rm \delta}_\alpha$ for some bijection $q : {\rm \Sigma}_\alpha \to S$.
This local mapping is obviously FSSP-compliant since it is local simulation from $\alpha$ to $\alpha$.

\subsection{The Exploration Algorithm}

\begin{figure}[h]
\SetInd{1em}{0.1em}
\noindent
\begin{minipage}[t]{.53\linewidth}
\begin{algorithm}[H]
    \Indp
    \Indm\explore{${\rm \Delta}_\alpha, h_\alpha, k$}\\
    \Indp
    $H \gets \{ h_\alpha \}$\\
    $H_{current} \gets \{ h_\alpha \}$\\

    \While{$\card{H_{current}}\ > 0$}{
        $H_{next} \gets \{ \}$\\
        \For{$h \in H_{current}$}{
            $S, H \gets \pertN({\rm \Delta}_\alpha, H, h, k)$\\
            \For{$h' \in (S \setminus H)$}{
                \If{$\isSimul(h', {\rm \Delta}_\alpha)$}{
                    $H_{next} \gets H_{next} \cup \{h'\}$\\
                    $H \gets H \cup \{h'\}$
                }
            }
        }
        $H_{current} \gets H_{next}$
    }
    \Return $H$
    \caption{
    \label{local-search-algo}
\end{algorithm}
\end{minipage}
\hfill
\begin{minipage}[t]{.47\linewidth}
\begin{algorithm}[H]
    \Indp
    \Indm $\pertN({\rm \Delta}_\alpha, H, h, k)$\\
    \Indp
            $S \gets {N}(h)$\\

            $h' \gets \perturbation(h, k)$\\
            \If{$h' \not\in H$}{
                $S \gets S \union {N}(h')$ \\
                \If{$\isSimul(h', {\rm \Delta}_\alpha)$}{
                    $H \gets H \union \{h'\}$
                }
            }
    \Return $S$, $H$
    \caption{
\end{algorithm}
\end{minipage}
\end{figure}

To explain the algorithm, let us first consider the last parameter $k$ to be $0$, so that line 7 of the $\explore$ algorithm can be considered to be simply $S \gets {N}(h)$.
In this case, the algorithm starts with $h_\alpha$, and explores its neighbors to collect all local simulations, then the neighbors of those local simulations to collect more local simulations, and so on so forth until the whole connected components of the sub-graph consisting only of the local simulations in collected.

More precisely, the variable $H$ collects all local simulations, $H_{current}$ contains the simulation discovered in the previous round and whose neighbors should be examined in current round, and the newly discovered local simulations are put in $H_{next}$ for the next round.
The function $\isSimul$ uses the super local transition table to construct the local transition relation of $\Phi_h$ and check if it is functional, \emph{i.e.}~ if it is a local transition function of a valid CA ${\rm \Gamma}_{\Phi_h}$.
By our construction, a valid CA is necessarily an FSSP solution making this operation really cheap.

When $k > 0$, the neighborhood operation is altered to add more neighbors.
A local mapping obtained by $k$ modifications is considered and its neighborhood is added to the original the normal neighborhood, in the hope of discovering another connected component of the local simulation subgraph.

\section{Analyzing the Results}
\label{result}

\subsection{Analyzing the 718 solutions}

As mentioned in the introduction, this study began by the desire to analyse the 718 solutions found in~\cite{DBLP:journals/asc/ClergueVF18}.
These solutions, numbered from 0 to 717, are freely available online.
We tried to search local simulation relation between them as done in~\cite{DBLP:journals/jca/NguyenM20}.
Firstly, we found a slight mistake since there are 12 pairs of equivalent solutions up to renaming of states:
(105, 676), (127, 659), (243, 599), (562, 626), (588, 619), (601, 609), (603, 689), (611, 651), (629, 714), (663, 684), (590, 596) and (679, 707).
This means that there are really 706 solutions, but we still refer to them as the 718 solutions with their original numbering.

