Deficiency of RbAp48 protein and memory loss

Memory is commonly referred to as the ability to encode, store, retain and subsequently recall information and past experiences in the human brain. This process involves many proteins, one of which is the Histone-binding protein RbAp48 (also known as RBBP4 or NURF55), encoded by the RBBP4 gene in humans.
Function.
RbAp48, also known as RBBP4 gene, encodes a nuclear protein, which belongs to a highly conserved family of WD40 repeat. This gene is present in many protein complexes that are involved in histone acetylation and deacetylation processes as well as chromatin assembly. This gene also belongs to the Mi-2/NuRD complex, also known as "nucleosome remodeling deacetylase complex" which plays a role in both ATP-dependent chromatin remodeling and histone deacetylase activities. This protein is also part of a co-repressor complex which is an important component of transcriptional silencing. This gene is widely available and can be found in several cellular proteins which bind directly to the retinoblastoma protein to regulate growth and cell proliferation. This protein also found in the transcriptional repression of E2F-responsive genes, which are a group of genes that encode for a family of transcription factors.
Biochemistry.
Experimental process.
To further distinguish age-related memory loss from Alzheimer's disease (AD), a subregion of the hippocampal formation called the dentate gyrus (DG) was further studied, since it is thought to be targeted by aging. Human postmortem tissue was collected from both DG and entorhinal cortex (EC). Entorhinal cortex is a neighboring subregion unaffected by aging and known to be implicated in age-related memory loss. After normalizing the expression of EC, 17 genes were manifested due to age-related changes in the DG. Mice were used as the experimental subjects to test whether the decline of RbAp48 was also related to age-related memory loss. The results were consistent with the human studies, where the level of RbAp48 protein was much lower in adults as compared to the young. To solidify these findings, magnetic resonance imaging (MRI) was performed which revealed that dysfunction occurred in the DG, corresponding to the regionally selective decreases in histone acetylation.
Mechanism.
The hippocampus is a brain region which has many interconnected subregions, with each region having its own distinct neuron populations playing an important role in encoding memory. Many studies showed that Alzheimer's disease (AD) ameliorates memory by first acting on the entorhinal cortex (EC) which is the region providing the main input conduit from the external sensors to the hippocampus. Scientists initially identified memory loss associated with aging as an early manifestation of Alzheimer's; however, more recent evidence suggests that a distinct process affects the dentate gyrus (DG), which is a subregion of the hippocampus, and causes memory deterioration. The hippocampal formation is made up of many interconnected subregions and plays a vital role in retaining memory. Each subregion contains a specific population of neurons which have distinct molecular expression and physiological properties. As a result, these regions are vulnerable to various pathogenic mechanisms. Although both AD and the normal aging process affect the hippocampus, studies showed that these two processes can be distinguished by two anatomical patterns of hippocampal dysfunctions. Postmortem studies suggest that the entorhinal cortex (EC) and the subiculum are the hippocampal subregions most affected by AD, whereas the dentate gyrus is relatively preserved in most cases. In contrast to AD, the normal aging process does not cause cell death or other pathognomonic abnormalities that result in memory loss. Rather, age-related memory loss is characterized by dysfunctioning neurons. These results from MRI and other studies suggest that the primary initial target of normal aging is the DG, whereas the EC is relatively preserved.
Clinical study on humans.
Guided by the pattern that distinguishes age-related hippocampal dysfunction from AD, scientists from Columbia University Medical Center collected the dentate gyrus (DG) from postmortem human brains. These DG were free from any detectable brain pathology. These experimental subjects from which the DG was taken ranged from 33 to 88 years of age. Scientist also harvested the EC from each brain and generated gene expression profiles with Affymetrix microarray chips, where each microarray was customized to each individual's brain area. Their hypothesis was driven by the analysis that the DG is preferentially affected by aging rather than AD. The gene expression in the DG was normalized to their expression in EC; the normalized values of DG were then analyzed to find the correlation between age of the experimental subjects. Scientists found that 17 normalized profiles showed an increase and decrease with correlation to age. With a P ≤ 0.005, scientists confirmed that the observed changes were not the product of age-related change but rather the product of their relative abundance in the EC. One of the biggest change in terms of gene expression was the expression of gene RbAp48, where the p value conformed to the pattern of normal age-associated hippocampal dysfunction. To further advance their studies, scientists collected EC and DG from an additional 10 healthy human brains with ages ranging from 49 to 81 years. After the level of RbAp48 and actin in every single tissue was measured using Western blot, they discovered that the level of RbAp48 decreased with the increasing age. The level of mRNA also decreased as the age of the subject increased in DG; however, the level of RbAp48 remained unchanged in the EC.
Clinical study on animals.
In mice, the RbAp48 protein is key component in histone acetylation, transcriptional regulation and in cyclic adenosine monophosphate (cAMP)-protein kinase element-binding protein CREB1 path way. Since histone acetylation and the cAMP-PKA-CREB1 pathway are extremely important for normal hippocampal function and aging in mice, scientists further investigate RbAp48 to test whether its modulation was the cause of age-related memory losses in animals, especially mice. By studying wild-type mice, Scientists discovered that RbAp48 was expressed at a much higher level in the hippocampus, particularly in the dentate gyrus (DG). This finding was consistent with what they found in mice tissue because RbAp48 protein was less abundant in the DG of adult mice, as compared to a lower expression level in adult. In addition, the age-related reduction of RbAp48 was only detected in the DG, whereas the region of EC was preserved. This finding further solidifies the previous discovery that aging only affects the DG and does not cause the dysfunction of EC.
DNA interaction.
In eukaryotic cells, DNA is wrapped around an octamer of histone proteins to form nucleosomes, which fold into higher-order chromatin structures. The nucleosome comprises two copies of histone H3 and histone H4. These nucleosomes form a heterotetramer and bind to DNA in the first step of nucleosome assembly. When DNA is replicated, nucleosomes need to be disassembled in front of the fork and the histones must then be transferred to the newly duplicated strands for reassembly. Studies of the in- vivo composition of histone H3 complexes, as well as the structural of the ASF1-H3-H4 complex, have shown that histone H3-H4 complexes are handled as a protein dimer.
Proteins RbAp48 is a key player in the assembly of nucleosomes. RbAp48 protein is a subunit of the chromatin-assembly factor-1 (CAF-1) complex, which assembles histones H3 and H4 onto newly replicated DNA to initiate nucleosomes assembly. RbAp48 protein is also found in numerous other protein complexes for regulation of chromatin structure. Studies show that RbAp48 interacts with H3-H4 dimers and imply that the function of RbAp48 is involved in numerous process such as chromatin assembly, remodeling and modifications; therefore, in many other chromatin-related processes, histones H3-H4 might be handled as a dimer. More generally, it seems plausible that the presence of RbAp48 may reflex the post-translational modifications of the nucleosome. As a result, this can affect the activities of neurons and ultimately impact the memory encoding ability
CREB complex.
CREB-binding protein, also known as CREBBP or CBP, is a protein that is encoded by the "CREBBP" gene in humans.
The CREB protein carries out its function by activating transcription, where interaction with transcription factors is managed by one or more CREB domains: the nuclear receptor interaction domain (RID), the CREB and MYB interaction domain (KIX), the cysteine/histidine regions (TAZ1/CH1 and TAZ2/CH3) and the interferon response binding domain (IBiD). The CREB protein domains, KIX, TAZ1 and TAZ2, each bind tightly to a sequence spanning both transactivation domains 9aaTADs of transcription factor p53.


