Complex functions of the central nervous system such as learning and memory are believed to result from the modulation of the synaptic transmission between neurons. The sequence of events leading to the fusion of synaptic vesicles at the presynaptic active zone and the detection of this signal at the postsynaptic density involve the activity of ion channels and neurotransmitter receptors. Their accumulation and dynamic exchange at synapses are dependent on their interaction with synaptic scaffolds. These are synaptic structures (...) composed of adaptor proteins that provide binding sites for receptors and channels as well as other synaptic proteins. While in its entirety the synaptic scaffold is a relatively stable structure, individual adaptor proteins exchange at a fast time scale. These properties of scaffolds help to ensure the stability of synaptic transmission while permitting the modulation of synaptic strength. Here, we review the dynamics of the synaptic scaffold and of adaptor proteins in relation to their roles in the organisation of the synapse as well as in the clustering and trafficking of receptor proteins. BioEssays 30:1062–1074, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

The developing neuromuscular junction has provided an important paradigm for studying synapse formation. An outstanding feature of neuromuscular differentiation is the aggregation of acetylcholine receptors (AChRs) at high density in the postsynaptic membrane. While AChR aggregation is generally believed to be induced by the nerve, the mechanisms underlying aggregation remain to be clarified. A 43‐kD protein (43k) normally associated with the cytoplasmic aspect of AChR clusters has long been suspected of immobilizing AChRs by linking them to the cytoskeleton. (...) In recent studies, the AChR clustering activity of 43k has, at last, been demonstrated by expressing recombinant AChR and 43k in non‐muscle cells. Mutagenesis of 43k has revealed distinct domains within the primary structure which may be responsible for plasma membrane targeting and AChR binding. Other lines of study have provided clues as to how nerve‐derived (extracellular) AChR‐cluster inducing factors such as agrin might activate 43k‐driven postsynaptic membrane specialization. (shrink)

Realism about quantum theory naturally leads to realism about the quantum state of the universe. It leaves open whether it is a pure state represented by a wave function, or an impure one represented by a density matrix. I characterize and elaborate on Density Matrix Realism, the thesis that the universal quantum state is objective but can be impure. To clarify the thesis, I compare it with Wave Function Realism, explain the conditions under which they are empirically equivalent, (...) consider two generalizations of Density Matrix Realism, and answer some frequently asked questions. I end by highlighting an implication for scientific realism. (shrink)

In this paper we prove that the preordering $\lesssim $ of provable implication over any recursively enumerable theory $T$ containing a modicum of arithmetic is uniformly dense. This means that we can find a recursive extensional density function $F$ for $\lesssim $. A recursive function $F$ is a density function if it computes, for $A$ and $B$ with $A\lnsim B$, an element $C$ such that $A\lnsim C\lnsim B$. The function is extensional if it preserves $T$-provable equivalence. Secondly, we (...) prove a general result that implies that, for extensions of elementary arithmetic, the ordering $\lesssim $ restricted to $\Sigma_{n}$-sentences is uniformly dense. In the last section we provide historical notes and background material. (shrink)

If the density matrix is treated as an objective description of individual systems, it may become possible to attribute the same objective significance to statistical mechanical properties, such as entropy or temperature, as to properties such as mass or energy. It is shown that the de Broglie--Bohm interpretation of quantum theory can be consistently applied to density matrices as a description of individual systems. The resultant trajectories are examined for the case of the delayed choice interferometer, for which (...) Bell [Int. J. Quantum chem. 155--159, (1980)] appears to suggest that such an interpretation is not possible. Bell’s argument is shown to be based upon a different understanding of the density matrix to that proposed here. (shrink)

