Classical Root Research Articles

Neither Populist Nor Neoclassical: The Classical Roots of the Competition Principle in American Antitrust

Most of the current critical views on American antitrust law focus on a supposed misinterpretation by modern, welfare-driven antitrust enforcers of the true meaning of the competition principle. The paper contributes to the debate by reconstructing the principle’s historical origin. While it did not feature in the Sherman Act, the competition principle was introduced by the Supreme Court during the formative era of antitrust law. Between 1897 and 1911 the Court proposed alternative versions of the principle; the one which eventually prevailed was neither populist nor neoclassical, as it was based on classical political economy and, in particular, on freedom of contract and “natural” values. Yet, this historical circumstance is not necessarily bad news for recent proposals to reform antitrust law.

Combinatorics of Generalized Exponents

Abstract We give a purely combinatorial proof of the positivity of the stabilized forms of the generalized exponents associated to each classical root system. In finite type $A_{n-1}$, we rederive the description of the generalized exponents in terms of crystal graphs without using the combinatorics of semistandard tableaux or the charge statistic. In finite type $C_{n}$, we obtain a combinatorial description of the generalized exponents based on the so-called distinguished vertices in crystals of type $A_{2n-1}$, which we also connect to symplectic King tableaux. This gives a combinatorial proof of the positivity of Lusztig $t$-analogs associated to zero-weight spaces in the irreducible representations of symplectic Lie algebras. We also present three applications of our combinatorial formula and discuss some implications to relating two type $C$ branching rules. Our methods are expected to extend to the orthogonal types.

On R-matrix valued Lax pairs for Calogero–Moser models

This article is devoted to the study of R-matrix-valued Lax pairs for N-body (elliptic) Calogero–Moser models. Their matrix elements are given by quantum R-matrices of Baxter–Belavin type. For the widely known Krichever’s Lax pair with spectral parameter is reproduced. First, we construct the R-matrix-valued Lax pairs for Calogero–Moser models associated with classical root systems. For this purpose we study generalizations of the D’Hoker–Phong Lax pairs. It appeared that in the R-matrix-valued case the Lax pairs exist in special cases only. The number of quantum spaces (on which R-matrices act) and their dimension depend on the values of coupling constants. Some of the obtained classical Lax pairs admit straightforward extension to the quantum case. In the end we describe a relationship of the R-matrix-valued Lax pairs to Hitchin systems defined on bundles with nontrivial characteristic classes over elliptic curve. We show that the classical analogue of the anisotropic spin exchange operator entering the R-matrix-valued Lax equations is reproduced in these models.

Active Stabilization of Slung Loads in High-Speed Flight Using Cable Angle Feedback

This paper addresses the problem of active stabilization of slung loads up to 130 kt. To demonstrate the method, simulations of a utility helicopter with a dynamic inversion controller (as its automatic flight control system) and a CONEX cargo container were used. An airspeed-scheduled controller utilizing cable angle feedback was designed for the nonlinear-coupled system by the classic root locus technique. Nonlinear simulations of straight and level flight at different airspeeds were used to validate the controller performance in stabilizing the load pendulum motions. Controller performance was also evaluated in complex maneuvers with different levels of turbulence. The results show that using cable angle feedback provides or improves system stability when turbulence is not included in the simulation. When light/moderate turbulence is present, sustained limit cycle oscillations are avoided by the use of the controller. For severe turbulence levels, the controller did not provide any significant improvement.

Aortic Root Sign

Appearance: The aortic root sign describes an anomalous circumflex coronary artery (ACCA) that emerges from the contralateral coronary sinus, and travels underneath the aorta to supply blood to its normal vascular territory. Explanation: The moniker, “aortic root sign,” was first coined by Page et al1 on conventional angiography to describe ACCA as arising from the proximal right coronary artery or right coronary sinus. The aberrant vessel courses inferiorly behind the aortic root within the groove between the left atrium and aorta,2 hence the term “aortic root sign” (Fig. 1).FIGURE 1: Fifty-six-year-old patient with atypical chest pain. A, Right anterior oblique ventriculogram from left heart catheterization demonstrates anomalous course of the left circumflex (LCX) en face below the aortic root (classic aortic root “dot” sign; thin arrow) (LV=left ventricle). B, Electrocardiogram-gated cardiac computed tomography (CT) matched in projection of the cardiac catheterization reveals the same signature appearance of the anomalous LCX (thin arrow). C, CT correlate of the conventional aortic root “dot” sign seen on an axial image from an electrocardiogram-gated CT reveals the anomalous LCX coursing inferior to the noncoronary sinus of the aortic root (medium arrow) (RA=right atrium, RV=right ventricle, LA=left atrium). D, Volume-rendered image of the aortic root demonstrates coronary origin from the right sinus of Valsalva (asterisk) with immediate takeoff of the anomalous LCX (arrowhead) from the normal right coronary artery (large arrow).Discussion: Traditionally coronary artery anomalies (CAAs) were thought to have little significance, and were often discovered as incidental findings on angiography. However, patients may present with clinically significant disease.2 In fact, CAAs are the second most common cause of sudden cardiac death in young athletes in the United States.2 ACCA was first described by Antopol and Kugel.3 The prevalence of ACCA reported in the coronary angiography literature ranges from 0.18% to 0.67%, making it the most common CAA. Some authors postulate that the oblique angulation of its origin predisposes ACCA to atherosclerosis. However, most clinicians agree that ACCA is a benign, asymptomatic anomaly. Indeed, the retroaortic course of ACCA, as described by the aortic root sign, rarely leads to ischemia or sudden cardiac death. On the contrary, CAAs that travel along an interarterial course between the aorta and pulmonary artery are more prone to ischemia during strenuous exercise.2 Despite the low risk of ischemia and sudden death with ACCA, recognition of this anomaly is still of great clinical importance because failure to identify this aberrant vessel can lead to adverse patient outcomes, especially during cardiac surgery. Therefore, it is crucial for the angiographer as well as the radiologist to be adept at recognizing ACCA and the other coronary anomalies, especially given the ease of diagnosis with noninvasive coronary imaging techniques, such as multidetector computed tomography4 and cardiac magnetic resonance imaging.5

Bootstrap Model Averaging Unit Root Inference

Classical unit root tests are known to suffer from potentially crippling size distortions, and a range of procedures have been proposed to attenuate this problem, including the use of bootstrap procedures. It is also known that the estimating equation’s functional form can affect the outcome of the test, and various model selection procedures have been proposed to overcome this limitation. In this paper, we adopt a model averaging procedure to deal with model uncertainty at the testing stage. In addition, we leverage an automatic model-free dependent bootstrap procedure where the null is imposed by simple differencing (the block length is automatically determined using recent developments for bootstrapping dependent processes). Monte Carlo simulations indicate that this approach exhibits the lowest size distortions among its peers in settings that confound existing approaches, while it has superior power relative to those peers whose size distortions do not preclude their general use. The proposed approach is fully automatic, and there are no nuisance parameters that have to be set by the user, which ought to appeal to practitioners.

Structural Break, Stock Prices of Clean Energy Firms and Carbon Market

This paper uses EU ETS carbon future price and Germany/UK clean energy firms stock indices to study the relationship between carbon market and clean energy market. By structural break test, it is found that the ‘non-stationary’ variables judged by classical unit root test do own unit roots and need taking first difference. After analysis of VAR and Granger causality test, no causal relationships are found between the two markets. However, when Hsiao’s version of causality test is employed, carbon market is found to have power in explaining the movement of stock prices of clean energy firms, and stock prices of clean energy firms also affect the carbon market.

Testing for Bubbles in Cryptocurrencies with Time-Varying Volatility

The recent evolution of cryptocurrencies has been characterized by bubble-like behavior and extreme volatility. While it is difficult to assess an intrinsic value to a specific cryptocurrency, one can employ recently proposed bubble tests that rely on recursive applications of classical unit root tests. This paper extends this approach to the case where volatility is time varying, assuming a deterministic long-run component that may take into account a decrease of unconditional volatility when the cryptocurrency matures with a higher market dissemination. Volatility also includes a stochastic short-run component to capture volatility clustering. The wild bootstrap is shown to correctly adjust the size properties of the bubble test, which retains good power properties. In an empirical application using eleven of the largest cryptocurrencies and the CRIX index, the general evidence in favor of bubbles is confirmed, but much less pronounced than under constant volatility.