Passive sampling

Passive sampling is an environmental monitoring technique involving the use of a collecting medium, such as a man-made device or biological organism, to accumulate chemical pollutants in the environment over time. This is in contrast to grab sampling, which involves taking a sample directly from the media of interest at one point in time. In passive sampling, average chemical concentrations are calculated over a device's deployment time, which avoids the need to visit a sampling site multiple times to collect multiple representative samples. Currently, passive samplers have been developed and deployed to detect toxic metals, pesticides, pharmaceuticals, radionuclides, polycyclic aromatic hydrocarbons (PAHs), polychlorinated biphenyls (PCBs), and other organic compounds in water, while some passive samplers can detect hazardous substances in the air.
Theory and application.
The underlying principle of passive sampling is the flow of contaminant molecules or ions from the sampling medium (air or water) onto a collecting medium (the passive sampler), due to Fick's first law of diffusion and, depending on the passive sampler, a greater binding affinity of contaminants with the collecting medium as compared to the sampling medium. As a result, contaminants concentrate on the collecting medium over time until they reach equilibrium with the surrounding medium. The use of passive sampling provides time-averaged concentrations of contaminants over the sampler's deployment period.
It is important to distinguish passive sampling from "active sampling", which has the same underlying principle but employs moving parts, such as pumps, to force the sampling medium onto a collecting medium. Passive sampling solely relies on molecular diffusion and the sorbing or binding of contaminants to agents in the samplers, which is why passive sampling is also called "diffusive sampling".
Passive sampling is also distinct from grab sampling, which is the collection of an air, water, or soil sample to analyze directly for contaminants. These samples represent a single point in time and provide information about contaminant concentration at one point in time, unlike passive sampling devices or organisms.
Many different kinds of passive samplers have been developed and have sampled many different contaminants, including:
Passive sampling in water.
Several kinds of passive sampling devices exist for monitoring pollutants present in water. In addition to these devices, organisms, such as mussels, living in the environment also "passively sample" contaminants (bioaccumulation) and can be used to monitor water pollution (biomonitoring).
Chemcatcher.
Chemcatcher can passively sample inorganic pollutants (metals) and a wide range of organic pollutants. It is composed of a single-use disc, with or without a membrane, sealed into a plastic support. Types of receiving phases and membranes vary greatly, depending on the target chemicals to be sampled. Time-averaged water concentrations of many chemical pollutants can be determined as long as sampling rate and the water flow rate are known.
Diffusive gradients in thin films (DGT).
Diffusive gradients in thin films (DGT) samplers passively sample ionic trace metals, as well as antibiotics, oxyanions, bisphenols, and nanoparticles in different configurations. They are composed of plastic pistons and caps, with a window that exposes a binding gel, diffusive gel, and filter membrane to the sampling water. They can be used in both freshwater and marine environments, as well as in the water located between freshwater and marine sediment particles, called "pore water" or "interstitial water". Once the mass of accumulated contaminants on the DGT sampler is known, the DGT equation (based on Fick's law) can be used to calculate the time averaged water concentration of contaminants.
Peepers.
Peepers are passive diffusion samplers used for metals in freshwater and marine sediment pore water, so they can be used to find areas that may have metal-contaminated sediments. Peepers are plastic vessels filled with clean water and covered in a dialysis membrane, which allows metals in sediment pore water to enter the water inside the peeper. They are usually placed deep enough into sediment to be in an anoxic environment, in which metals will be soluble enough to sample. If the peepers are deployed long enough so the sediment pore water and contained peeper water reach equilibrium, they can accurately provide metal concentrations in sampled sediment pore water.
Polar organic chemical integrative sampler (POCIS).
Polar organic chemical integrative samplers (POCIS) sample polar organic contaminants with a log octanol-water partition coefficient (Kow) value that is less than 3. Examples of these types of chemicals include polar pesticides, pharmaceuticals, illicit drugs, flame retardants, and drug metabolites. The POCIS is composed of variable numbers of solid sorbent discs attached to a support rod and encased in a metal cage, and has two possible sorbent configurations, the pesticide-POCIS and pharmaceutical-POCIS. As long as the amount of water passing over the sampler is known, polar organic contaminant water concentrations can be calculated after extracting sorbed contaminants from a POCIS.
Semipermeable membrane devices (SPMDs).