Two of the most difficult problems in the foundations of physics are (1) what gives rise to the arrow of time and (2) what the ontology of quantum mechanics is. They are difficult because the fundamental dynamical laws of physics do not privilege an arrow of time, and the quantum-mechanical wave function describes a high-dimensional reality that is radically different from our ordinary experiences. -/- In this paper, I characterize and elaborate on the ``Wentaculus” theory, a new approach to time’s (...) arrow in a quantum universe that offers a unified solution to both problems. Central to the Wentaculus are (i) Density Matrix Realism, the idea that the quantum state of the universe is objective but can be impure, and (ii) the Initial Projection Hypothesis, a new law of nature that selects a unique initial quantum state. On the Wentaculus, the quantum state of the universe is sufficiently simple to be a law, and the arrow of time can be traced back to an exact boundary condition. It removes the intrinsic vagueness of the Past Hypothesis, eliminates the Statistical Postulate, provides a higher degree of theoretical unity, and contains a natural realization of “strong determinism." I end by responding to four recent objections. In a companion paper, I elaborate on Density Matrix Realism. (shrink)

Nelson Goodman’s theory of symbol systems expounded in his Languages of Art has been frequently criticized on many counts (cf. list of secondary literature in the entry “Goodman’s Aesthetics” of Stanford Encyclopedia of Philosophy and Sect. 3 below). Yet it exerts a strong influence and is treated as one of the major twentieth-century theories on the subject. While many of Goodman’s controversial theses are criticized, the technical notions he used to formulate them seem to have been treated as neutral tools. (...) One such technical notion is that of the density of symbol systems. This serves to distinguish linguistic symbols from pictorial representations (after Goodman entirely rejected resemblance in that role) and is a crucial part of Goodman’s explanation of what constitutes aesthetic experience (and so indirectly what is art). Thus its significance for Goodman’s theory is fundamental. The aim of this paper is a detailed, logical analysis of this notion. It turns out that Goodman’s definition is highly problematic and cannot be applied to symbol systems in the way Goodman envisaged. To conclude, Goodman’s theory is problematic not just because of its controversial theses but also because of logical problems with the technical notions used at its very core. Hence the controversial claims are not simply contestable, but inaccurately expressed. (shrink)

In noun phrase coordinate constructions, there is a strong tendency for the syntactic structure of the second conjunct to match that of the first; the second conjunct in such constructions is therefore low in syntactic information. The theory of uniform information density predicts that low-information syntactic constructions will be counterbalanced by high information in other aspects of that part of the sentence, and high-information constructions will be counterbalanced by other low-information components. Three predictions follow: lexical probabilities will be lower (...) in second conjuncts than first conjuncts; lexical probabilities will be lower in matching second conjuncts than nonmatching ones; and syntactic repetition should be especially common for low-frequency NP expansions. Corpus analysis provides support for all three of these predictions. (shrink)

The partial ordering of Medvedev reducibility restricted to the family of Π0 1 classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a Π0 1 class, which we call a ``c.e. separating class''. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes.

We show that there exist uncountably many pairwise nonisomorphic density-like ideals on $\omega $ which are not generalized density ideals. In addition, they are nonpathological. This answers a question posed by Borodulin-Nadzieja et al. in [this Journal, vol. 80, pp. 1268–1289]. Lastly, we provide sufficient conditions for a density-like ideal to be necessarily a generalized density ideal.

There are many computational problems which are generally “easy” to solve but have certain rare examples which are much more difficult to solve. One approach to studying these problems is to ignore the difficult edge cases. Asymptotic computability is one of the formal tools that uses this approach to study these problems. Asymptotically computable sets can be thought of as almost computable sets, however every set is computationally equivalent to an almost computable set. Intrinsic density was introduced as a (...) way to get around this unsettling fact, and which will be our main focus.Of particular interest for the first half of this dissertation are the intrinsically small sets, the sets of intrinsic density $0$. While the bulk of the existing work concerning intrinsic density was focused on these sets, there were still many questions left unanswered. The first half of this dissertation answers some of these questions. We proved some useful closure properties for the intrinsically small sets and applied them to prove separations for the intrinsic variants of asymptotic computability. We also completely separated hyperimmunity and intrinsic smallness in the Turing degrees and resolved some open questions regarding the relativization of intrinsic density.For the second half of this dissertation, we turned our attention to the study of intermediate intrinsic density. We developed a calculus using noncomputable coding operations to construct examples of sets with intermediate intrinsic density. For almost all $r\in $, this construction yielded the first known example of a set with intrinsic density r which cannot compute a set random with respect to the r-Bernoulli measure. Motivated by the fact that intrinsic density coincides with the notion of injection stochasticity, we applied these techniques to study the structure of the more well-known notion of MWC-stochasticity.prepared by Justin Miller.E-mail: [email protected]: https://curate.nd.edu/show/6t053f4938w. (shrink)

