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In this article, we ask how traces of political violence in the Atacama Desert and in the Sonoran Desert are created and how they are (or are not) transformed into archives. The political violence we study is of different types and takes place in different periods: state violence under the civil–military dictatorship (1973-1990) in the Atacama; violence as a product of migratory policies (from 1994 to the present) of the US–Mexican border in the Sonoran Desert in Arizona; and, mass death and disappearance as the product of successive governments' "war on drugs" (from 2006 to the present) in Sonora, Mexico. This article is based on our academic ethnographic work and volunteering with grassroots organizations. In these three arid spaces, we met different groups: family members and activists searching for political prisoners disappeared in the 1970s by the Pinochet regime; activists searching for migrants, dead or alive, lost in the Sonoran Desert in Arizona; and families digging in the earth, unearthing clandestine graves and hoping one day to find the remains of their loved ones. We argue that these different search practices create traces when these groups uncover what the perpetrators wanted to hide. These processes that create traces, then create archives when the situated and lived experience of searching and tracing is translated into artifacts that can be detached from their context and acquire multiple uses outside their place of production. [ABSTRACT FROM AUTHOR]

Jeon, Kang, and Kim defined the Zagier lifts between harmonic weak Maass forms of negative integral weights and half integral weights. These lifts were defined by establishing that traces related to cycle integrals of harmonic weak Maass forms of integral weights appear as Fourier coefficients of harmonic weak Maass forms of half integral weights. For fundamental discriminants d and δ , they studied δ -th Fourier coefficients of the d-th Zagier lift with respect to the condition that d δ is not a perfect square. For d δ being a perfect square, the interpretation of coefficients in terms of traces is not possible due to the divergence of cycle integrals. In this paper, we provide an alternate definition of traces called modified trace in the condition that d δ is a perfect square and interpret such coefficients in terms of the modified trace. [ABSTRACT FROM AUTHOR]

Let [ n ] = X 1 ∪ X 2 ∪ X 3 be a partition with ⌊ n 3 ⌋ ≤ | X i | ≤ ⌈ n 3 ⌉ and define G = { G ⊂ [ n ] : | G ∩ X i | ≤ 1 , 1 ≤ i ≤ 3 } . It is easy to check that the trace G ∣ Y : = { G ∩ Y : G ∈ G } satisfies | G ∣ Y | ≤ 12 for all 4-sets Y ⊂ [ n ] . In the present paper, we prove that if F ⊂ 2 [ n ] satisfies | F | > | G | and n ≥ 28 , then | F ∣ C | ≥ 13 for some C ⊂ [ n ] , | C | = 4 . Several further results of a similar flavor are established as well. [ABSTRACT FROM AUTHOR]

EBV+ diffuse large B cell lymphoma (DLBCL) not otherwise specified (NOS) is a new entity confirmed by the World Health Organization (WHO) in 2017. In this new entity, the virus may contribute to a tolerogenic microenvironment. Traces of the virus have been described in DLBCL with more sensitive methods, in cases that were originally diagnosed as negative. The aim of this study was to analyze the expression of immune response genes in the tumor microenvironment to disclose the role of the virus and its traces in DLBCL. In 48 DLBCL cases, the expression of immune response genes and the presence of molecules that induce tolerance, such as TIM3, LAG3 and PDL1 by immunohistochemistry (IHC), were studied. To broaden the study of the microenvironment, tumor-associated macrophages (TMAs) were also explored. No significant differences were observed in the expression of immune response genes in the EBV+ DLBCL and those cases that were EBV− DLBCL but that exhibited viral traces, assessed by ViewRNA assay. Only the EBV+ DLBCL cases displayed a significantly higher increase in the expression of CD8 and cytotoxic T cells detected by gene expression analysis, and of PDL1 in tumor cells and in the expression of CD68 in the tumor microenvironment detected by IHC, not observed in those cases with viral traces. The increase in CD8 and cytotoxic T cells, PDL1 and CD68 markers only in EBV+ DLBCL may indicate that traces of viral infection might not have influence in immune response markers. [ABSTRACT FROM AUTHOR]