Semipermeable membrane devices (SPMDs) passively sample nonpolar organic contaminants with a log octanol-water partition coefficient (Kow) value greater than 3. Examples of these types of chemicals include polycyclic aromatic hydrocarbons (PAHs), polychlorinated biphenyls (PCBs), polybrominated diphenyl ethers (PBDEs), chlorinated pesticides, dioxins, and furans. SPMDs are composed of sealed plastic tubing filled with triolein, in which nonpolar organics are very soluble and which serves as a representation of the fatty tissues of aquatic organisms. The tubing is then weaved between metal rods and enclosed in a metal cage. The sampler can be made in varying lengths of tubing for different applications, since sampling rate depends on the surface area of tubing exposed to the water. As long as the amount of water passing over the sampler is known, nonpolar organic contaminant water concentrations can be calculated after extracting contaminants from a SPMD.
Stabilized liquid membrane devices (SLMDs).
Stabilized liquid membrane devices (SLMDs) passively sample ionic metals in freshwater. They are made of low-density polyethylene plastic tubing sections that are sealed on both ends and filled with an equal mixture of oleic acid and metal chelating agent. They work by interacting with calcium and magnesium ions in freshwater, which forms a hydrophobic film on the outside the SLMD plastic membrane in which the chelating agent can bind to metals in the sampling water. They have been deployed for up to month-long periods in the field, alone or covered by a plastic tube housing to mediate water flow. Metal weight accumulated by a SLMD over its deployment period can be calculated and divided by the SLMD deployment time to get an average metal weight accumulated per time unit, but currently, no method has been developed to convert this to an average metal concentration. In addition, SLMD sampling rates greatly vary with water flow rate, which plastic housings can be used to control.
Passive sampling in air.
Passive sampling can also be accomplished for contaminants in the air, including airborne particles and hazardous vapors and gases. This can be done with man-made devices or with biomonitoring organisms, such as lichens.
Sorbent tubes.
Sorbent tubes are passive samplers for volatile organic compounds (VOCs). They are glass tubes filled with adsorbing materials, such as charcoal or silica gel, which the air to be sampled passes through. The adsorbing materials remove VOCs from the air that passes through them, and the VOCs can be desorbed and analyzed. Air concentrations can be calculated using the amount of air that flowed through the sorbent tube and the amount of contaminants desorbed.
Advantages.
Contaminant concentrations from passive sampling reflect average contamination throughout the sampler deployment time, meaning the sample will capture contaminant concentration fluctuations over the whole deployment period. Traditional grab sampling does not do this, since collected samples only represent a single moment in time and multiple grab samples must be taken to observe variation in contaminant concentrations over time. This integrative sampling method can also can result in the detection of chemicals present at such low concentrations that they would be undetected in a grab sample, due to concentration of the chemicals on the sampler over time. As a result, passive sampling has the potential to be a less time-intensive, less expensive and more accurate sampling method than grab sampling.
In addition, passive samplers are often easy to use and deploy, have no pumps or moving parts, and do not require electricity, since they rely on the molecular diffusion of contaminants or binding of contaminants to agents within the samplers, unlike active sampling. They may also be inexpensive and simple to construct, such as SLMDs, which only require sealed plastic tubing and two chemical components.
Passive sampling may also more accurately reflect metal concentrations that are bioavailable to organisms than other sampling methods. For example, the SPMD sampler uses a semipermeable membrane and triolein (a triglyceride), both of which mimic toxicant uptake by organism fatty tissue. However, this depends on the type of passive sampler used, since some samplers, such as peepers, rely solely on molecular diffusion, which may be too simple to be reflective of the complex processes of contaminant uptake in an organism.
Disadvantages.
Since passive sampling provides information about average contaminant concentrations, all possible concentrations over the sampler deployment time are included in this average value. However, there is no way of finding out the complete range of contaminant concentrations over the deployment time at a single site with only passive sampling. If high and low concentrations of contaminants throughout the sampling period are needed, other sampling methods should be used in conjunction with passive sampling.
Not all passive samplers have universally accurate ways to convert contaminant masses accumulated into water concentrations, which are used in government regulation, such as the United States Environmental Protection Agency Clean Water Act. With some samplers, as with the DGT, this can be done using equations developed for the samplers, but not all samplers have these. Passive sampler deployment time is also limited depending on the sampler's capacity; for example, SLMDs have been deployed for month-long periods, but may reach saturation and stop sampling much sooner if metal concentrations and water flow rates are high enough. However, this issue is avoidable if literature on the relevant passive sampler is examined for background information about sampler capacity and ideal deployment times prior to deployment.