Once local simulation relation established between the 718 solutions, we analyzed in the number of connected components and found 193 while expecting only a few.
When there is a local simulation $h$ from a CA $\alpha$ and a CA $\beta$, the number of differences between $h_\alpha$ and $h$ varies a lot, but the median value is 3.

\subsection{Analyzing the Local Simulations}

To find more FSSP solutions, we implemented many algorithms, gradually simplifying them into the one presented in this paper.
It has been run on an Ubuntu Marvin machine with 32 cores of 2.00GHz speed and 126Gb of memory.
However, the implementation being sequential, only two cores was used by the program.
The original plan was to generate as many solutions as possible but we had some problems with the management of quotas in the shared machine.
So we only expose the some selected data to show the relevance of the approach.

When running the program with the solution 355 and $k = 0$, the program used 14Gb of memory and stopped after 27.5 hours and found 9,584,134 local simulations!
A second run of the program for this solution with $k = 3$ found 11,506,263 local simulations after 80.5 hours.
This indicates that perturbations are useful but the second run find only 1922129 additional local simulations but its computing time is three times more than the first run.
Testing whether a local simulation belongs to set $H$ obviously takes more and more times as more local mappings are discovered but there might be some understanding to gain about the proper mapping landscape too in order to improve the situation.

The transition table for the original Mazoyer's solution can be found in~\cite{DBLP:journals/tcs/Mazoyer87}, but also in~\cite{DBLP:journals/ijuc/UmeoHS05} together with other minimal-time solution transition table.
When running the program of the original Mazoyer's solution with different values of $k$ with obtained the following number of new solutions for different runs.
The behavior with $k=1$ seems to be pretty robust, but the bigger number of results is obtained with $k = 2$.

\begin{center}
\begin{tabular}{|l|l|}
    \hline
    k & number of solutions found by 10 different runs \\
    \hline \hline
    0 & \textbf{644} \\
    \hline
    1 & 20682, 17645, 20731, 16139, \textbf{20731}, 9538, 20626, 20682, 20054, 20490 \\
    \hline
    2 & 9451, 9451, 20595, 8241, \textbf{37275}, 3817, 17421, 8241, 17317, 19895 \\
    \hline
    3 & 644, 644, 644, 644, 644, 644, 644, 731, 8241, \textbf{8241} \\
    \hline
    4 & 644, 644, 644, 2908, 644, 644, 644, 644, 644, \textbf{8241} \\
    \hline
    5 & 644, 644, 644, 644, 644, 644, 644, 644, 644, 644 \\
    \hline
\end{tabular}
\end{center}

Note that while the solutions do not have less states, the number of transitions do change.
We show in Figure~\ref{fig:668_origine} the solution 668 (the only Mazoyer-like solutions found among the 718 solutions), and one of its simulations having less transition in Figure~\ref{fig:355_origine}.
For fun, we also show in Figure~\ref{fig:355_locSim} and~\ref{fig:668_locSim} a local simulation having alternating states at time $2n-3$, illustrating how local simulation rearrange locally the information.
The identical part in represented with lighter colors to highlight the differences.

\begin{proposition}
   There are at least many millions of minimum-time 6-state FSSP solutions.
\end{proposition}

\section{Conclusion}
\label{conclusion}

This paper presents only a small part of many ongoing experimentations.
The notion of local simulation presented here is just a particular case of the notion of cellular field that can be used more broadly to investigate these questions.
For example, we relate here only the small cones $\{d(t-dt,p+dp) \mid dt \in \{0,1\}, dp \in \itv{-dt}{+dt} \}$ of any space-time diagram $d$ in local mappings.
If we increase the range of $dt$ in this definition to be $\itv{0}{h}$ for some $h > 1$, we allow CA to be transformed to a bigger extent.

Another justification for this extension is that the composition of two local simulations is not a local simulation.
In fact, composing an $h$-local simulation with an $h'$-local simulation produces an $(h+h')$-local simulation in general.
A 0-local simulation is just a (possibly non-injective) renaming of the states.

Note that since local mappings of local mappings are not local mappings, running the above algorithm on new found solutions should a priori generate more solutions!
Of course, a more exhaustive study is required.