In this paper we fix and consider to be an unbounded, locally compact, non-complete metric measure space equipped with a doubling measure supporting a -Poincaré inequality such that is a uniform domain in its completion . We realize the trace of functions in the Dirichlet–Sobolev space on the boundary as functions in the homogeneous Besov space for suitable ; here, is equipped with a non-atomic Borel regular measure . We show that if satisfies a -codimensional condition with respect to for some , then there is a bounded linear trace operator and a bounded linear extension operator that is a right-inverse of . [ABSTRACT FROM AUTHOR]

This essay has the purpose of underlying how an analytic approach about traces, marks and footprints is an important contribution to sociology at digital era. To achieve this goal, the essay takes the central idea of the book "What People Leave Behind Marks, Traces, Footprints and their Relevance to Knowledge Society", like sources to show a first presentation of a sociology of vestiges to elaborate one vision of experience in the sociology of emotions endeavours. We have followed the ideas of this book as an open door to understand how absences, symptoms and messages are the possibility of constitution a sociology of vestige in a digital world. The main argumentative structure is (a) we briefly present the place of trace on social analysis, (b) the epistemic power of etymology of the terms is synthesized, (c) we show the use of traces in classical social research, (d) vestiges as absences, symptoms and messages are schematized, and finally a door towards a sociology of experience through vestiges is open. This essay is an opportunity to draw attention to the importance of elaborating an analysis of the vestiges to understand the human experience in the framework of a sociology on digital emotions. [ABSTRACT FROM AUTHOR]

We give the equations of the n-th symmetric product X n / S n of a flat affine scheme X = Spec A over a commutative ring F. As a consequence, we find a closed immersion into the coarse moduli space parameterizing n-dimensional linear representations of A. This is done by exhibiting an isomorphism between the ring of symmetric tensors over A and the ring generated by the coefficients of the characteristic polynomial of polynomials in commuting generic matrices giving representations of A. Using this we derive an isomorphism of the associated reduced schemes over an infinite field. When the characteristic is zero we show that this isomorphism is an isomorphism of schemes and we express it in term of traces. [ABSTRACT FROM AUTHOR]

Given a compact (Hausdorff) group G and a closed subgroup H of G, in this paper we present symbolic criteria for pseudo-differential operators on the compact homogeneous space G/H characterizing the Schatten–von Neumann classes S r (L 2 (G / H)) for all 0 < r ≤ ∞. We go on to provide a symbolic characterization for r-nuclear, 0 < r ≤ 1 , pseudo-differential operators on L p (G / H) with applications to adjoint, product and trace formulae. The criteria here are given in terms of matrix-valued symbols defined on noncommutative analogue of phase space G / H × G / H ^. Finally, we present an application of aforementioned results in the context of the heat kernels. [ABSTRACT FROM AUTHOR]

The principal aim in this paper is to employ a recently developed unified approach to the computation of traces of resolvents and ζ -functions to efficiently compute values of spectral ζ -functions at positive integers associated with regular (three-coefficient) self-adjoint Sturm–Liouville differential expressions τ . Depending on the underlying boundary conditions, we express the ζ -function values in terms of a fundamental system of solutions of τ y = z y and their expansions about the spectral point z = 0 . Furthermore, we give the full analytic continuation of the ζ -function through a Liouville transformation and provide an explicit expression for the ζ -regularized functional determinant in terms of a particular set of this fundamental system of solutions. An array of examples illustrating the applicability of these methods is provided, including regular Schrödinger operators with zero, piecewise constant, and a linear potential on a compact interval. [ABSTRACT FROM AUTHOR]

A large part of the Antarctic surface is covered by lichens since they can withstand extreme environmental conditions. Lichens are primary colonizers and contribute to soil formation by deteriorating rocks through a combination of chemical and physical mechanisms. Therefore, fossil remains found exposed on the surface are usually colonized by epilithic and endolithic lichens. The objective of this work is to determine the biodeterioration generated by lichens on fossil remains and its taphonomic implications. We identified the presence of the euendolithic lichens Lecidea andersonii and Athallia holocarpa growing into fossil penguin bones from Antarctica. The bioerosive damage was evaluated using light and electron microscopic techniques. Pits corresponding to apothecium and sinuous thin fissures remodeled, or in some cases produced, by hyphae were distinguished from the cracks originating from physical weathering. The maximum depth that hyphae extend inside the bone, probably constrained by the light supply, was established to be 2.5 mm. We provided a tool for the reconstruction of the chronology of the taphonomic events, describing the type and magnitude of the damage into the bones. [ABSTRACT FROM AUTHOR]

The Murnaghan–Nakayama rule is a combinatorial rule for the character values of symmetric groups. We give a new combinatorial proof by explicitly finding the trace of the representing matrices in the standard basis of Specht modules. This gives an essentially bijective proof of the rule. A key lemma is an extension of a straightening result proved by the second author to skew tableaux. Our module theoretic methods also give short proofs of Pieri's rule and Young's rule. [ABSTRACT FROM AUTHOR]

In this paper, we establish weighted L q – L p -maximal regularity for linear vector-valued parabolic initial-boundary value problems with inhomogeneous boundary conditions of static type. The weights we consider are power weights in time and in space, and yield flexibility in the optimal regularity of the initial-boundary data and allow to avoid compatibility conditions at the boundary. The novelty of the followed approach is the use of weighted anisotropic mixed-norm Banach space-valued function spaces of Sobolev, Bessel potential, Triebel–Lizorkin and Besov type, whose trace theory is also subject of study. [ABSTRACT FROM AUTHOR]

Non-normative genders and sexualities are often framed in research and popular discourse in terms of difference. This descriptor not only signals their departure from social norms, it also promotes the assumption that people who do not identify with traditional binary categories perceive themselves as different, and that their gender or sexuality is the core reason for this. This notion of difference seems particularly ripe for interrogation at a time when traditional categories of gender and sexuality are being disrupted by a burgeoning catalogue of non-binary and hyper-specific identity labels among young people on social network sites and elsewhere. What are we to make of difference in this emergent landscape? We explore this question, drawing on findings from a recent qualitative study of two social generations of Australians who do not identify heteronormatively. Our analysis suggests that the notion of sexuality and gender difference as a coherent basis for identity was far from straightforward in either generation, even though difference figured in notably divergent ways in the two groups. We consider what these tensions around difference might mean for the contemporary politics of gender and sexual identity categories. [ABSTRACT FROM AUTHOR]

The Chinese Mādhyamikas Seng Zhao 374–414, Jizang 549–623, and Zhiyi 538–597 try to demonstrate that the linguistic strategies in the textual transmission of the Buddha's teaching give us access to a sense of "liberation" which reaches beyond language. For them, this ineffable sense is what constitutes the dharma in the shape of sūtra and śāstra. Liberation is considered the constitutive but hidden "root" of all the teachings transmitted via the canonical word, those again account for the Buddha's "traces" guiding back to the meaning of that root. The practitioner's comprehension of the dharma must embrace this circular mutuality of "root and traces," reconciling speech with silence. The article discusses two philosophical aspects: (1) Chinese Madhyamaka semantics and pragmatics exploring the various signifying functions in our use of language, and (2) the hermeneutical approach that the Chinese masters develop in their exegetical works to unravel such a sense of "liberation" in reference to the textual transmission of Indian Mahāyāna thought. [ABSTRACT FROM AUTHOR]

Eigenvalues of tensors play an increasingly important role in many aspects of applied mathematics. The characteristic polynomial provides one of a very few ways that shed lights on intrinsic understanding of the eigenvalues. It is known that the characteristic polynomial of a third order three dimensional tensor has a stunning expression with more than 20000 terms, thus prohibits an effective analysis. In this article, we are trying to make a concise representation of this characteristic polynomial in terms of certain basic determinants. With this, we can successfully write out explicitly the characteristic polynomial of a third order three dimensional tensor in a reasonable length. An immediate benefit is that we can compute out the third and fourth order traces of a third order three dimensional tensor symbolically, which is impossible in the literature. [ABSTRACT FROM AUTHOR]

Stalked crinoids have long been considered sessile. In the 1980s, however, observations both in the field and of laboratory experiments proved that some of them (isocrinids) can actively relocate by crawling with their arms on the substrate, and dragging the stalk behind them. Although it has been argued that this activity may leave traces on the sediment surface, no photographs or images of the traces produced by crawling crinoids have been available. Herein, we present results of neoichnological experiments using the shallowest species of living stalked crinoid, Metacrinus rotundus, dredged from Suruga Bay (near the town of Numazu, Shizuoka Prefecture, ~ 140 m depth). Our results demonstrate that isocrinids produce characteristic locomotion traces, which have some preservation potential. They are composed of rather deep and wide, sometimes weakly sinuous, central drag marks left by the stalk and cirri, and short, shallow scratch marks made by the arms. Based on the functional morphology and taphonomy, it has been argued that the ability to autotomize the stalk and relocate had already evolved in the oldest stem-group isocrinids (holocrinids), likely in response to increased benthic predation pressure during the so-called Mesozoic marine revolution. Our data show that this hypothesis may be corroborated in the future by ichnological findings, which may provide more direct proof of active locomotion in Triassic holocrinids. [ABSTRACT FROM AUTHOR]