Society for Consciousness Studies

The Society for Consciousness Studies (SCS) is a professional scholarly organization founded in San Francisco. The Society aims to promote a multidisciplinary approach to human and animal consciousness studies. Allan Combs is the founder and president, and founding members of SCS include Combs, Imants Barušs, Julie Mossbridge, Jeffrey Martin, Ben Goertzel, Stephen A. Schwartz, Chris Fields, Laurel McCormick, Stanley Krippner, Carolyn Cooke, Frank Echenhofer, Jayne Gackenbach, Eugene Taylor, Etzel Cardeña, Zoran Josipovic, James Clement van Pelt, and Kate Noble.
History.
The SCS began in 2012 as a collaboration among a group of scholars in the nascent field of consciousness studies who were seeking a professionally rigorous but philosophically open forum for communication with each other and for collaborating on research and scholarly projects.
During its first year, the SCS held several informal meetings in the San Francisco area to discuss the teaching of consciousness studies. It held its first full conference in June 2014 in San Francisco at the California Institute of Integral Studies. Fifty talks and were presented at this conference. During subsequent years the ISCS has held yearly conferences alternating between the West Coast in San Francisco and the East Coast at Yale University. Presenters have represented a wide range of research and scholarship, including the original founders of the Society and world-renowned speakers in the field such as Deepak Chopra, Nancy Ellen Abrams, Bernard Baars, and Ervin Laszlo.
The 2019 Conference, "Consciousness and Spirit II", was held at the Graduate Institute (Bethany, Connecticut) and at the []Yale Divinity School]\ (New Haven) May 31-June 2, 2018. The first "Consciousness and Spirit" conference was presented at Yale in 2008 by the Society for the Anthropology of Consciousness.
Membership and Publications.
Over the past three years, membership in the Society for Consciousness Studies has grown to nearly 200 present members, including doctoral students and scholars from Europe, North and South America, Africa, and Asia.
As of 2018, notable members on the Society's board of directors include Combs, Imants Barušs, Deepak Chopra, Ben Goertzel, and Stanley Krippner.
The Society has a two-tiered membership that includes "incidental short reports" on research, scholarship, and application fields that are influenced by consciousness studies.
The Society also is available to publish and review programs and courses on consciousness studies in North America and elsewhere, as well as publishing incidental reviews of important publications.


List of autonomous areas by country

This list of autonomous areas arranged by country gives an overview of autonomous areas of the world. An autonomous area is defined as an area of a country that has a degree of autonomy, or has freedom from an external authority. It is typical for it to be geographically distant from the country, or to be populated by a national minority. Countries that include autonomous areas are often federacies. The autonomous areas differ from federal units and independent states in the sense that they, in relation to the majority of other sub-national territories in the same country, enjoy a special status including some legislative powers, within the state (for a detailed list of federated units, see Federated state).
This list includes areas that are internationally recognized, as well as some that are generally unrecognized., The definition of an "autonomous area" varies from country to country, so the native term as defined by the respective country's government is listed, and the English translation of the term is included.
Autonomous areas.
Created by international agreements.
Notes:
Created by internal statutes.
All territories called "autonomous".
In a number of countries, all territories or regions of a particular type are called "autonomous". Depending on the case, this may or may not reflect a special devolution of powers or freedom from external authority.
Other entities called "autonomous".
A number of entities are also officially called "autonomous", though they do not have an exceptional freedom from external authority, and would not fall under the definition of autonomous area. They are listed here for clarity.


Avenue of Mysteries

Avenue of Mysteries is a 2015 novel by American author John Irving, his 14th novel. The book was published in November 2015 by Simon & Schuster.
Synopsis.
The narrative traces the life of Juan Diego, an aging writer, who travels to the Philippines while struggling with his memories of growing up as a boy in Mexico. As Ron Charles in "The Washington Post" noted,
Reception.
Initial reviews just before and after publication of "Avenue of Mysteries" were, in general, laudatory. In the "New York Times Book Review", novelist Tayari Jones was particularly effusive in her admiration, even though she was careful to distinguish "Avenue of Mysteries" from Irving's masterpieces, among these "The Cider House Rules" and "A Prayer for Owen Meany". If below the standard of these latter novels, nevertheless Jones thought that "Avenue of Mysteries" held its own:
Kirkus Reviews offered the novel muted praise: "although not as irresistible as early works such as "The World According to Garp" and "The Hotel New Hampshire", a welcome return to form." "Washington Post Book World" editor Ron Charles found vintage Irving here, the author casting familiar elements and themes within "new permutations" amidst "a particularly touching and sometimes farcical story of two siblings and their makeshift family." This same reviewer also noted that although Irving does not shirk from depicting a "dangerous, violent world", the story was cast in a semi-comical glow that was reminiscent of John Steinbeck's "Cannery Row".