Our guess is that, with a properly large notion of such simulations, it should be possible to classify the 718 solutions into only a few equivalence classes, more or less in two groups: the ``mid-way division'' solutions and the ''two-third division'' solutions.
This results also represents an important step in the understanding of automatic optimization of CA.

Finally, the content of Section~\ref{sec:correctness-preserving} about the preservation of correctness by FSSP-compliant local simulation is really interesting because of the simplicity of checking FSSP-compliance.
It implies that a proof of correctness of a small FSSP solution can indeed be made on some huge, possibly infinite, simulating CA where everything is explicit as considered in~\cite{DBLP:conf/acri/MaignanY14,DBLP:journals/jca/MaignanY16}.
This can be applied to ease the formal proof of correctness of Mazoyer's solution.
Up to our knowledge, it is known to be long and hard but also to be the only proof to be precise enough to actually be implemented in the Coq Proof Assistant~\cite{duprat:hal-02101837}.

We would like to give special thanks to Jean-Baptiste Yun\`es who pointed us the 718 solutions paper.
If we are right, he also partly inspired the work who lead to the 718 solutions by a discussion during a conference.

\begin{figure}
\centering
\begin{subfigure}{.45\textwidth}
\centering
\includegraphics[width=\textwidth]{img/668_ori_93rule.pdf}
\caption{original solution 668: 93 rules}
\label{fig:668_origine}\label{fig:two-third}
\end{subfigure}
\hspace*{1cm}
\begin{subfigure}{.45\textwidth}
\centering
\includegraphics[width=\textwidth]{img/668_sim_90rule.pdf}
\caption{a local simulation of 668: 90 rules}
\label{fig:668_locSim}
\end{subfigure}
\vspace{.1cm}
\newline

\begin{subfigure}{.45\textwidth}
\centering
\includegraphics[width=\textwidth]{img/355_ori_101rule.pdf}
\caption{original solution 355}
\label{fig:355_origine}\label{fig:half}
\end{subfigure}
\hspace*{1cm}
\begin{subfigure}{.45\textwidth}
\centering
\includegraphics[width=\textwidth]{img/355_sim_102rule.pdf}
\caption{a local simulation of 355}
\label{fig:355_locSim}
\end{subfigure}
\caption{Some FSSP space-time diagrams of size 31}
\label{fig:dgm}
\end{figure}

\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


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Here is what you should do. Look for the features and the main points that your agency mainly focuses in. Then compare these with your expectations. If some of these matches, then you should think about going ahead with the discussion. Another idea can be- you take a few days off just to browse through thousands of websites that match your kind, and see which sites blow your mind and which sites irritate you. The sites that bore you are probably lame, slow, full of excessive content and so on. May be the columns are not made in the proper order, or may be the graphics are not right. Once you know- what works and what doesn't; it will be easier for you to sit with your hired company and point out the desirable and avoidable points- all one by one!
Sometimes only the knowledge and skills are not sufficient. A company may be providing SEO services in India, but you also need to dig in and know about the emotions involved and check with what dedication these people work- how serious they are! You don't need machines, you need a team. And teams work better when positive emotions are involved.