Water Institutional Arrangements of FalajAl Daris in the Sultanate of Oman

Oman, which is located on the Southern East of Arabian Peninsula, classified as holding a semi-arid climate with an average annual rainfall of 100 mm. Therefore, agricultural production in Oman is fully dependent in irrigation. More than one third is supplied by the ancient aflaj (sing. Falaj), which provide 680 x 106 m3 of water per year and irrigate of an area of 26,500 ha. There is two commonly known definition of the aflaj; the locally defined from the classic Arabic root as to divide the water among its shareholders. In addition, the modern technical definition as trenches and tunnels, which are dug in the ground, to convey the accumulated rainfall water table to the irrigated area in the villages. This study explore some of the existing institutional arrangements found within Falajdaris, at the waliyat (city) of Nizwalocated in the Dakhillya governmental, Sultanate of Oman. This study uses mainly face-To-face interviews with local administrative falaj agents to explore and discuss the most operated mechanized of the institutional arrangements. The study concluded that there is strong relationship between FalajDaris institutional arrangements development and physical water variability. Int. J. Soc. Sc. Manage. Vol. 5, Issue-1: 31-42

Libertarianism after Nozick

AbstractRobert Nozick's Anarchy, State, and Utopia made libertarianism a major theory in political philosophy. However, the book is often misread as making impractical, question‐begging arguments on the basis of a libertarian self‐ownership principle. This essay explains how academic philosophical libertarianism since Robert Nozick has returned to its humanistic, classical liberal roots. Contemporary libertarians largely work within the PPE (politics, philosophy, and economics) tradition and do what Michael Huemer calls “non‐ideal, non‐theory.” They more or less embrace rather than reject ideals of social justice, and they accept that positive liberty is important. The difference between them and Left‐liberals is not so much a dispute over fundamental values, but empirical disagreements about the extent of market versus government failure.In contemporary political philosophy, libertarianism remains a significant but influential minority position. Nevertheless, many philosophers have little sense of how libertarian and classical liberal thought has developed and changed after Robert Nozick's seminal Anarchy, State, and Utopia, published in 1974. This essay provides a short guide.The terms “libertarianism” and “classical liberalism” refer to a body of related views about politics, philosophy, and economics. As a body of related ideas, classical liberalism has the unity of a neighborhood more than a house. That said, libertarians and classical liberals generally tend to argue for following two sets of claims: As a matter of justice, each individual has an extensive set of negative civil and economic rights, which cannot easily be overridden in the name of utility, stability, or desirable cultural goals. Granting everyone a wide scope of personal and economic liberty tends to generate good consequences, while restrictions on liberty tend to produce bad consequences. Classical liberals accept that markets and civil society can fail, but they argue government agents generally lack both the competence and the motivation to intervene in ways that fix rather than exacerbate the problems (Mueller, ). The first set of arguments is deontological; the second is consequentialist.Early classical liberal thinkers, such as Adam Smith, Adam Ferguson, and David Hume, did not quite recognize this distinction. They made both arguments without any apparent worry that these were different kinds of argument.But Robert Nozick, the most famous libertarian philosopher of the Twentieth Century, seemed to focus almost entirely on rebutting deontological arguments against libertarianism with providing deontological arguments of his own. This tendency, along with the radical contrarianism of certain other mid‐Twentieth Century libertarians, seems to cause the perception that libertarians are impractical and inhumane (Barry, ; Sachs, ).In contrast to Nozick, contemporary classical liberal thought is largely pre‐occupied with social justice issues and with assessing the expected consequences of adopting various institutions and policies. In a sense, this a return to Adam Smith and origins of classical liberal thought: Contemporary classical liberals are not so much synthesizing left‐liberalism and classical liberalism as they are instead clarifying the basic concerns that have driven mainline classical liberal thought all along.