Fiducial inference

Fiducial inference is one of a number of different types of statistical inference. These are rules, intended for general application, by which conclusions can be drawn from samples of data. In modern statistical practice, attempts to work with fiducial inference have fallen out of fashion in favour of frequentist inference, Bayesian inference and decision theory. However, fiducial inference is important in the history of statistics since its development led to the parallel development of concepts and tools in theoretical statistics that are widely used. Some current research in statistical methodology is either explicitly linked to fiducial inference or is closely connected to it.
Background.
The general approach of fiducial inference was proposed by Ronald Fisher. Here "fiducial" comes from the Latin for faith. Fiducial inference can be interpreted as an attempt to perform inverse probability without calling on prior probability distributions. Fiducial inference quickly attracted controversy and was never widely accepted. Indeed, counter-examples to the claims of Fisher for fiducial inference were soon published. These counter-examples cast doubt on the coherence of "fiducial inference" as a system of statistical inference or inductive logic. Other studies showed that, where the steps of fiducial inference are said to lead to "fiducial probabilities" (or "fiducial distributions"), these probabilities lack the property of additivity, and so cannot constitute a probability measure.
The concept of fiducial inference can be outlined by comparing its treatment of the problem of interval estimation in relation to other modes of statistical inference.
Fisher designed the fiducial method to meet perceived problems with the Bayesian approach, at a time when the frequentist approach had yet to be fully developed. Such problems related to the need to assign a prior distribution to the unknown values. The aim was to have a procedure, like the Bayesian method, whose results could still be given an inverse probability interpretation based on the actual data observed. The method proceeds by attempting to derive a "fiducial distribution", which is a measure of the degree of faith that can be put on any given value of the unknown parameter and is faithful to the data in the sense that the method uses all available information.
Unfortunately Fisher did not give a general definition of the fiducial method and he denied that the method could always be applied. His only examples were for a single parameter; different generalisations have been given when there are several parameters. A relatively complete presentation of the fiducial approach to inference is given by Quenouille (1958), while Williams (1959) describes the application of fiducial analysis to the calibration problem (also known as "inverse regression") in regression analysis. Further discussion of fiducial inference is given by Kendall & Stuart (1973).
The fiducial distribution.
Fisher required the existence of a sufficient statistic for the fiducial method to apply. Suppose there is a single sufficient statistic for a single parameter. That is, suppose that the conditional distribution of the data given the statistic does not depend on the value of the parameter. For example, suppose that "n" independent observations are uniformly distributed on the interval formula_1. The maximum, "X", of the "n" observations is a sufficient statistic for ω. If only "X" is recorded and the values of the remaining observations are forgotten, these remaining observations are equally likely to have had any values in the interval formula_2. This statement does not depend on the value of ω. Then "X" contains all the available information about ω and the other observations could have given no further information.
The cumulative distribution function of "X" is
Probability statements about "X"/ω may be made. For example, given "α", a value of "a" can be chosen with 0  <  "a"  <  1 such that
Thus
Then Fisher might say that this statement may be inverted into the form
In this latter statement, ω is now regarded as variable and "X" is fixed, whereas previously it was the other way round. This distribution of ω is the "fiducial distribution" which may be used to form fiducial intervals that represent degrees of belief.
The calculation is identical to the pivotal method for finding a confidence interval, but the interpretation is different. In fact older books use the terms "confidence interval" and "fiducial interval" interchangeably. Notice that the fiducial distribution is uniquely defined when a single sufficient statistic exists.
The pivotal method is based on a random variable that is a function of both the observations and the parameters but whose distribution does not depend on the parameter. Such random variables are called pivotal quantities. By using these, probability statements about the observations and parameters may be made in which the probabilities do not depend on the parameters and these may be inverted by solving for the parameters in much the same way as in the example above. However, this is only equivalent to the fiducial method if the pivotal quantity is uniquely defined based on a sufficient statistic.
A fiducial interval could be taken to be just a different name for a confidence interval and give it the fiducial interpretation. But the definition might not then be unique. Fisher would have denied that this interpretation is correct: for him, the fiducial distribution had to be defined uniquely and it had to use all the information in the sample.
Status of the approach.
Fisher admitted that "fiducial inference" had problems. Fisher wrote to George A. Barnard that he was "not clear in the head" about one problem on fiducial inference, and, also writing to Barnard, Fisher complained that his theory seemed to have only "an asymptotic approach to intelligibility". Later Fisher confessed that "I don't understand yet what fiducial probability does. We shall have to live with it a long time before we know what it's doing for us. But it should not be ignored just because we don't yet have a clear interpretation".
Lindley showed that fiducial probability lacked additivity, and so was not a probability measure. Cox points out that the same argument applies to the so-called "confidence distribution" associated with confidence intervals, so the conclusion to be drawn from this is moot. Fisher sketched "proofs" of results using fiducial probability. When the conclusions of Fisher's fiducial arguments are not false, many have been shown to also follow from Bayesian inference.
In 1978, J. G. Pederson wrote that "the fiducial argument has had very limited success and is now essentially dead". Davison wrote "A few subsequent attempts have been made to resurrect fiducialism, but it now seems largely of historical importance, particularly in view of its restricted range of applicability when set alongside models of current interest."
However, fiducial inference is still being studied and its principles appear valuable for some scientific applications. In the mid-2010s, the psychometrician Yang Liu developed generalized fiducial inference for models in item response theory and demonstrated favorable results compared to frequentist and Bayesian approaches. Other current work in fiducial inference is ongoing under the name of confidence distributions.