text:
MusicThreats & Promises
Flagpole's at SXSW; Hear New Music from Dictator
by Gordon Lamb March 18, 2015
This week, Flagpole is in Austin, TX for South By Southwest. Thus, this week's column is only gonna accentuate the positive. Why? Because we prefer to put our best foot forward when we're guests in someone else's town. So, if you're wondering why the crappy record by your ridiculous band isn't mentioned, that's why.
SPEAKING OF WHICH: As featured in last week's issue, this also means it's time for the annual Athens in Austin party. It'll happen Saturday, Mar. 21 at Side Bar (602 E. 7th St.) and will run from noon–7 p.m. Featured performers are White Violet, Grand Vapids, Shehehe, Pinecones, Faux Ferocious, Chief Scout, Concord America, Tall Tall Trees, Andrew Combs, Dana Swimmer, Family and Friends, Music Band, New Madrid and Reptar. The party was organized by the Georgia Theatre and is sponsored by Normaltown Records, Chase Park Transduction, the Athens Convention & Visitors Bureau, Athens Intensified (full disclosure: that's my organization), Cottonseed Studios, the 40 Watt Club, Grindhouse Killer Burgers, Alabama startup space Round House, Bohemian Guitars, Newk's Eatery, We're hEAR For You, UGA's Terry College Of Business, Macon publication The Blue Indian and, of course, Flagpole. If you're in Austin this week, come out and hang with us. For more info, see athensinaustin.com.
AND ALSO: Our live SXSW coverage is over on Homedrone, and my more off-the-cuff remarks can be found via Twitter @gordonlamb.
SAY WHAT?: In related news, We're hEAR For You co-founder and executive director Katie Carmody will appear at SXSW as part of the moderated panel "Be Hear Now: Hearing Protection Is Music's Future." WHFY is best known locally for its canisters of free earplugs at local music venues, but it's also a steadily growing nonprofit with a presence at several major festivals and other cities around the U.S. The panel happens Wednesday, Mar. 18 in room 10A of the Austin Convention Center. Hearing loss is an important issue for regular gig-goers. For those in Athens wanting to check out exactly how much damage they may have done over the years and how to prevent more, the UGA Speech and Hearing Clinic has you covered. They're conducting free hearing and speech screenings Friday, Mar. 20 from 9 a.m.–noon. They're located on campus at 593 Aderhold Hall (110 Carlton St.), and can be reached by phone at 706-542-4598.
HELTER SKELTER: The quickly approaching Slingshot Festival, which runs Mar. 26–28, has released single tickets for its headlining shows. Added together, they'd total $142, which should make the full-on passes—priced at $70—a lot more attractive. But, if you insist on doling out your cash piecemeal, far be it from me to stop you. The shows available for now for purchase are James Murphy, DJ Windows 98 and Michael Lachowski ($30); Jamie xx ($20); Reptar and Skylar Spence ($20); Nosaj Thing, Clark and Rival Consoles ($15); Andy Hull, Ryley Walker and Roadkill Ghost Choir ($15); Omar Souleyman ($15); Japan Nite! headlined by Peelander-Z ($15); and Single Mothers and Monsoon ($12). These seven shows, as stupendously great as some of them are, are also only a tiny slice of everything happening with Slingshot. Spend some time over at slingshotathens.com and explore some of the incredible offerings.
RULER REPRESENTIN': Hard-hitting Athens rapper Travis "Dictator" West released a new track last week named, appropriately enough, "Concrete." It was produced by Red "BeatMan" Johnson for Official Productions. Coming just a few months after his last track, "Watered Down," it's both more club-oriented and more hardcore. Dictator's vocals come at a rapid-fire pace, but avoid being so fast that there's no way to distinguish the lyrics. All in all, it's a fine slice of Athens hip hop that will hopefully lead to a new full-length album soon. Dig it at soundcloud.com/dictatortharuler.
BITS-N-BOBS: Although generally a little too heavy for the "dream-pop" tag, Fake Flowers may be able to sneak through its back door with their new single, "Don't Cry, Kiddo." It's the first track off a new upcoming EP titled Wonder Wave that's supposed to come out this week. Check it on Homedrone… Yet another happening has been added to the weird world of Mr. Blank, and this time it's an afterparty—two weeks later, mind you—to his just-wrapped Carnivale of Black Hearts double feature event. This party happens at Flicker Theatre & Bar this Saturday, Mar. 21. It'll feature a presentation by the organizers of the in-the-planning-stages Classic City Fringe Festival, plus live performances by iNTELLi G, Mr. Blank, PsyleNts and the aforementioned Carnivale's own Weird & Wandering Sideshow. See facebook.com/carnivaleblackhearts for info.
Athens in AustinClassic City Fringe FestivalDictatorFake FlowersFlicker Theatre & BarGeorgia TheatreKatie CarmodyMr. BlankmusicRed "BeatMan" JohnsonSlingshot FestivalSXSWThreats and PromisesUGA Speech and Hearing Clinic
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Jamie Hood's Trial Will Cost More Than $300,000
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