Odd Moments Research Articles

Timing strategy performance in the crude oil futures market

The rewards to speculative trading in the crude oil futures market are assessed. For investors who adopt timing strategies that maximise their (iso-elastic) utility during each trading session, the rewards can be economically significant providing that transaction costs are small. Moreover, we are able to show via a decomposition of performance that the bulk of this benefit is due to their ability to predict realised volatility (that is, the second realised moment). The benefits derived from predicting other realised moments either require unrealistic levels of skill (all odd moments) or an infeasible degree of risk aversion (the fourth moment and higher even moments).

Minimax theory of estimation of linear functionals of the deconvolution density with or without sparsity

The present paper considers the problem of estimating a linear functional $\Phi=\int_{-\infty}^{\infty}\varphi(x)f(x)\,dx$ of an unknown deconvolution density $f$ on the basis of $n$ i.i.d. observations, $Y_{1},\ldots,Y_{n}$ of $Y=\theta+\xi$, where $\xi$ has a known pdf $g$, and $f$ is the pdf of $\theta$. The objective of the present paper is to develop the a general minimax theory of estimating $\Phi$, and to relate this problem to estimation of functionals $\Phi_{n}=n^{-1}\sum_{i=1}^{n}\varphi(\theta_{i})$ in indirect observations. In particular, we offer a general, Fourier transform based approach to estimation of $\Phi$ (and $\Phi_{n}$) and derive upper and minimax lower bounds for the risk for an arbitrary square integrable function $\varphi$. Furthermore, using technique of inversion formulas, we extend the theory to a number of situations when the Fourier transform of $\varphi$ does not exist, but $\Phi$ can be presented as a functional of the Fourier transform of $f$ and its derivatives. The latter enables us to construct minimax estimators of the functionals that have never been handled before such as the odd absolute moments and the generalized moments of the deconvolution density. Finally, we generalize our results to the situation when the vector $\mathbf{{\theta}}$ is sparse and the objective is estimating $\Phi$ (or $\Phi_{n}$) over the nonzero components only. As a direct application of the proposed theory, we automatically recover multiple recent results and obtain a variety of new ones such as, for example, estimation of the mixing probability density function with classical and Berkson errors and estimation of the $(2M+1)$-th absolute moment of the deconvolution density.

Significance of distinct electron-correlation effects in determining the ( P,T )-odd electric dipole moment of Yb171

Parity and time-reversal violating electric dipole moment (EDM) of $^{171}$Yb is calculated accounting for the electron correlation effects over the Dirac-Hartree-Fock (DHF) method in the relativistic Rayleigh-Schr\"odinger many-body perturbation theory, with the second (MBPT(2) method) and third order (MBPT(3) method) approximations, and two variants of all-order relativistic many-body approaches, in the random phase approximation (RPA) and coupled-cluster (CC) method with singles and doubles (CCSD method) framework. We consider electron-nucleus tensor-pseudotensor (T-PT) and nuclear Schiff moment (NSM) interactions as the predominant sources that induce EDM in a diamagnetic atomic system. Our results from the CCSD method to EDM ($d_a$) of $^{171}$Yb due to the T-PT and NSM interactions are found to be $d_a = 4.85(6) \times 10^{-20} \langle \sigma \rangle C_T \ |e| \ cm$ and $d_a=2.89(4) \times 10^{-17} {S/(|e|\ fm^3)}$, respectively, where $C_T$ is the T-PT coupling constant and $S$ is the NSM. These values differ significantly from the earlier calculations. The reason for the same has been attributed to large correlation effects arising through non-RPA type of interactions among the electrons in this atom that are observed by analyzing the differences in the RPA and CCSD results. This has been further scrutinized from the MBPT(2) and MBPT(3) results and their roles have been demonstrated explicitly.

First measurement of T -odd moments in D0→KS0π+π−π0 decays

We report the first measurement of the $T$-odd moments in the decay $D^{0} \rightarrow K_{S}^{0} \pi^{+} \pi^{-} \pi^{0}$ from a data sample corresponding to an integrated luminosity of $966\,{\rm fb}^{-1}$ collected by the Belle experiment at the KEKB asymmetric-energy $e^+ e^-$ collider. From these moments we determine the $CP$-violation-sensitive asymmetry $a_{CP}^{T\text{-odd}} = \left[-0.28 \pm 1.38 ~(\rm{stat.}) ^{+0.23}_{-0.76} ~(\rm{syst.})\right] \times 10^{-3}$, which is consistent with no $CP$ violation. In addition, we perform $a_{CP}^{T\text{-odd}}$ measurements in different regions of the $D^{0} \rightarrow K_{S}^{0} \pi^{+} \pi^{-} \pi^{0}$ phase space; these are also consistent with no $CP$ violation.

Camera identification based on very low bit rate videos with overall noise pattern having time varying statistics

This paper proposes a method for performing the camera identification based on very low bit rate videos with the overall noise patterns having time varying statistics. First, the overall noise pattern of each frame of each video is converted to a vector. Then, the odd order statistic moments of these vectors are computed. By performing the principal component analysis, only the most major component of each statistic moment vector is attained. These components of all the frames form a feature vector for each video. To minimize the intraclass separation and maximize the interclass separation, the linear discriminant analysis is performed. As many eigenvalues of the interclass separation matrix are close to zero, the column vectors which span the null spaces of the corresponding matrices are found and the feature vector of each video is projected to these columns and forms a new vector. It is found that these new vectors are pairwisely linear separable. Hence, a bank of perceptrons can be applied to perform the camera identification. Computer numerical simulations show that our proposed method significantly outperforms the conventional correlation based method and the conventional support vector machine based method.

Luke Lea, the Legionnaires, and the Legacy of Two Wars: The Politics of Memory in the Mind of a Nashville Progressive, 1915-1945

Luke Lea, the Legionnaires, and the Legacy of Two Wars:The Politics of Memory in the Mind of a Nashville Progressive, 1915-1945 Robert Hunt (bio) Over the Christmas and New Year's holidays of 1918–1919, Luke Lea, colonel of the Tennessee-raised 114th Field Artillery, tried to capture Wilhelm II, the former German kaiser, and take him to Paris as World War I's prize criminal. Although Lea had no orders to make this attempt, he was a well-placed, old-money white southerner used to taking matters into his own hands. He had raised the 114th himself when war was declared by the United States in 1917, and he had led the unit with distinction during the worst fighting in America's major battle—the Meuse-Argonne offensive. When the armistice process began, Lea learned that the German emperor had absconded to Holland, and, as the colonel saw it, this attempt to flee was shameless. Lea believed that the kaiser had headed a militarist system in an atrocious war and now, in defeat, was trying to escape the consequences of his acts. As Lea later said, "the American soldier in his heart demanded punishment of the Kaiser for his crime against civilization."1 Despite the odds, the adventurers came closer to succeeding than one might presume. When the war ended, Lea's unit was stationed close to Holland, and through fortuitous local contacts the colonel learned of the kaiser's location. He quickly recruited a few volunteers from his unit, procured two automobiles, and made the try. His party actually made it [End Page 617] to the estate where Wilhelm was staying. However, because Lea wanted to persuade the emperor to go rather than kidnap him, the mission failed. The kaiser refused to surrender. Thus, the colonel and company had nothing else to do but retreat. In a superb anticlimax, U.S. Army authorities chose not to court-martial Lea, though they concluded he had committed "a most indiscreet act for any officer of the [American Expeditionary Forces (AEF)]." Officially, the incident ended here.2 Thus began the curious journey of a memory. At first glance, the raid seemed to call the result of the entire war effort into question. Lea would hardly have been so reckless or self-indulgent unless he had severe doubts about the peace, and his private war diary certainly reveals as much.3 And, of course, he was not alone. Thus, the kaiser incident was actually a dark episode, or at the least an indication of dangerous loose ends left by the war. But Lea did not use the event in this way, at least not at first. Quite the contrary, he seemed to forget it entirely, burying it underneath his career as a southern Progressive politician. And he did have an important career to pursue. He had become a major figure in state politics before the war started. He had founded the Nashville Tennessean in the twentieth century's first decade, using it to advance a Prohibitionist and Progressive agenda, and then was selected for the U.S. Senate in 1911. Returning to Tennessee from France after the war, he became Governor Austin L. Peay's right-hand man. As part of his role in this capacity Lea officiated at public commemorations of what he described at this point as America's total victory in the war. Apparently, for Lea, Jazz Age prosperity had filed off the sharp edges from the events of 1918.4 [End Page 618] However, the memory journey took a turn. The kaiser story suddenly became important when Lea's personal and political life collapsed. During his time as Peay's assistant, Lea earned the reputation of being a boss, and his enemies got their moment at the end of the 1920s to topple him. Then, during the Depression, he endured a prison term, because he was charged and convicted of bank fraud (he was later pardoned).5 Like the country itself, he fell a long way after the high of the 1920s. It was at this juncture that Lea turned his mind back to his odd moment in history, writing while in prison a long narrative...

CP Asymmetries (& T Violation) in Known Matter – and Beyond

Finding \cp~violation (\CPV ) in 1964 produced a real revolution in the fundamental dynamics, although the community did not understand it right away. The paper by Kobayashi \& Maskawa \cite{KM} appeared in 1973 to describe \CPV~in classes of three (or more) families of quarks, non-minimal Higgs' dynamics and/or charged right-handed currents. The Standard Model is defined now with three families of quarks. It can describe the measured \cp~ \& \ot~violation in kaon and $B$ mesons at least as the leading source. None has been found in baryons, charm mesons, top quarks and EDMs -- except from `hot' news from LHCb data about {\bf T}-odd moment in $\Lambda_b^0 \to p \pi^-\pi^+\pi^-$ \cite{LHCbtalk}. We have failed the explain our matter vs. anti-matter huge asymmetry. Even when there is no obvious connections with that asymmetry, it makes sense to probe \CPV~for the signs of New Dynamics \& their features. Furthermore we have to measure regional \CPV~in many-body final states with accuracy. I discuss EDMs, axion's impact on cosmology \& its connection with Dark Matter; finally I talk about \CPV~in leptonic dynamics.

Rhetoric and Power: The Drama of Classical Greece

Rhetoric and Power: The Drama of Classical Greece

High-order generalisation of the diagnostic scaling for turbulent boundary layers

ABSTRACTThe diagnostic scaling concept, introduced for the streamwise turbulence intensity in wall-bounded turbulent flows (Alfredsson, Segalini and Örlü, Phys. Fluids 2011;23:041702), is here extended and generalised not only for the higher even-order central statistical moments, but also for the odd moments and thereby the probability density distribution of the streamwise velocity fluctuations. Turbulent boundary layer data up to a friction Reynolds number of 60,000 are employed and demonstrate the feasibility of the diagnostic scaling for the data throughout the logarithmic and wake regions. A comparison with the generalised logarithmic law for even-order moments by Meneveau and Marusic (J. Fluid Mech. 2013;719:R1) based on the attached-eddy hypothesis, is reported. The diagnostic plot provides an apparent Reynolds-number-independent scaling of the data, and is exploited to reveal the functional dependencies of the constants needed in the attached-eddy-based model. In particular, the invariance of the lowest order diagnostic scaling poses an intriguing incompatibility with the asymptotic constancy of the Townsend–Perry constant.

Image noise level estimation based on higher-order statistics

Noise level estimation is a required step for many preprocessing algorithms in computer vision such as image denoising. In this paper, a model-based technique for additive white Gaussian noise level estimation is proposed via matching moments of eligible transform coefficients of a single image. We assume that noise and image signals are independent and seek to use an image transform that preserves distribution characteristics of noise. This transform should also result in coefficients with a generalized Gaussian distribution for the image itself. We use block-based discrete cosine transform (DCT) and discrete wavelet transform (DWT) which are shown to satisfy these requirements. The proposed method fits the histogram of AC coefficients of all DCT blocks or histogram of all high frequency wavelet coefficients with a generalized Gaussian distribution and attempts to estimate the noise variance through matching the estimated and true values of moments. Since the modeled distributions are symmetric and hence all odd moments are zero, our approach involves solving a nonlinear system of equations based on the method of moments using only even moments. The performance of the proposed method is compared to those of the best prevalent algorithms proposed for noise level estimation using patch-based and model-based techniques. The results on three different image databases show that the proposed scheme outperforms previous techniques in general.

Lyric Hewn from Language

Lyric Hewn from Language Rob Stanton (bio) Green Oil Jean Donnelly Further Other Book Works www.furtherotherbookworks.com/index.php 106 Pages; Print, $15.95 Jean Donnelly never claims the poems in Green Oil, her second full-length collection (and third in an impressive run of titles from new-ish Colorado-based press Further Other Book Works), are translations of Francis Ponge’s poems. This is a good thing: her “project” in this book (and, yes, what she attempts here really does deserve that often-abused term) is subtly unlike any other act of translation I can think of. It isn’t a loyal/academic version that sacrifices poetic “bounce” to fidelity, nor is it what Dryden (followed by Robert Lowell) termed an “imitation,” spinning a more-or-less new poem from the same topic and/or mood as the source. Neither is it a strictly homophonic translation, à la Zukofsky’s Catullus (1969), because it doesn’t attempt to convey, at any degree of remove, the meaning of the original. Nor is it quite like recent examples of “method” translation, such as Christian Hawkey’s Ventrakl (2010) and Sawako Nakayasu’s Mouth: Eat Color (2011), in that, while Donnelly’s versions do seek a kind of communion between her English and Francis Ponge’s French, it remains very much an issue of language and is not about trying to invest in or identify with the personality of the author. In its use of homophony to create new, counter-intuitive meaning, it is perhaps closer in spirit to David Melnick’s Men in Aida (1983), but Green Oil is neither as systematic nor as thematically unified as that work’s flights of parodic fantasy. Instead, the original French is used more as subliminal trigger than as something possessing its own individual agency. Overall, the book has the feel, charmingly, of a whim that gained traction, momentum, then grew into a book…. Even a brief example demonstrates how idiosyncratic Donnelly’s method is. Here is the first poem of the book’s opening sequence, “atoms”: insidewe are masonson view declassifiednumbers & all downour armoris a lit placardthat says so The composite image is both funny and menacing. We are (apparently) “masons,” “inside” a structure; we are perilously “on view,” subject to some unidentified authority that can strip us of our identity (turn us into “numbers”) and announce that we are no longer a risk (“declassified”). Given the threat we (apparently) represent is now (apparently) neutralized, our “armor” may or may not be obsolescent—either way, we are conspicuously advertising our status via “a lit placard.” A conflict is implied between essential privacy (“inside/we are”) and public visibility, surveillance seemingly having the upper hand. The French source could not be more different: “Il y a dans la maison une vieille paysanne de quarte-vingt-cinq ans dans son armoire-lit (lit-placard)” (in John Montagne’s translation, “in the house there is an old peasant woman of eighty-five years in her settle bed [cupboard couch]”). The combination of detached observation and revisionist precision (that parenthetical alternative!) is typical of Ponge’s style (which Donnelly accurately labels “precise, nearly clinical, and often wry”), but unless you want to see that style as a form of surveillance (it is, arguably) there is very little to connect the original words to what Donnelly has mined from them. Aside from odd moments of direct translation (“inside” for “dans”), the English words stem as much from visual cues as acoustic ones: “maison une vieille” becomes “masons / on view,” “de quartre” suggests “declassified,” “vingtcinq” gets rendered generically as “numbers,” “ans dans son armoire” becomes “& // all down / our armor” and, finally, “lit-placard” was clearly too tempting not to transfer whole. Donnelly has thus leapfrogged over Ponge into an entirely new poem. She calls this method a “listening at the threshold of the material traces” and it represents both a continuation and intensification of her earlier work. One common thread is an implied staking out—firm but not didactic—of a “lyric freedom,” be it in the realm of erotic verse (the julia set), cataloguing travelogue (“Anthem”), freewheeling memoir of pregnancy...