Theoretical motivation for general relativity

A theoretical motivation for general relativity, including the motivation for the geodesic equation and the Einstein field equation, can be obtained from special relativity by examining the dynamics of particles in circular orbits about the earth. A key advantage in examining circular orbits is that it is possible to know the solution of the Einstein Field Equation "a priori". This provides a means to inform and verify the formalism.
General relativity addresses two questions:
The former question is answered with the geodesic equation. The second question is answered with the Einstein field equation. The geodesic equation and the field equation are related through a principle of least action. The motivation for the geodesic equation is provided in the section Geodesic equation for circular orbits. The motivation for the Einstein field equation is provided in the section Stress–energy tensor.
Geodesic equation for circular orbits.
Kinetics of circular orbits.
For definiteness consider a circular earth orbit (helical world line) of a particle. The particle travels with speed v. An observer on earth sees that length is contracted in the frame of the particle. A measuring stick traveling with the particle appears shorter to the earth observer. Therefore, the circumference of the orbit, which is in the direction of motion appears longer than formula_1 times the diameter of the orbit.
In special relativity the 4-proper-velocity of the particle in the inertial (non-accelerating) frame of the earth is
where c is the speed of light, formula_3 is the 3-velocity, and formula_4 is
The magnitude of the 4-velocity vector is always constant
where we are using a Minkowski metric
The magnitude of the 4-velocity is therefore a Lorentz scalar.
The 4-acceleration in the earth (non-accelerating) frame is
where formula_9 is c times the proper time interval measured in the frame of the particle. This is related to the time interval in the Earth's frame by
Here, the 3-acceleration for a circular orbit is
where formula_12 is the angular velocity of the rotating particle and formula_13 is the 3-position of the particle.
The magnitude of the 4-velocity is constant. This implies that the 4-acceleration must be perpendicular to the 4-velocity. The inner product of the 4-acceleration and the 4-velocity is therefore always zero. The inner product is a Lorentz scalar.
Curvature of spacetime: Geodesic equation.
The equation for the acceleration can be generalized, yielding the geodesic equation
where formula_16 is the 4-position of the particle and formula_17 is the curvature tensor given by
where formula_19 is the Kronecker delta function, and we have the constraints
and
It is easily verified that circular orbits satisfy the geodesic equation. The geodesic equation is actually more general. Circular orbits are a particular solution of the equation. Solutions other than circular orbits are permissible and valid.
Ricci curvature tensor and trace.
The Ricci curvature tensor is a special curvature tensor given by the contraction
The trace of the Ricci tensor, called the scalar curvature, is
The geodesic equation in a local coordinate system.
Consider the situation in which there are now two particles in nearby circular polar orbits of the earth at radius formula_24 and speed formula_25.
The particles execute simple harmonic motion about the earth and with respect to each other. They are at their maximum distance from each other as they cross the equator. Their trajectories intersect at the poles.
Imagine we have a spacecraft co-moving with one of the particles. The ceiling of the craft, the formula_26 direction, coincides with the formula_13 direction. The front of the craft is in the formula_28 direction, and the formula_29 direction is to the left of the craft. The spacecraft is small compared with the size of the orbit so that the local frame is a local Lorentz frame. The 4-separation of the two particles is given by formula_30. In the local frame of the spacecraft the geodesic equation is given by
and
is the curvature tensor in the local frame.
Geodesic equation as a covariant derivative.
The equation of motion for a particle in flat spacetime and in the absence of forces is
If we require a particle to travel along a geodesic in curved spacetime, then the analogous expression in curved spacetime is
where the derivative on the left is the covariant derivative, which is the generalization of the normal derivative to a derivative in curved spacetime. Here
is a Christoffel symbol.
The curvature is related to the Christoffel symbol by
Metric tensor in the local frame.
The interval in the local frame is
where
This gives a metric of
in the local frame.
The inverse of the metric tensor formula_44 is defined such that
where the term on the right is the Kronecker delta.
The transformation of the infinitesimal 4-volume formula_46 is
where g is the determinant of the metric tensor.
The differential of the determinant of the metric tensor is
The relationship between the Christoffel symbols and the metric tensor is
Principle of least action in general relativity.
The principle of least action states that the world line between two events in spacetime is that world line that minimizes the action between the two events. In classical mechanics the principle of least action is used to derive Newton's laws of motion and is the basis for Lagrangian dynamics. In relativity it is expressed as
between events 1 and 2 is a minimum. Here S is a scalar and
is known as the Lagrangian density. The Lagrangian density is divided into two parts, the density for the orbiting particle formula_53 and the density formula_54 of the gravitational field generated by all other particles including those comprising the earth,
In curved spacetime, the "shortest" world line is that geodesic that minimizes the curvature along the geodesic. The action then is proportional to the curvature of the world line. Since S is a scalar, the scalar curvature is the appropriate measure of curvature. The action for the particle is therefore