We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in (...) contrast to a general belief that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed. (shrink)

We review the early works which were precursors of the Conceptual Density Functional Theory. Starting from Thomas–Fermi approximation and from the exact formulation of Density Functional Theory by Hohenberg and Kohn’s theorem, we will introduce electronegativity and the theory of hard and soft acids and bases. We will also present a general introduction to the Fukui functions, and their relation with nucleophilicity and electrophilicity, with an emphasis towards the importance of these concepts for chemical reactivity.

The following strong form of density of definable types is introduced for theoriesTadmitting a fibered dimension functiond: given a modelMofTand a definable setX⊆Mn, there is a definable typepinX, definable over a code forXand of the samed-dimension asX. Both o-minimal theories and the theory of closed ordered differential fields are shown to have this property. As an application, we derive a new proof of elimination of imaginaries for CODF.

We study connections between classical asymptotic density, computability and computable enumerability. In an earlier paper, the second two authors proved that there is a computably enumerable set A of density 1 with no computable subset of density 1. In the current paper, we extend this result in three different ways: The degrees of such sets A are precisely the nonlow c.e. degrees. There is a c.e. set A of density 1 with no computable subset of nonzero (...) density. There is a c.e. set A of density 1 such that every subset of A of density 1 is of high degree. We also study the extent to which c.e. sets A can be approximated by their computable subsets B in the sense that A\B has small density. There is a very close connection between the computational complexity of a set and the arithmetical complexity of its density and we characterize the lower densities, upper densities and densities of both computable and computably enumerable sets. We also study the notion of "computable at density r" where r is a real in the unit interval. Finally, we study connections between density and classical smallness notions such as immunity, hyperimmunity, and cohesiveness. (shrink)

This paper proposes a formalization of the class of sentences quantified by most, which is also interpreted as proportion of or majority of depending on the domain of discourse. We consider sentences of the form “Most A are B”, where A and B are plural nouns and the interpretations of A and B are infinite subsets of \. There are two widely used semantics for Most A are B: \ > C \) and \ > \dfrac{C}{2} \), where C denotes (...) the cardinality of a given finite set X. Although is more descriptive than, it also produces a considerable amount of insensitivity for certain sets. Since the quantifier most has a solid cardinal behaviour under the interpretation majority and has a slightly more statistical behaviour under the interpretation proportional of, we consider an alternative approach in deciding quantity-related statements regarding infinite sets. For this we introduce a new semantics using natural density for sentences in which interpretations of their nouns are infinite subsets of \, along with a list of the axiomatization of the concept of natural density. In other words, we take the standard definition of the semantics of most but define it as applying to finite approximations of infinite sets computed to the limit. (shrink)

For [Formula: see text], the coarse similarity class of A, denoted by [Formula: see text], is the set of all [Formula: see text] such that the symmetric difference of A and B has asymptotic density 0. There is a natural metric [Formula: see text] on the space [Formula: see text] of coarse similarity classes defined by letting [Formula: see text] be the upper density of the symmetric difference of A and B. We study the metric space of coarse (...) similarity classes under this metric, and show in particular that between any two distinct points in this space there are continuum many geodesic paths. We also study subspaces of the form [Formula: see text] where [Formula: see text] is closed under Turing equivalence, and show that there is a tight connection between topological properties of such a space and computability-theoretic properties of [Formula: see text]. We then define a distance between Turing degrees based on Hausdorff distance in the metric space [Formula: see text]. We adapt a proof of Monin to show that the Hausdorff distances between Turing degrees that occur are exactly 0, [Formula: see text], and 1, and study which of these values occur most frequently in the senses of Lebesgue measure and Baire category. We define a degree a to be attractive if the class of all degrees at distance [Formula: see text] from a has measure 1, and dispersive otherwise. In particular, we study the distribution of attractive and dispersive degrees. We also study some properties of the metric space of Turing degrees under this Hausdorff distance, in particular the question of which countable metric spaces are isometrically embeddable in it, giving a graph-theoretic sufficient condition for embeddability. Motivated by a couple of issues arising in the above work, we also study the computability-theoretic and reverse-mathematical aspects of a Ramsey-theoretic theorem due to Mycielski, which in particular implies that there is a perfect set whose elements are mutually 1-random, as well as a perfect set whose elements are mutually 1-generic. Finally, we study the completeness of [Formula: see text] from the perspectives of computability theory and reverse mathematics. (shrink)