LPM Density Functions for the Computation of the SD Efficient Set

The equivalence between partial moments and stochastic dominance dates back to Bawa [1] and Fishburn [2]. We present a test for first, second, and third degree stochastic dominance between two variables using Lower Partial Moments. The results uphold Hadar and Russell’s [3] original conclusions about the odd moments of preferred prospects. We recall Nawrocki’s [4] research comparing Mean/Variance portfolios against the continuum of risk-averse investors using Lower Partial Moments. The excess skewness of the LPM portfolios clearly demonstrates the preference of positive skewness for risk-averse investors. Finally, we provide an algorithm for efficiently determining stochastic dominance efficient sets among large numbers of variables.

Generating Some Symmetric Semi-classical Orthogonal Polynomials

AbstractWe show that ifvis a regular semi-classical form (linear functional), then the symmetric formudefined by the relationx2σu= -λv, where (σƒ)(x) = f (x2) and the odd moments ofuare 0, is also regular and semi-classical form for every complex λ except for a discrete set of numbers depending onv. We give explicitly the three-term recurrence relation and the structure relation coefficients of the orthogonal polynomials sequence associated withuand the class of the formuknowing that ofv. We conclude with an illustrative example.

Radon odd radial harmonic Fourier moments in detecting cloned forgery image

Over the past decades, due to the progress of computing abilities and easy access to powerful photo editing software, more digital photos and images are created commonplace. Unfortunately, this technology progress may also bring with a big risk of the information security. Image region cloning is a popular and simple manner to create realistic forgery images. Most relevant researches have been carried out, but the methods based on those researches are only able to detect some simple duplicated successfully. So we present a new Radon Odd Radial Harmonic Fourier Moments (RORHFMs) method. Compared with other relevant methods, this method is more robust to resist post-processed operations, such as anti-translation, anti-rotation, anti-scaling, anti-mirror operations and resisted Gaussian noise contamination. We also introduce an auxiliary circle template to slide and detect the suspicious image in order to locate the cloned region. The invariant moment features of image are extracted and analyzed by our method. Each feature of similar region is arranged orderly by Lexicographic sorting for detecting. Pearson Correlation Coefficient is applied to calculate and classify the statistical data. Then, the statistical data is searched, analyzed. At last, the original coordinates of cloned and pasted region are detected and denoted. Extensive experiments verified better robustness of RORHFMs method than other relevant methods in detecting cloned forgery.

A REMARK ON TAIL DISTRIBUTIONS OF PARTITION RANK AND CRANK

We examine the tail distributions of integer partition ranks and cranks by investigating tail moments, which are analogous to the positive moments introduced by Andrews et al. [‘The odd moments of ranks and cranks’, J. Combin. Theory Ser. A120(1) (2013), 77–91].

McEwan. The Strange Case of the Resurrected Penis in 'Solid Geometry'

IT might seem odd to object to the lack of realist continuity in a short story where people are made to disappear according to a mathematical formula, but can anyone explain why Captain Nicholls’ penis is on the narrator’s table at the beginning of ‘Solid Geometry’? I have read First Love, Last Rites many times, and taught it to first-year undergraduates for seven years, and not one of my students has even noticed, let alone been able to explain the anomaly. The narrator starts his account with the purchase of the penis at an auction in 1875: ‘in a beautiful state of preservation’. He proudly, metonymically, boasts that that same penis is still with him: ‘to the left sits Capt. Nicholls in the glass jar’ (note the definitive article (‘the glass jar’), implying a continuity of preservation). He is, here, calmly relating the history of past events which led him to make his wife ‘disappear’ by the magic of ‘solid geometry’, hence the cryptic foreshadowing: ‘I used to think that at the end of it all I would try, if it was possible, to divorce my wife Maisie, but now there is no need at all’. But surely the preserved penis should not now be next to him. It has already (in the story he is about to tell) been ruined in the battle of the sexes. In that account Maisie has smashed the glass jar, in refutation of her husband’s phallocentric, but sterile, obsessions, and the penis has been exposed as a newly grotesque object: ‘My stomach heaved as the foreskin began to come away in my fingers’. The narrator has ceremoniously, symbolically, buried it—wrapped in newspaper—under the geraniums in the garden. And then he has planned his premeditated geometrical revenge. So what are we to believe about the renaissance of the penis? Has he recovered it in its dishevelled state, dug it up, held it together, stuck the foreskin back in place, cleaned it up, bought another twelve-inch piece of laboratory glassware (which should not be ‘the glass jar’, but ‘another’ or ‘a new’ glass jar), and again preserved it (as a sign of his patriarchal victory, perhaps). If so, surely we are due some hint. Rather, this seems an odd moment of authorial forgetting. Has McEwan ever been asked about it? Are there other readings? What explains the mysterious reappearance of the preserved penis?

Distorted local shadows

We introduce the notion of a local shadow for a black hole and determine its shape for the particular case of a distorted Schwarzschild black hole. Considering the lowest-order even and odd multiple moments, we compute the relation between the deformations of the shadow of a Schwarzschild black hole and the distortion multiple moments. For the range of values of multiple moments that we consider, the horizon is deformed much less than its corresponding shadow, suggesting the horizon is more `rigid'. Quite unexpectedly we find that a prolate distortion of the horizon gives rise to an oblate distortion of the shadow, and vice-versa.

Relation of system dimensionality and order parameters.

Orientational order parameters are useful metrics for characterizing the probability distribution for vector-valued quantities such as the dipole moment or optical axis of molecules in materials such as liquid crystals and organic glasses. These parameters are the moments of the underlying orientational probability distribution. Many molecular systems can be characterized using a single centrosymmetric (even) moment. For dipolar systems, an applied electric or magnetic field can break the symmetry of the system, leading to nonzero acentric (odd) moments. For complex systems, it is difficult to characterize the nature of the bulk structures and to quantitatively understand the relationship between acentric and centrosymmetric moments. We have found that it is useful to relate the moments of the distribution in terms of an apparent dimensionality of the ordering process. Here we show that the idea of noninteger dimensionality, originally introduced by Stillinger, provides a useful method to characterize the relation between centrosymmetric and acentric orientational order parameters. Applying dimensional constraints is equivalent to removing rotational degrees of freedom or constraining rotation within a restricted volume. Simulations based on simple examples—using restoring potentials on arrays of independent dipoles—and on complex many-body Monte Carlo simulations of dipolar spheroids are described. An analysis of the results illustrates the utility of fractional dimensionality to describe ordering in materials.

K-Optimal Gradient Encoding Scheme for Fourth-Order Tensor-Based Diffusion Profile Imaging.

The design of an optimal gradient encoding scheme (GES) is a fundamental problem in diffusion MRI. It is well studied for the case of second-order tensor imaging (Gaussian diffusion). However, it has not been investigated for the wide range of non-Gaussian diffusion models. The optimal GES is the one that minimizes the variance of the estimated parameters. Such a GES can be realized by minimizing the condition number of the design matrix (K-optimal design). In this paper, we propose a new approach to solve the K-optimal GES design problem for fourth-order tensor-based diffusion profile imaging. The problem is a nonconvex experiment design problem. Using convex relaxation, we reformulate it as a tractable semidefinite programming problem. Solving this problem leads to several theoretical properties of K-optimal design: (i) the odd moments of the K-optimal design must be zero; (ii) the even moments of the K-optimal design are proportional to the total number of measurements; (iii) the K-optimal design is not unique, in general; and (iv) the proposed method can be used to compute the K-optimal design for an arbitrary number of measurements. Our Monte Carlo simulations support the theoretical results and show that, in comparison with existing designs, the K-optimal design leads to the minimum signal deviation.

Limit distributions of three-state quantum walks: The role of coin eigenstates

We analyze two families of three-state quantum walks which show the localization effect. We focus on the role of the initial coin state and its coherence in controlling the properties of the quantum walk. In particular, we show that the description of the walk simplifies considerably when the initial coin state is decomposed in the basis formed by the eigenvectors of the coin operator. This allows us to express the limit distributions in a much more convenient form. Consequently, striking features which are hidden in the standard basis description are easily identified. Moreover, the dependence of moments of the position distribution on the initial coin state can be analyzed in full detail. In particular, we find that in the eigenvector basis the even moments and the localization probability at the origin depend only on incoherent combination of probabilities. In contrast, odd moments and localization outside the origin are affected by the coherence of the initial coin state.