where formula_57 is an unknown constant. This constant will be determined by requiring the theory to reduce to Newton's law of gravitation in the nonrelativistic limit.
The Lagrangian density for the particle is therefore
The action for the particle and the earth is
We find the world line that lies on the surface of the sphere of radius r by varying the metric tensor. Minimization and neglect of terms that disappear on the boundaries, including terms second order in the derivative of g, yields
where
is the Hilbert stress–energy tensor of the field generated by the earth.
The relationship, to within an unknown constant factor, between the stress-energy and the curvature is
Stress–energy tensor.
Newton's law of gravitation.
Newton's Law of Gravitation in non-relativistic mechanics states that the acceleration on an object of mass formula_63 due to another object of mass formula_64 is equal to
where formula_66 is the gravitational constant, formula_13 is a vector from mass formula_64 to mass formula_63 and formula_24 is the magnitude of that vector. The time t is scaled with the speed of light c
The acceleration formula_72 is independent of formula_63.
For definiteness. consider a particle of mass formula_63 orbiting in the gravitational field of the earth with mass formula_64. The law of gravitation can be written
where formula_77 is the average mass density inside a sphere of radius formula_24.
Gravitational force in terms of the 00 component of the stress–energy tensor.
Newton's law can be written
where formula_80 is the volume of a sphere of radius formula_24. The quantity formula_82 will be recognized from special relativity as the rest energy of the large body, the earth. This is the sum of the rest energies of all the particles that compose earth. The quantity in the parentheses is then the average rest energy density of a sphere of radius formula_24 about the earth. The gravitational field is proportional to the average energy density within a radius r. This is the 00 component of the stress–energy tensor in relativity for the special case in which all the energy is rest energy. More generally
where
where formula_86 is the 4-velocity.
The 00 component of the stress–energy tensor can be generalized to the relativistic case as a linear combination of the two terms
where
4-acceleration due to gravity.
The 4-acceleration due to gravity can be written
Unfortunately, this acceleration is nonzero for formula_90 as is required for circular orbits. Since the magnitude of the 4-velocity is constant, it is only the component of the force perpendicular to the 4-velocity that contributes to the acceleration. We must therefore subtract off the component of force parallel to the 4-velocity. This is known as Fermi–Walker transport. In other words,
This yields
The force in the local frame is
Einstein field equation.
We obtain the Einstein field equation by equating the acceleration required for circular orbits with the acceleration due to gravity
This is the relationship between curvature of spacetime and the stress–energy tensor.
The Ricci tensor becomes
The trace of the Ricci tensor is
Comparison of the Ricci tensor with the Ricci tensor calculated from the principle of least action, Theoretical motivation for general relativity#Principle of least action in general relativity identifying the stress–energy tensor with the Hilbert stress-energy, and remembering that A+B=1 removes the ambiguity in A, B, and C.
and
This gives
The field equation can be written
where
This is the Einstein field equation that describes curvature of spacetime that results from stress-energy density. This equation, along with the geodesic equation have been motivated by the kinetics and dynamics of a particle orbiting the earth in a circular orbit. They are true in general.
Solving the Einstein field equation.
Solving the Einstein field equation requires an iterative process. The solution is represented in the metric tensor
Typically there is an initial guess for the tensor. The guess is used to calculate Christoffel symbols, which are used to calculate the curvature. If the Einstein field equation is not satisfied, the process is repeated.
Solutions occur in two forms, vacuum solutions and non-vacuum solutions. A vacuum solution is one in which the stress–energy tensor is zero. The relevant vacuum solution for circular orbits is the Schwarzschild metric. There are also a number of exact solutions that are non-vacuum solutions, solutions in which the stress tensor is non-zero.
Solving the geodesic equation.
Solving the geodesic equations requires knowledge of the metric tensor obtained through the solution of the Einstein field equation. Either the Christoffel symbols or the curvature are calculated from the metric tensor. The geodesic equation is then integrated with the appropriate boundary conditions.
Electrodynamics in curved spacetime.
Maxwell's equations, the equations of electrodynamics, in curved spacetime are a generalization of Maxwell's equations in flat spacetime (see Formulation of Maxwell's equations in special relativity). Curvature of spacetime affects electrodynamics. Maxwell's equations in curved spacetime can be obtained by replacing the derivatives in the equations in flat spacetime with covariant derivatives. The sourced and source-free equations become (cgs units):
and
where formula_107 is the 4-current, formula_108 is the field strength tensor, formula_109 is the Levi-Civita symbol, and
is the 4-gradient. Repeated indices are summed over according to Einstein summation convention. We have displayed the results in several common notations.
The first tensor equation is an expression of the two inhomogeneous Maxwell's equations, Gauss' law and the Ampère's law with Maxwell's correction. The second equation is an expression of the homogeneous equations, Faraday's law of induction and Gauss's law for magnetism.
The electromagnetic wave equation is modified from the equation in flat spacetime in two ways, the derivative is replaced with the covariant derivative and a new term that depends on the curvature appears.
where the 4-potential is defined such that
We have assumed the generalization of the Lorenz gauge in curved spacetime