It is well known that density matrices can be used in quantum mechanics to represent the information available to an observer about either a system with a random wave function (“statistical mixture”) or a system that is entangled with another system (“reduced density matrix”). We point out another role, previously unnoticed in the literature, that a density matrix can play: it can be the “conditional density matrix,” conditional on the configuration of the environment. A precise definition (...) can be given in the context of Bohmian mechanics, whereas orthodox quantum mechanics is too vague to allow a sharp definition, except perhaps in special cases. In contrast to statistical and reduced density matrices, forming the conditional density matrix involves no averaging. In Bohmian mechanics with spin, the conditional density matrix replaces the notion of conditional wave function, as the object with the same dynamical significance as the wave function of a Bohmian system. (shrink)

Abstract.The partial ordering of Medvedev reducibility restricted to the family of Π01 classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a Π01 class, which we call a ``c.e. separating class''. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes.

We prove several theorems about the cardinal $\mathfrak{g}$ associated with groupwise density. With respect to a natural ordering of families of nond-ecreasing maps fromω toω, all families of size $< \mathfrak{g}$ are below all unbounded families. With respect to a natural ordering of filters onω, all filters generated by $< \mathfrak{g}$ sets are below all non-feeble filters. If $\mathfrak{u}< \mathfrak{g}$ then $\mathfrak{b}< \mathfrak{u}$ and $\mathfrak{g} = \mathfrak{d} = \mathfrak{c}$ . (The definitions of these cardinals are recalled in the introduction.) (...) Finally, some consequences deduced from $\mathfrak{u}< \mathfrak{g}$ by Laflamme are shown to be equivalent to $\mathfrak{u}< \mathfrak{g}$. (shrink)

This paper presents some finite combinatorics of set systems with applications to model theory, particularly the study of dependent theories. There are two main results. First, we give a way of producing lower bounds on $\mathrm {VC}_{\mathrm {ind}}$-density and use it to compute the exact $\mathrm {VC}_{\mathrm {ind}}$-density of polynomial inequalities and a variety of geometric set families. The main technical tool used is the notion of a maximum set system, which we juxtapose to indiscernibles. In the second (...) part of the paper we give a maximum set system analogue to Shelah’s characterization of stability using indiscernible sequences. (shrink)

Lower plasma levels of high-density lipoproteins in adolescents with type 2 diabetes have been associated with a higher pulse wave velocity, a marker of arterial stiffness. Evidence suggests that HDL proteins or particle subspecies are altered in T2D and these may drive these relationships. In this work, we set out to reveal any specific proteins and subspecies that are related to arterial stiffness in youth with T2D from proteomics data. Plasma and PWV measurements were previously acquired from lean and (...) T2D adolescents. Each plasma sample was separated into 18 fractions and evaluated by mass spectrometry. Then, we applied a validated network-based computational approach to reveal HDL subspecies associated with PWV. Among 68 detected phospholipid-associated proteins, we found that seven were negatively correlated with PWV, indicating that they may be atheroprotective. Conversely, nine proteins show positive correlation with PWV, suggesting that they may be related to arterial stiffness. Intriguingly, our results demonstrate that apoA-I and histidine-rich glycoprotein may reverse their protective roles and become antagonistic in the setting of T2D. Furthermore, we revealed two arterial stiffness-associated HDL subspecies, each of which contains multiple PWV-related proteins. Correlation and disease association analyses suggest that these HDL subspecies might link T2D to its cardiovascular-related complications. (shrink)

Analyzing the effective content of the Lebesgue density theorem played a crucial role in some recent developments in algorithmic randomness, namely, the solutions of the ML-covering and ML-cupping problems. Two new classes of reals emerged from this inquiry: thepositive density pointswith respect toeffectively closed sets of reals, and a proper subclass, thedensity-one points. Bienvenu, Hölzl, Miller, and Nies have shown that the Martin-Löf random positive density points are exactly the ones that do not compute the halting problem. (...) Treating this theorem as our starting point, we present several new results that shed light on how density, randomness, and computational strength interact. (shrink)

Alcohol use disorder is one of the most common substance use disorders contributing to both behavioral and cognitive impairments in patients with AUD. Recent neuroimaging studies point out that AUD is a typical disorder featured by altered functional connectivity. However, the details about how voxel-wise functional coordination remain unknown. Here, we adopted a newly proposed method named functional connectivity density to depict altered voxel-wise functional coordination in AUD. The novel functional imaging technique, FCD, provides a comprehensive analytical method for (...) brain's “scale-free” networks. We applied resting-state functional MRI toward subjects to obtain their FCD, including global FCD, local FCD, and long-range FCD. Sixty-one patients with AUD and 29 healthy controls were recruited, and patients with AUD were further divided into alcohol-related cognitive impairment group and non-cognitive impairment group. All subjects were asked to stay stationary during the scan in order to calculate the resting-state gFCD, lFCD, and lrFCD values, and further investigate the abnormal connectivity alterations among AUD-NCI, ARCI, and HC. Compared to HC, both AUD groups exhibited significantly altered gFCD in the left inferior occipital lobe, left calcarine, altered lFCD in right lingual, and altered lrFCD in ventromedial frontal gyrus. It is notable that gFCD of the ARCI group was found to be significantly deviated from AUD-NCI and HC in left medial frontal gyrus, which changes probably contributed by the impairment in cognition. In addition, no significant differences in gFCD were found between ARCI and HC in left parahippocampal, while ARCI and HC were profoundly deviated from AUD-NCI, possibly reflecting a compensation of cognition impairment. Further analysis showed that within patients with AUD, gFCD values in left medial frontal gyrus are negatively correlated with MMSE scores, while lFCD values in left inferior occipital lobe are positively related to ADS scores. In conclusion, patients with AUD exhibited significantly altered functional connectivity patterns mainly in several left hemisphere brain regions, while patients with AUD with or without cognitive impairment also demonstrated intergroup FCD differences which correlated with symptom severity, and patients with AUD cognitive impairment would suffer less severe alcohol dependence. This difference in symptom severity probably served as a compensation for cognitive impairment, suggesting a difference in pathological pathways. These findings assisted future AUD studies by providing insight into possible pathological mechanisms. (shrink)

We classify the asymptotic densities of the sets according to their level in the Ershov hierarchy. In particular, it is shown that for, a real is the density of an n‐c.e. set if and only if it is a difference of left‐ reals. Further, we show that the densities of the ω‐c.e. sets coincide with the densities of the sets, and there are ω‐c.e. sets whose density is not the density of an n‐c.e. set for any.

We study the Vapnik–Chervonenkis density of definable families in certain stable first-order theories. In particular, we obtain uniform bounds on the VC density of definable families in finite $\mathrm {U}$-rank theories without the finite cover property, and we characterize those abelian groups for which there exist uniform bounds on the VC density of definable families.

We show that for any ω-r.e. degree d and n-r.e. degree b with d

Mathematical Logic in Philosophy of Mathematics

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The main result of this paper is an improvement of the upper bound on the cardinal invariant $cov^*(L_0)$ that was discovered in [11]. Here $L_0$ is the ideal of subsets of the set of natural numbers that have asymptotic density zero. This improved upper bound is also dualized to get a better lower bound on the cardinal $non^*(L_0)$. En route some variations on the splitting number are introduced and several relationships between these variants are proved.

Concerning Post's problem for Kleene degrees and its relativization, Hrbacek showed in [1] and [2] that if V = L, then Kleene degrees of coanalytic sets are dense, and then for all K ⊆ωω, there are N1 sets which are Kleene semirecursive in K and not Kleene recursive in each other and K. But the density of Kleene semirecursive in K Kleene degrees is not obtained from these theorems. In this note, we extend these theorems by showing that if (...) V = L, then for all K ⊆ ωω, Kleene semirecursive in K Kleene degrees are dense above K. (shrink)

The derivation of the expression for the density matrix of scattered particles in terms of that of the incident ones, taking different impact parameters into account, shows that under well-specified and realistic conditions, the final density matrix is of the same kind as the initial one. Thus the final mixed state after a collision can be used directly as the initial mixed state in a subsequent collision. Contrary to a recent claim by Band and Park, there are no (...) “fundamental difficulties with quantum mechanical collision theory.”. (shrink)

We construct a G δ set G ⊆ ω ω ×2 ω with null vertical sections such that each perfect set P ⊆2 ω meets almost all vertical sections of G in the following sense: we can define from P subsets S of ω of density zero such that whenever the section determined by x ∈ ω ω does not meet P , then x ∈ S for all but finitely many i . This generalizes theorems of Mokobodzki and (...) Brendle et al. 185–199). (shrink)

This paper is an attempt to count the proportion of tautologies of some intermediate logics among all formulas. Our interest concentrates especially on Medvedev’s logic and its fragment over language with one propositional variable.

The human brain shows neuroplastic adaptations induced by motor skill training. However, the description of the plastic architecture of the whole-brain network in resting-state is still limited. In the present study, we aimed to detect how motor training affected the density distribution of whole-brain resting-state functional connectivity (FC) brain in fast-ball student-athletes using resting-state functional magnetic resonance imaging (fMRI) data of student-athletes (SA), and non-athlete healthy controls (NC). The voxel-wise data-driven graph theory approach, namely global functional connectivity density (...) (gFCD) mapping was applied. The results showed that the SA group exhibited significantly decreased gFCD in brain regions centered at left triangular part of inferior frontal gyrus (IFG), extending to opercular part of left IFG and middle frontal gyrus (MFG) compared with NC group. The findings supported the idea of an increased neural efficiency of athletes’ brain in the brain regions associated with attentional-motor modulation and executive control. Furthermore, the behavioral results demonstrated that in the SA group, faster executive control reaction time was associated with smaller gFCD values in left IFG. The findings implied that the motor skill training would decrease the numbers of FC in IFG to accelerate the execution control with high attentional demands, and focus the attention to the target detection the athletes are interested in. (shrink)

We investigate the evolution of linear density contrasts obtained with respect to a homogeneous spatially flat Friedman-Lemaître–Robertson–Walker background by solving the density contrast equations governed by Newtonian and MONDian force laws using symmetry-based approach. We find eight-parameter Lie group symmetries for the linear order density perturbation equation for the Newtonian case whereas the density contrast equation follows only one parameter Lie group symmetry in MONDian case. We use Lie symmetries to find the group invariant solutions from (...) invariant curve condition. The physical features of the evolution for various mode of density contrast with respect to the global cosmic background density in homogeneous isotropic cosmological models have been investigated using analytical group invariant solutions along with their numerical solutions. An account for cosmological density contrast and mass fluctuation also have been provided. We also have shown that the MONDian force law generates higher amplitudes in the density fluctuation, results in a more rapid structure formation that cannot be possible under the Newtonian force law. (shrink)

The notion of measurement plays a central role in human cognition. We measure people’s height, the weight of physical objects, the length of stretches of time, or the size of various collections of individuals. Measurements of height, weight, and the like are commonly thought of as mappings between objects and dense scales, while measurements of collections of individuals, as implemented for instance in counting, are assumed to involve discrete scales. It is also commonly assumed that natural language makes use of (...) both types of scales and subsequently distinguishes between two types of measurements. This paper argues against the latter assumption. It argues that natural language semantics treats all measurements uniformly as mappings from objects (individuals or collections of individuals) to dense scales, hence the Universal Density of Measurement (UDM). If the arguments are successful, there are a variety of consequences for semantics and pragmatics, and more generally for the place of the linguistic system within an overall architecture of cognition. (shrink)

Motivated by a recent proof of free choices in linking equations to the experiments they describe, I clarify some relations among purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and operator-valued measures), thereby allowing applications of these entities to the modeling of a wider variety of physical situations. I relate conditional probabilities associated with projection-valued measures to conditional density operators identical, in some cases but not in others, to the usual reduced density operators. (...) While a fatal obstacle precludes associating conditional density operators with general non-projective measures, tensor products of general positive operator-valued measures (POVMs) are associated with conditional density operators. This association together with the free choice of probe particles allows a postulate of state reductions to be replaced by a theorem. An application shows an equivalence between one form of quantum key distribution and another with respect to certain eavesdropping attacks. (shrink)

We show that every nontrivial interval in the recursively enumerable degrees contains an incomparable pair which have an infimum in the recursively enumerable degrees.

The presence of agriculture is diminishing in today’s society: it provides only a small percentage of jobs, and the number of visible farms that can provide exposure to agricultural processes is continuously decreasing. We hypothesize that the direct involvement with farm activities or interaction with farmers and visual appreciation of agricultural processes of all kinds, influences rural inhabitants’ relationship to agriculture. We assume that the latter plays a role in how far inhabitants are attached to their place, and more specifically, (...) perceive rural place. In this paper, we aim to initiate a discussion on this complex social relationship and suggest a model to capture fine interactions between relationship to agriculture and rural place attachment. We examine the direct and indirect effects from the density of resident farmers on these interactions. We set up a model using data from empirical research in Germany conducted in 2016. We surveyed rural inhabitants and interviewed farmers in villages purposefully sampled based on high and low density of resident farmers. To reveal underlying relationships among the latent constructs and more directly measurable indicators, as well as the indirect effect of farm presence on place attachment through its effect on forming perceptions about agriculture, we operationalized our analysis using a structural equation model. Besides a good model fit, our initial results indicate that rural inhabitants form stronger relationship to agriculture when the density of resident farmers is higher. Further, farm presence and attachment to rural place are positively related, but needs to be better captured. (shrink)

We present a population density and moment-based description of the stochastic dynamics of domain $${\text{Ca}}^{2+}$$ -mediated inactivation of L-type $${\text{Ca}}^{2+}$$ channels. Our approach accounts for the effect of heterogeneity of local $${\text{Ca}}^{2+}$$ signals on whole cell $${\text{Ca}}^{2+}$$ currents; however, in contrast with prior work, e.g., Sherman et al. :985–995, 1990), we do not assume that $${\text{Ca}}^{2+}$$ domain formation and collapse are fast compared to channel gating. We demonstrate the population density and moment-based modeling approaches using a 12-state Markov (...) chain model of an L-type $${\text{Ca}}^{2+}$$ channel introduced by Greenstein and Winslow :2918–2945, 2002). Simulated whole cell voltage clamp responses yield an inactivation function for the whole cell $${\text{Ca}}^{2+}$$ current that agrees with the traditional approach when domain dynamics are fast. We analyze the voltage-dependence of $${\text{Ca}}^{2+}$$ inactivation that may occur via slow heterogeneous domain [ $${\text{Ca}}^{2+}$$ ]. Next, we find that when channel permeability is held constant, $${\text{Ca}}^{2+}$$ -mediated inactivation of L-type channels increases as the domain time constant increases, because a slow domain collapse rate leads to increased mean domain [ $${\text{Ca}}^{2+}$$ ] near open channels; conversely, when the maximum domain [ $${\text{Ca}}^{2+}$$ ] is held constant, inactivation decreases as the domain time constant increases. Comparison of simulation results using population densities and moment equations confirms the computational efficiency of the moment-based approach, and enables the validation of two distinct methods of truncating and closing the open system of moment equations. In general, a slow domain time constant requires higher order moment truncation for agreement between moment-based and population density simulations. (shrink)