On the Kato problem and extensions for degenerate elliptic operators

We study the Kato problem for degenerate divergence form operators. This was begun by Cruz-Uribe and Rios who proved that given an operator $L_w=-w^{-1}{\rm div}(A\nabla)$, where $w\in A_2$ and $A$ is a $w$-degenerate elliptic measure (i.e, $A=w\,B$ with $B$ an $n\times n$ bounded, complex-valued, uniformly elliptic matrix), then $L_w$ satisfies the weighted estimate $\|\sqrt{L_w}f\|_{L^2(w)}\approx\|\nabla f\|_{L^2(w)}$. Here we solve the $L^2$-Kato problem: under some additional conditions on the weight $w$, the following unweighted $L^2$-Kato estimates hold $$ \|L_w^{1/2}f\|_{L^2(\mathbb{R}^n)}\approx\|\nabla f\|_{L^2(\mathbb{R}^n)}. $$ This extends the celebrated solution to the Kato conjecture by Auscher, Hofmann, Lacey, McIntosh, and Tchamitchian, allowing the differential operator to have some degeneracy in its ellipticity. For example, we consider the family of operators $L_\gamma=-|x|^{\gamma}{\rm div}(|x|^{-\gamma}B(x)\nabla)$, where $B$ is any bounded, complex-valued, uniformly elliptic matrix. We prove that there exists $\epsilon>0$, depending only on dimension and the ellipticity constants, such that $$ \|L_\gamma^{1/2}f\|_{L^2(\mathbb{R}^n)}\approx\|\nabla f\|_{L^2(\mathbb{R}^n)}, \qquad -\epsilon<\gamma<\frac{2\,n}{n+2}. $$ This gives a range of $\gamma$'s for which the classical Kato square root $\gamma=0$ is an interior point. Our main results are obtained as a consequence of a rich Calder\'on-Zygmund theory developed for some operators associated with $L_w$. These results, which are of independent interest, establish estimates on $L^p(w)$, and also on $L^p(v\,dw)$ with $v\in A_\infty(w)$, for the associated semigroup, its gradient, the functional calculus, the Riesz transform, and square functions. As an application, we solve some unweighted $L^2$-Dirichlet, Regularity and Neumann boundary value problems for degenerate elliptic operators.

Tolkien's Classical Beowulf and England's Heroic Age

Tolkien's Classical Beowulf and England's Heroic Age Jane Chance (bio) J.R.R. Tolkien's writing is not generally regarded today as having been greatly influenced by the classics. However, in the mid-eighties, Robert E. Morse noted that just as the modern poet "[T. S.] Eliot sees Vergil, not a Nordic myth, at the center of European civilization," rather surprisingly, "if we look, we may find he is at the heart of Middle Earth" (Evocation of Virgil 55). Believing that Tolkien was trying to understand how Virgil had "revitalized" the epic form—which he sought to do as well in The Lord of the Rings—Morse singled out their common denominator as the two authors' shared reliance on history (Evocation of Virgil 53). Further, Morse added, "The languages, geography, and political ties described in The Lord of the Rings are reminiscent of Rome, the Latin League, and Rome's empire" (Evocation of Virgil 45). This observation may come as no surprise: Tolkien had studied both Latin and Greek from the age of eleven at King Edward's School and received a Classical Exhibition Prize at Exeter, where he originally intended to study "Classical Moderations." In his first year Tolkien studied Latin and Greek, but switched in his second to the modern languages of Old Norse, Gothic, Old and Middle English. His knowledge of and familiarity with the works of Virgil, Homer, and Plato, according to Humphrey Carpenter, certainly influenced his works of fantasy as fully as Gothic, Old and Middle English, and Old Norse have (Bio 33–71). In this regard, the major classical roots of and analogues to Tolkien's fantasy narratives have been previously identified: Morse traces the Virgilian influence of the exile and flight of Aeneas on the exile and wandering of Bilbo and Frodo and the fighting of Aragorn; further, just as Dido serves as a model for Denethor, both stewards of the city succumb to passion (Morse, "From Snake to Caterpillar," np). Other scholars have similarly adduced parallels between the heroes and gods of Virgil and Tolkien's own characters and creations in The Hobbit, The Lord of the Rings, and The Silmarillion, and earlier or variant versions of both found in The History of Middle-earth. In addition, David Greenman has identified the source for the patterns of escape and return in "The Fall of Gondolin" and The Return [End Page 59] of the King as both Virgilian and Homeric ("Aeneidic and Odyssean Patterns," 4–9). Aeneas's need to flee from the old Troy to create a new empire in Rome and that of Tolkien's Tuor to escape match Odysseus's need to return to Penelope in Ithaka and that of the four Hobbits to return to the Shire. Kenneth J. Reckford also notes similarities between Odysseus and Bilbo in The Hobbit, as well as between the Trolls and the Cyclops (particularly Polyphemus), and Gandalf and Pallas Athena ("'There and Back Again'" 5–9). In studying the Homeric parallels in The Lord of the Rings Mac Fenwick recognizes a "Homeric catalogue" (as Tolkien described it in a draft of "Minas Tirith" (WR 229), in the Gondorian nobles who usher in their men for the last defense (Fenwick 17–23, 50). Fenwick also notes that Tolkien frequently calls the Riders of Rohan "heroic 'Homeric' horsemen. More importantly, Fenwick cites Tolkien as pointing to the necessity for a writer of a "tale of this sort" as needing to "consult your roots," because "a man of the North-west of the Old World will set his heart and the action of his tale in an imaginary world of that air, and that situation" (Letters 212).1 Equally interesting for understanding Tolkien's classicism is Fenwick's perception that the women of Homer—helpful Circe and Calypso and their antitypes, the female monsters, the Sirens, Scylla and Charybdis—either aid or challenge the journey of Odysseus, in a manner similar to the roles of the females Galadriel and her antithesis Shelob, as mediated by Frodo and Sam. Fenwick's point is that Tolkien borrows from the Homeric epic in building the maturation of his heroes: "In both, the hero's success depends not...

Superrigidity from Chevalley groups into acylindrically hyperbolic groups via quasi-cocycles

We prove that every homomorphism from the elementary Chevalley group over a finitely generated unital commutative ring associated with a reduced irreducible classical root system of rank at least 2, and ME analogues of such groups, into an acylindrically hyperbolic group has an absolutely elliptic image. This result provides a non-arithmetic generalization of homomorphism superrigidity of Farb–Kaimanovich–Masur and Bridson–Wade

The classical roots of the Austrian theory of capital and entrepreneurship

The paper deals with the continuities and discontinuities between some classical, Austrian and neo-Austrian authors with regard first to the theory of capital and then to the theory of entrepreneurship. Part I focuses on the elements of continuity between the classical and the Austrian theory of capital. These elements have been singled out by dealing first with the distinction between individual and national capital; and then with the difference between the resulting circulating-fixed capital and free-invested capital distinctions in the light, first, of the concept of roundaboutness and, then, of the method of vertical integration. Part II focuses on the elements of continuity between the Austrian theory of individual behaviour and the classical theory of national wealth. The distinctions between logical and historical time and between economics of time and economics in time are used to assess the links between the theory of capital as developed by the classics and Bohm-Bawerk, on the one hand, and the theory of entrepreneurship as developed by the neo-Austrians, on the other.

Macdonald–Koornwinder moments and the two-species exclusion process

Introduced in the late 1960’s (Macdonald et al. in Biopolymers 6:1–25, 1968; Spitzer in Adv Math 5:246–290, 1970), the asymmetric exclusion process (ASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice with open boundaries. It has been known for awhile that there is a tight connection between the partition function of the ASEP and moments of Askey–Wilson polynomials (Uchiyama et al. in J Phys A 37(18):4985–5002, 2004; Corteel and Williams in Duke Math J 159(3):385–415, 2011; Corteel et al. in Trans Am Math Soc 364(11):6009–6037, 2012), a family of orthogonal polynomials which are at the top of the hierarchy of classical orthogonal polynomials in one variable. On the other hand, Askey–Wilson polynomials can be viewed as a specialization of the multivariate Macdonald–Koornwinder polynomials (also known as Koornwinder polynomials), which in turn give rise to the Macdonald polynomials associated to any classical root system via a limit or specialization (van Diejen in Compos Math 95(2):183–233, 1995). In light of the fact that Koornwinder polynomials generalize the Askey–Wilson polynomials, it is natural to ask whether one can find a particle model whose partition function is related to Koornwinder polynomials. In this article we answer this question affirmatively, by showing that Koornwinder moments at $$q=t$$ are closely connected to the partition function for the two-species exclusion process.

Roughness of oxide glass subcritical fracture surfaces

AbstractAn original setup combining a very stable loading stage, an atomic force microscope and an environmental chamber, allows to obtain very stable subcritical fracture propagation in oxide glasses under controlled environment, and subsequently to finely characterize the nanometric roughness properties of the crack surfaces. The analysis of the surface roughness is conducted both in terms of the classical root mean square roughness to compare with the literature, and in terms of more physically adequate indicators related to the self‐affine nature of the fracture surfaces. Due to the comparable nanometric scale of the surface roughness, the AFM tip size and the instrumental noise, a special care is devoted to the statistical evaluation of the metrologic properties. The roughness amplitude of several oxide glasses was shown to decrease as a function of the stress intensity factor, to be quite insensitive to the relative humidity and to increase with the degree of heterogeneity of the glass. The results are discussed in terms of several modeling arguments concerning the coupling between crack propagation, material's heterogeneity, crack tip plastic deformation and water diffusion at the crack tip. A synthetic new model is presented combining the predictions of a model by Wiederhorn et al (J Non‐Cryst Solids, 353, 1582‐1591, 2007) on the effect of the material's heterogeneity on the crack tip stresses with the self‐affine nature of the fracture surfaces.

Generalized reflection root systems

We study a combinatorial object, which we call a GRRS (generalized reflection root system); the classical root systems and GRSs introduced by V. Serganova are examples of finite GRRSs. A GRRS is finite if it contains a finite number of vectors and is called affine if it is infinite and has a finite minimal quotient. We prove that an irreducible GRRS containing an isotropic root is either finite or affine; we describe all finite and affine GRRSs and classify them in most of the cases.

English

By introducing polynomials in matrix entries, six determinants are evaluated which may be considered extensions of Vandermonde-like determinants related to the classical root systems.

The analysis and detection of hypernasality based on a formant extraction algorithm

In the clinical practice, the effective assessment of cleft palate speech disorders is important. For hypernasal speech, the resonance between nasal cavity and oral cavity causes an additional nasal formant. Thus, the formant frequency is a crucial cue for the judgment of hypernasality in cleft palate speech. Due to the existence of nasal formant, the peak merger occurs to the spectrum of nasal speech more often. However, the peak merger could not be solved by classical linear prediction coefficient root extraction method. In this paper, a method is proposed to detect the additional nasal formant in low-frequency region and obtain the formant frequency. The experiment results show that the proposed method could locate the nasal formant preferably. Moreover, the formants are regarded as the extraction features to proceed the detection of hypernasality. 436 phonemes, which are collected from Hospital of Stomatology, are used to carry out the experiment. The detection accuracy of hypernasality in cleft palate speech is 95.2%.

Assessment of motor skill task performance with a task progress-weighted error measure

A quantitative measure has been developed for the assessment and skill ordering of target-cued motor control and coordination task performances. It is similar to the classical root mean square error (RMSE) measure but modified with task progress weighting that attenuates with target proximity to its destination and amplifies as data sampling occurrences accumulate prior to task completion. The measure has the same mathematical form whether the task design is of the tracing type or of the tracking type, and thus can be used in cross task type comparisons. The new measure is applied to a few simple hypothetical task performances in order to illustrate some of its properties, and then applied to actual experimental data from a tracing task and a tracking task to demonstrate its use.