Journal of Scientific Exploration


Bobi Jones

Robert Maynard Jones (20 May 1929 – 22 November 2017), generally known as Bobi Jones, was a Welsh Christian academic and one of the most prolific writers in the history of the Welsh language. A versatile master of poetry, fictional prose and criticism, he was born in Cardiff in 1929, educated at the University of Wales, Cardiff (now Cardiff University) and University College Dublin. Jones held the chair in Welsh language at Aberystwyth from 1980 until his retirement. He died on 22 November 2017.
Author.
"Bobi Jones is an author of great significance, not least for non-Welsh speakers. Himself having learnt Welsh, his work offers an insight, more so than the work of most authors whose first language is Welsh, into the significance of Welsh language and culture, particularly because of the strong intellectual or reflective element in his work. Deeply involved with the language and its culture, passionately committed to the best things in Welsh life, there is in his work - even at moments of high intensity - an element of detachment, an ability to step aside and see the wonder of Wales, its beauty and its tragedy, with an outsider's reflective, almost analytical gaze." – John Emyr
Christian.
Bobi Jones was a Christian leaning firmly to Calvinism. He attended a denominational chapel in Aberystwyth until 1970 when he joined a Welsh Evangelical Church which had been established in the town a few years earlier. He therefore followed a trend among Evangelicals of the time in leaving the old Christian denominations (see also Evangelical Movement of Wales and Dr Martyn Lloyd-Jones), on finding that evangelical churches best suited his reformed theology. He had a regular column in the Welsh-language magazine of the Evangelical Movement of Wales, "Y Cylchgrawn Efengylaidd", discussing the Christian heritage of Welsh literature.
Welshman.
Jones was a Welsh nationalist and a strong supporter of the Welsh language. He would argue that culture and the nation are ordained of God and that therefore sustaining their existence is a form of praise to God. His ideas on nationalism and on politics in general are best put forward in his book "Crist a Chenedlaetholdeb (Christ and Nationalism)", published in 1994.
His view on sustaining the Welsh language and his contribution to it are unique. Many Welsh scholars such as R Tudur Jones contributed through support for pressure groups such as "Cymdeithas yr Iaith Gymraeg". Jones was a supporter of such campaigns, but his major contribution to promoting the language was in teaching Welsh to adults.
Having learnt Welsh himself, he held that the key to restoring the Welsh language was to win over the non-Welsh speakers of Wales, as opposed to putting all the energy into campaigning for the rights of existing Welsh speakers. He felt that in addition to protesting over their rights to the government, Welsh speakers should themselves act positively. In adult teaching, he was the founder of CYD: "Cymdeithas y Dysgwyr" (Learners' Society), which arranges night classes in Welsh throughout Wales, and remained its honorary President until his death. Though a republican in his views, he taught Welsh to Prince Charles when the latter attended the University of Wales, Aberystwyth, in the summer of 1969, leading up to his investiture as Prince of Wales.


Werner Lehfeldt

Werner Lehfeldt (born 22 May 1943, Perleberg) is a German Slavist.
Lehfeldt attended primary school "Goethe-Oberschule" in Perleberg and after the escape from East Germany, from 1960 to 1962 the "Ostseegymnasium" in Timmendorfer Strand, where he graduated in 1962. From 1962, he studied Slavic Studies at the Universities of Mainz, Hamburg, Sarajevo and Bochum, receiving a degree in Bochum in 1967 in Slavic Studies and history. He continued to work there the same year as a researcher. In 1973 he habilitated in Bochum and in 1976 was appointed as the Chair in the Department of Slavic Linguistics at the University of Konstanz. In 1980 he declined an offer from the University of Hamburg and also in 1991 as a professor at the University of Geneva, where he taught as a guest professor for one semester. Between 1979 and 1989 he taught for ten semesters at the University of Basel. In 1991 he finally took a position at the University of Göttingen, where he led the Department of Slavic Philology from April 1992 until his retirement on 30 September 2011.
Since 1992 he was a corresponding member of the Croatian Academy of Arts and Sciences. Since 1994 he was a member of the "Akademie gemeinnütziger Wissenschaften" in Erfurt, and since 2011 a member of the Brunswick Scientific Society. On 9 February 1996 he became a full member of Philology and History class of the Göttingen Academy of Sciences and Humanities. On 1 April 2006 to 31 March 2012 he became a chairman of this class and a vice president of the Academy. On 28 October 2010 he received an honorary degree from the Moscow Institute of Russian Language by the Russian Academy of Sciences. On 19 April 2012 he received an honorary degree by the University of Kazan.
Since 1983 Lehfeldt was a co-editor of the journal "Russian Linguistics", from 1993 to 2006 a leading co-editor and an editor-in-chief.
His main research areas include: