An Algebraic-Coding Equivalence to the Maximum Distance Separable Conjecture

We formulate an Algebraic-Coding Equivalence to the Maximum Distance Separable Conjecture. Specifically, we present novel proofs of the following equivalent statements. Let $(q,k)$ be a fixed pair of integers satisfying $q$ is a prime power and $2\leq k \leq q$. We denote by $\mathcal{P}_q$ the vector space of functions from a finite field $\mathbb{F}_q$ to itself, which can be represented as the space $\mathcal{P}_q := \mathbb{F}_q[x]/(x^q-x)$ of polynomial functions. We denote by $\mathcal{O}_n \subset \mathcal{P}_q$ the set of polynomials that are either the zero polynomial, or have at most $n$ distinct roots in $\mathbb{F}_q$. Given two subspaces $Y,Z$ of $\mathcal{P}_q$, we denote by $\langle Y,Z \rangle$ their span. We prove that the following are equivalent. [A] Suppose that either: 1. $q$ is odd 2. $q$ is even and $k \not\in \{3, q-1\}$. Then there do not exist distinct subspaces $Y$ and $Z$ of $\mathcal{P}_q$ such that: 3. $dim(\langle Y, Z \rangle) = k$ 4. $dim(Y) = dim(Z) = k-1$. 5. $\langle Y, Z \rangle \subset \mathcal{O}_{k-1}$ 6. $Y, Z \subset \mathcal{O}_{k-2}$ 7. $Y\cap Z \subset \mathcal{O}_{k-3}$. [B] Suppose $q$ is odd, or, if $q$ is even, $k \not\in \{3, q-1\}$. There is no integer $s$ with $q \geq s > k$ such that the Reed-Solomon code $\mathcal{R}$ over $\mathbb{F}_q$ of dimension $s$ can have $s-k+2$ columns $\mathcal{B} = \{b_1,\ldots,b_{s-k+2}\}$ added to it, such that: 8. Any $s \times s$ submatrix of $\mathcal{R} \cup \mathcal{B}$ containing the first $s-k$ columns of $\mathcal{B}$ is independent. 9. $\mathcal{B} \cup \{[0,0,\ldots,0,1]\}$ is independent. [C] The MDS conjecture is true for the given $(q,k)$.Comment: This is version: 5.6.18. arXiv admin note: substantial text overlap with arXiv:1611.0235

MARKET CONDUCT UNDER GOVERNMENT PRICE INTERVENTION IN THE U.S. DAIRY INDUSTRY

The degree of market power exercised by fluid and manufactured processors in the U.S. dairy industry is estimated. AppelbaumÂ’'s quantity-setting conjectural variation approach is cast into a switching regime framework to account for the two market regimes created by the existence of the dairy price support program: (a) government supported regime (market price is at the support price) and (b) market equilibrium regime (market price is above the support price). The model is also used to test whether government price intervention has a pro-competitive to anti-competitive influence on market conduct.Agricultural and Food Policy,

Subnanosecond Fluctuations in Low-Barrier Nanomagnets

Fast magnetic fluctuations due to thermal torques have useful technological functionality ranging from cryptography to probabilistic computing. The characteristic time of fluctuations in typical uniaxial anisotropy magnets studied so far is bounded from below by the well-known energy relaxation mechanism. This time scales as $\alpha^{-1}$, where $\alpha$ parameterizes the strength of dissipative processes. Here, we theoretically analyze the fluctuating dynamics in easy-plane and antiferromagnetically coupled nanomagnets. We find in such magnets, the dynamics are strongly influenced by fluctuating intrinsic fields, which give rise to an additional dephasing-type mechanism for washing out correlations. In particular, we establish two time scales for characterizing fluctuations (i) the average time for a nanomagnet to reverse|which for the experimentally relevant regime of low damping is governed primarily by dephasing and becomes independent of $\alpha$, (ii) the time scale for memory loss of a single nanomagnet|which scales as $\alpha^{-1/3}$ and is governed by a combination of energy dissipation and dephasing mechanism. For typical experimentally accessible values of intrinsic fields, the resultant thermal-fluctuation rate is increased by multiple orders of magnitude when compared with the bound set solely by the energy relaxation mechanism in uniaxial magnets. This could lead to higher operating speeds of emerging devices exploiting magnetic fluctuations

The Validity of Evaluation Results: Assessing Concurrence Across Compositionality Benchmarks

NLP models have progressed drastically in recent years, according to numerous datasets proposed to evaluate performance. Questions remain, however, about how particular dataset design choices may impact the conclusions we draw about model capabilities. In this work, we investigate this question in the domain of compositional generalization. We examine the performance of six modeling approaches across 4 datasets, split according to 8 compositional splitting strategies, ranking models by 18 compositional generalization splits in total. Our results show that: i) the datasets, although all designed to evaluate compositional generalization, rank modeling approaches differently; ii) datasets generated by humans align better with each other than they with synthetic datasets, or than synthetic datasets among themselves; iii) generally, whether datasets are sampled from the same source is more predictive of the resulting model ranking than whether they maintain the same interpretation of compositionality; and iv) which lexical items are used in the data can strongly impact conclusions. Overall, our results demonstrate that much work remains to be done when it comes to assessing whether popular evaluation datasets measure what they intend to measure, and suggest that elucidating more rigorous standards for establishing the validity of evaluation sets could benefit the field.Comment: CoNLL202

Breaking Barriers: Diversity and Equity in Chemistry

This book is being made available in both PDF and ePub formats for the convenience of the reader.The field of chemistry has long been associated with the pursuit of objective facts and the uncovering of the building blocks of our universe. However, this view can often exclude the important role that diversity, equity, and inclusion (DEI) play in the advancement of scientific knowledge. By highlighting the contributions of minority chemists and integrating DEI principles into chemistry education, we can promote a more inclusive environment and foster greater understanding of the complex connections between chemistry and society. In the first section, we provide a biography of each chemist, discussing their personal and professional lives and how their minority identity has interacted with their careers. The second section summarizes their research and accomplishments in the field of chemistry, emphasizing the importance of their work and the implications it has had on the broader scientific community. Finally, the third section explores how their research is related to the topics and contents taught in general chemistry, creating a connection between the material students learn in the classroom and the real-world applications of chemistry. In recent years, there has been a growing recognition of the need to incorporate DEI into STEM education, and chemistry is no exception. Despite this, there remains a scarcity of learning materials that directly introduce diversity and equality in chemistry education. As a result, students may view chemistry as an isolated discipline that is removed from the broader community. This book aims to challenge that perception by introducing readers to minority chemists, their research, and the ways in which their work is related to topics taught in general chemistry courses. By exploring the lives and research of chemists who come from diverse backgrounds, we hope to showcase the importance of diverse perspectives in the advancement of the field and inspire a new generation of scientists who embrace and promote DEI in their own work. Each chapter of this book is divided into three main sections, highlighting the personal and professional lives of these extraordinary individuals and demonstrating the impact their work has had on the field

Experimental quantum key distribution with source flaws

Decoy-state quantum key distribution (QKD) is a standard technique in current quantum cryptographic implementations. Unfortunately, existing experiments have two important drawbacks: the state preparation is assumed to be perfect without errors and the employed security proofs do not fully consider the finite-key effects for general attacks. These two drawbacks mean that existing experiments are not guaranteed to be secure in practice. Here, we perform an experiment that for the first time shows secure QKD with imperfect state preparations over long distances and achieves rigorous finite-key security bounds for decoy-state QKD against coherent attacks in the universally composable framework. We quantify the source flaws experimentally and demonstrate a QKD implementation that is tolerant to channel loss despite the source flaws. Our implementation considers more real-world problems than most previous experiments and our theory can be applied to general QKD systems. These features constitute a step towards secure QKD with imperfect devices.Comment: 12 pages, 4 figures, updated experiment and theor

The reciprocal relationship among Chinese senior secondary students’ intrinsic and extrinsic motivation and cognitive engagement in learning mathematics : A three-wave longitudinal study

In the present longitudinal study, cross-lagged path models were applied to investigate the potential reciprocal relationships between senior secondary school students’ motivation and their cognitive engagement, using data from 623 Chinese senior secondary school students across 2 years. The 623 students completed self-reported measures of motivation and engagement at three time points within 2 years. The results suggest that the participants held a mixed type of intrinsic and extrinsic motivation to learn mathematics and did not hold a deep level of cognitive engagement in mathematics learning. Compared with their extrinisic motivation, their intrinsic motivation to learn mathematics was more closely related to their cognitive engagement in mathematics learning, which points to a stronger reciprocal effect between their cognitive engagement and intrinsic motivation. The findings suggest that societal and cultural factors, such as the strong examination culture and high external expectations might be influential factors affecting the reciprocal relationships among students’ motivation and cognitive engagement

CT virtual endoscopy and 3D stereoscopic visualisation in the evaluation of coronary stenting

The aim of this case report is to present the additional value provided by CT virtual endoscopy and 3D stereoscopic visualisation when compared with 2D visualisations in the assessment of coronary stenting. A 64-year old patient was treated with left coronary stenting 8 years ago and recently followed up with multidetector row CT angiography. An in-stent restenosis of the left coronary artery was suspected based on 2D axial and multiplanar reformatted images. 3D virtual endoscopy was generated to demonstrate the smooth intraluminal surface of coronary artery wall, and there was no evidence of restenosis or intraluminal irregularity. Virtual fly-through of the coronary artery was produced to examine the entire length of the coronary artery with the aim of demonstrating the intraluminal changes following placement of the coronary stent. In addition, stereoscopic views were generated to show the relationship between coronary artery branches and the coronary stent. In comparison with traditional 2D visualisations, virtual endoscopy was useful for assessment of the intraluminal appearance of the coronary artery wall following coronary stent implantation, while stereoscopic visualisation improved observers’ understanding of the complex cardiac structures. Thus, both methods could be used as a complementary tool in cardiac imaging

A Higher-Order Calculation of npnp Scattering in Cut-Off Effective Field Theory

We report a next-to-leading-order (NLO) chiral perturbation theory calculation of the neutron-proton scattering cross section in the ${}^1S_0$ channel using a cut-off regularization. The inclusion of two-pion exchanges in the irreducible diagrams -- or potential -- figuring at NLO is found to be important in enlarging the domain of validity of the effective field theory. We are able to reproduce the {\it empirical} scattering phase shift up to p=300 MeV -- which is comparable to the cutoff scale involved -- with an agreement which is superior to results of other effective field theory approaches. We also discuss the role of the cutoff as a renormalization prescription and the importance of the explicit pion degree of freedom in scattering process.Comment: Substantial changes made in texts and Fig.2. To appear in Phys. Lett.