We give necessary and sufficient conditions on the symbols to guarantee that the corresponding pseudo-differential operators are nuclear from $$L^{p_1}({\mathbb {S}}^1)$$ into $$L^{p_2}({\mathbb {S}}^1)$$ for $$1\le p_1,p_2<\infty $$ . Applications are given to adjoints of nuclear pseudo-differential operators from $$L^{p_2'}({\mathbb {S}}^1)$$ into $$L^{p_1'}({\mathbb {S}}^1)$$ for $$1\le p_1,p_2<\infty $$ and products of nuclear pseudo-differential operators on $$L^p({\mathbb {S}}^1),\,1\le p<\infty $$ . [ABSTRACT FROM AUTHOR]

The identification of species presents in food is important due to many reasons. Some of them are economic fraud and/or sanitary problems, which could arise from inaccurate identifications of the composition of food products. Adulteration of processed meat generally occurs when there is a considerable price differential between raw materials from different species. Also, it occurs too when trying to introduce raw material of dubious origin, or even raw materials prohibited in some countries for cultural reasons. For example, dog traces were discovered in pet food in Spain in early 2013. This work describes development and validation of two real-time PCR methods, one for dog detection and other one for cat in foodstuffs. The method is based on specific primers/TaqMan probe sets that amplify a fragment of the Cytochrome oxidase subunit I sequences. TaqMan probes allow rapid and accurate assessment of even very small quantities of contaminants, even in thermally treated products. The detection limit was 2 and 0.2 pg of the target DNA from dog and cat, respectively. The methodology was validated to check how the degree of food processing affects the applicability of this technique. Additionally, a total of 100 samples from pet food, farm animal products and raw material were analyzed to apply the developed methodology to commercial samples. Possible applications of these methods are as process control, food security, traceability verification in commercial trade and the correct application of food labelling regulations. In conclusion, the real-time PCR methodology described herein represents a useful tool for the detection of dog and cat traces in all kind of products, including processed products that have undergone aggressive treatments (canned meals and feeds). [ABSTRACT FROM AUTHOR]

We give the basic theory of pseudo-differential operators on finite abelian groups. In the case of a group with two elements, we give a criterion for invertibility of these operators and we also give a solution of the spectral invariance problem for these operators. [ABSTRACT FROM AUTHOR]

Let a trace be a computably enumerable set of natural numbers such that $${V^{[m]} = \{n : \langle n, m\rangle \in V \}}$$ is finite for all m, where $${\langle^{.},^{.}\rangle}$$ denotes an appropriate pairing function. After looking at some basic properties of traces like that there is no uniform enumeration of all traces, we prove varied results on traceability and variants thereof, where a function $${f : \mathbb{N} \rightarrow \mathbb{N}}$$ is traceable via a trace V if for all $${m, \langle f(m), m\rangle \in V.}$$ Then we turn to lattices V a trace. Here, we study the close relationship to $${\mathcal{E} = (\{A : A \subseteq \mathbb{N} \quad c.e.\}, \subseteq)}$$ , automorphisms, isomorphisms, and isomorphic embeddings. [ABSTRACT FROM AUTHOR]

Pseudo-differential operators with operator-valued symbols on the Heisenberg group $${\mathbb{H }}^n$$ are introduced. We give necessary and sufficient conditions on the symbols for which these operators are in the Hilbert-Schmidt class. These Hilbert-Schmidt operators are then identified with Weyl transforms with symbols in $$L^2({\mathbb{R }}^{2n+1}\times {\mathbb{R }}^{2n+1}).$$ We also give a characterization of trace class pseudo-differential operators on the Heisenberg group $${\mathbb{H }}^n$$ . A trace formula for these trace class operators is presented. [ABSTRACT FROM AUTHOR]

Purpose: Intra-vaginal traces can serve as supporting physical evidence of vaginal penetration in sex-crime cases. Vaginal trace sampling guidelines prescribe using a speculum and swabs or swabs only. The use of Locard's exchange theory requires samples of trace materials to always be contamination-free and of accurately known origin. If traces from the outer genital area are accidentally introduced into the vagina during sampling, these traces may be recorded as originating in a location where they were not present at the time of evidence collection. The goal of this study was to assess the risks of false positive findings in vitro of traces found inside the vagina due to trace dislocation caused by current vaginal trace sampling methods (swab-only or with speculum), and for a new method that uses a sleeve accessory to prevent trace dislocation. Methods: Starch solution was applied to the labia of three clean female genitalia mock-ups with vaginas of various diameters and structures. The speculum, swab-only, and sleeve methods were each used 30 times on each mock-up, giving a total of 90 repetitions of each method. Iodine was used to determine whether any starch traces had been introduced vaginally. Results: The speculum and swab-only methods gave 100 and 63-87 % false positive results respectively due to trace dislocation. The sleeve method reduced this to 2 % (0 % after correction). Conclusions: The results suggest that there is a need to conduct clinical in vivo studies to determine whether these results translate into everyday practice and to ensure reliable trace sampling in sex-crime cases. [ABSTRACT FROM AUTHOR]

The formation of several by-products from the photodegradation of testosterone was previously observed under laboratory conditions. The objectives of the manuscript were to complete the identification of testosterone's photoproducts and to develop an analytical method for the detection of testosterone as well as its three main photoproducts in natural sunlit surface waters. To accomplish these tasks, an efficient extraction method was developed based on solid-phase extraction, followed by the use of liquid chromatography coupled to tandem mass spectrometry, a selective and sensitive detection method. This analytical procedure has the capability of detecting target analytes in the ng/L range, with recoveries above 80 %. The methodology was successfully applied to the analysis of testosterone and its photoproducts in several surface waters. [ABSTRACT FROM AUTHOR]

Traces of Augoichnus dituberculatus on Hypermorphocrinus magnospinosus and some other crinoids are described from the reef deposits of the Sarginian Horizon near the village of Ryabinovka, in the vicinity of Krasnoufimsk. Usually these are groups of shallow depressions, egg-shaped in outline, 4-5 mm long, similarly oriented, with a marginal groove, paired tubercles, and a deeper subcentral region. Less commonly the depressions are deep and occasionally even can perforate the skeleton. It is possible that these traces were left by gastropods, which could have moved on the surface of crinoids and fed at their expense. [ABSTRACT FROM AUTHOR]

The mathematical nature of modern science is an outcome of a contingent historical process, whose most critical stages occurred in the seventeenth century. 'The mathematization of nature' (Koyré , From the closed world to the infinite universe, 5) is commonly hailed as the great achievement of the 'scientific revolution', but for the agents affecting this development it was not a clear insight into the structure of the universe or into the proper way of studying it. Rather, it was a deliberate project of great intellectual promise, but fraught with excruciating technical challenges and unsettling epistemological conundrums. These required a radical change in the relations between mathematics, order and physical phenomena and the development of new practices of tracing and analyzing motion. This essay presents a series of discrete moments in this process. For mediaeval and Renaissance philosophers, mathematicians and painters, physical motion was the paradigm of change, hence of disorder, and ipso facto available to mathematical analysis only as idealized abstraction. Kepler and Galileo boldly reverted the traditional presumptions: for them, mathematical harmonies were embedded in creation; motion was the carrier of order; and the objects of mathematics were mathematical curves drawn by nature itself. Mathematics could thus be assigned an explanatory role in natural philosophy, capturing a new metaphysical entity: pure motion. Successive generations of natural philosophers from Descartes to Huygens and Hooke gradually relegated the need to legitimize the application of mathematics to natural phenomena and the blurring of natural and artificial this application relied on. Newton finally erased the distinction between nature's and artificial mathematics altogether, equating all of geometry with mechanical practice. [ABSTRACT FROM AUTHOR]

Let τ be a faithful normal semi-finite trace on a von Neumann algebra M, $\tilde \tau $ is the extension of τ on the set of all (in general, unbounded) self-adjoint positive operators affiliated with M. We study inequalities of the form where f, w are nonnegative real-valued functions, A and B are unbounded self-adjoint positive operators affiliated with algebra M such that A ≤ B. A new characterization of the traces related to these inequalities will be shown. [ABSTRACT FROM AUTHOR]

n h-set is a non-empty compact subset of the Euclidean n-space which supports a finite Radon measure for which the measure of balls centered on the subset is essentially given by the image of their radius by a suitable function h. In most cases of interest such a subset has Lebesgue measure zero and has a fractal structure. We prove the existence of solutions for the so-called fractal Dirichlet problem for such h-sets. The 'construction' of the solutions is based on the consideration of complete o.n. systems for convenient function spaces on the fractals. These systems are obtained combining properties of traces with integral representations (obtained with the help of Green's functions) for the so-called fractal Laplacian. [ABSTRACT FROM AUTHOR]

This essay draws upon race theory, psychoanalysis, and pastoral care to address the remnants of past and current racial trauma in the African American psyche. The metaphor of 'traces on the blackboard' is the chief means by which I attempt to delineate how African Americans, although experiencing new echelons of social progress, are still struggling to eliminate the distorted models of self-identification which were promulgated by the dominant culture. I also discuss the failure of psychodynamic psychotherapies to address the traces of racism, make proposals for how they may go about identifying these traces, and explore the role that pastoral care and, in particular, pastoral counseling may play in enervating these traces. [ABSTRACT FROM AUTHOR]

The aim of this study was to develop an efficient, sensitive and reliable analytical method for the determination of traces of steroid hormones (including oestrogen, androgens and progestagens) and corticosteroids in soil. A method of sample preparation involving pressurized liquid extraction (PLE) and solid-phase extraction (SPE) was developed for the determination of six steroids and five corticosteroids in soils, followed by analysis by liquid chromatography-tandem mass spectrometry. The conditions employed for PLE involved acetone/methanol (50:50) as the extracting solvent, a temperature of 80 °C, two cycles and a static time of 5 min. The extraction was followed by a SPE clean-up based on a polymeric phase. With use of protocol, a residual matrix effect was, however, highlighted. The limit of detection in soil was 0.08–0.89 ng/g for steroids and 0.09–2.84 ng/g for corticosteroids. [ABSTRACT FROM AUTHOR]

Formal power series over non-commuting variables have been investigated as representations of the behavior of automata with multiplicities. Here we introduce and investigate the concepts of aperiodic and of star-free formal power series over semirings and partially commuting variables. We prove that if the semiring K is idempotent and commutative, or if K is idempotent and the variables are non-commuting, then the product of any two aperiodic series is again aperiodic. We also show that if K is idempotent and the matrix monoids over K have a Burnside property (satisfied, e.g. by the tropical semiring), then the aperiodic and the star-free series coincide. This generalizes a classical result of Schützenberger (Inf. Control 4:245–270, ) for aperiodic regular languages and subsumes a result of Guaiana et al. (Theor. Comput. Sci. 97:301–311, ) on aperiodic trace languages. [ABSTRACT FROM AUTHOR]

A space A (ℝ n ) with A = B or A = F and s ∈ ℝ, 0 < p,q < ∞ either has a trace in L p (Γ), where Γ is a compact d-set in ℝ n with 0 < d < n, or D(ℝ n Γ) is dense in it. Related dichotomy numbers are introduced and calculated. [ABSTRACT FROM AUTHOR]

Considering the Sobolev type function classes on a metric space equipped with a Borel measure we address the question of compactness of embeddings of the space of traces into Lebesgue spaces on the sets of less “dimension.” Also, we obtain compactness conditions for embeddings of the traces of the classical Sobolev spaces W on the “zero” cusp with a Hölder singularity at the vertex. [ABSTRACT FROM AUTHOR]

A rapid, extraction-spectrophotometric determination of trace amounts of lead in heavy metal salts is proposed. Owing to application of ammonia as masking agent, the extraction system cryptand (2.2.2)-eosin-chlorobenzene exhibits very high selectivity towards transition metal cations. Using standard addition method, lead is determined without matrix separation in nitrates, chlorides, acetates and sulphates of such metals as Ag, Cd, Ni, Cu and Zn. The effect of matrix on lead extraction efficiency and blank value is also discussed. The high sensitivity and selectivity of the proposed method allow to determine of lead at the level 10−10. [ABSTRACT FROM AUTHOR]