Nonstandard methods for bounds in differential polynomial rings

Motivated by the problem of the existence of bounds on degrees and orders in checking primality of radical (partial) differential ideals, the nonstandard methods of van den Dries and Schmidt ["Bounds in the theory of polynomial rings over fields. A nonstandard approach.", Inventionnes Mathematicae, 76:77--91, 1984] are here extended to differential polynomial rings over differential fields. Among the standard consequences of this work are: a partial answer to the primality problem, the equivalence of this problem with several others related to the Ritt problem, and the existence of bounds for characteristic sets of minimal prime differential ideals and for the differential Nullstellensatz.Comment: 18 page

Harnessing the power of topology in oxide electronics for future IT components

Whirling magnetic textures can have topological properties, enhancing their stability over and above that derived from energetic considerations. Such structures have been proposed as data carriers in next-generation post-Moore computing. Whilst abundantly observed in ferromagnets, their antiferromagnetic counterparts are more elusive. Interest in antiferromagnetic topological textures for device applications is growing, due to their predicted ultra-fast, deflection-free dynamics whilst being robust against external fields. In this thesis, I develop processes for imaging, nucleating and controlling topological textures in antiferromagnets, targeted towards their integration in next-generation racetrack-based oxide electronics. The prototypical canted antiferromagnet α-Fe2O3 is used throughout as an interesting test case, due to the family of topological textures present at room temperature that can be repeatedly nucleated via a Kibble-Zurek-like quench. I developed analytical and micromagnetic models for topological textures in A-type antiferromagnets, focusing on the scaling of textures with relevant material parameters, allowing us to push towards the ultra-small sizes relevant for device applications. This was also used to predict the existence of the long sought-after topological antiferromagnetic skyrmions. I investigated freestanding crystalline α-Fe2O3 nanomembranes, a novel form of matter developed by my collaborators. One key conclusion of these experiments was that defects strongly affect the first-order Morin transition, whilst maintaining the Kibble-Zurek phenomenology observed in thin films attached to substrates. Magnetic fields cause domain repopulation in this canted AFM, but topological textures were observed to be stable in the presence of moderate field perturbations. Finally, freestanding crystal membranes can host relatively large strains compared to attached thin films or bulk crystals, which have similar lateral dimensions but the latter are drastically thicker. This was used to produce an athermal route to nucleate topological textures and tune domain populations, opening novel pathways for exploring Kibble-Zurek phenomenology in crystal membranes, as well as providing an interesting route towards device applications

Erie SLAPP Back

Dozens of states have enacted anti-Strategic Lawsuits Against Public Participation (SLAPP) laws to counter SLAPP suits, or lawsuits filed to silence a defendant who has spoken out against a plaintiff. The primary goal of a SLAPP suit is not to win on the merits, but rather to discourage the defendant from exercising their right to free speech by threatening excessively expensive litigation. State anti-SLAPP laws provide for special motions to dismiss, discovery limitations, and fee shifting, all designed to allow a defendant to expeditiously dispose of the SLAPP suit before engaging in costly discovery. This Article discusses the development of state anti-SLAPP laws and the evolution of the Erie doctrine through the Shady Grove decision, ultimately examining how lower courts have struggled to make sense of Shady Grove in the context of state anti-SLAPP special motions to dismiss. This Article then discusses the various theoretical solutions that have been offered for this dilemma, concluding that the conflict between state anti-SLAPP laws and the Federal Rules of Civil Procedure is unavoidable and irreconcilable under the Rules Enabling Act and Erie and its progeny. Based on this analysis, this Article concludes that federal courts sitting in diversity cannot apply state anti-SLAPP laws. The only mechanism for accomplishing the specifically defined purpose of state anti-SLAPP laws in federal court is for the Congress to adopt a federal anti-SLAPP law that would supplement the operation of the Federal Rules of Civil Procedure

Registration, Fairness, and General Jurisdiction

I. Introduction II. In the Beginning Was “Presence” III. When “Presence” Ceased to Mean “Presence” IV. What’s “Fairness” Got to Do with It? V. The Doctrine of General Jurisdiction After International Shoe ... A. Perkins. v. Benguet Consolidated Mining Co. ... B. Helicopteros Nacionales de Colombia, S.A. v. Hall VI. The Death of General Jurisdiction? ... A. Goodyear Dunlop Tires Operations, S.A. v. Brown … B. Daimler v. Bauman VII. Registration and General Jurisdiction ... A. Introduction ... B. Circuit Split: Pre-Daimler, Post-International Shoe … C. Post-Daimler Cases Concluding that Consent-By-Registration Is a Valid Basis for the Exercise of Personal Jurisdiction ... D. Post-Daimler Cases Concluding that Consent-By-Registration Is Not a Valid Basis for the Exercise of Personal Jurisdiction VIII. Conclusion: A Middle Pat

Because of Sex

Many Americans currently believe that federal law prohibits discrimination because of sexual orientation and gender identity in the workplace. While it is true that Title VII of the Civil Rights Act of 1964 (“Title VII”) prohibits employers from discriminating because of an employee’s race, color, religion, sex, or national origin, courts and legislators have historically been slow to extend these protections to LGBT workers. The result of this reluctance is that LGBT employees remain largely unprotected under an unpredictable patchwork of laws and policies, consisting of presidential executive orders, private employer initiatives, city and county ordinances, gubernatorial executive orders, and state legislation. As a result, discrimination in the workforce remains a constant in the lived experience of LGBT persons. As of 2016, thirty-two states and the District of Columbia had taken some steps, either legislatively or through executive action, to limit or prohibit workplace discrimination on the bases of gender identity or sexual orientation. Yet even among these states, victims of workplace discrimination based on sexual orientation or gender identity were provided redress through a private right of action in only twenty-two states and the District of Columbia. Section I of this article discusses this background. Section II article discusses development of the prohibition against discrimination “because of sex” that is contained in Title VII, including the legislative history of Title VII and the initial interpretations of the meaning of “because of sex” in the Title VII context. Section III is focused on general questions regarding the applications of Title VII to claims of discrimination based on sexual orientation, with Sections IV and V focused more specifically on treatment by the EEOC and the courts, respectively, of the question of whether Title VII prohibits discrimination based on sexual orientation. Section VI, the concluding section of this article, examines the theories through which Title VII has been seen by courts to prohibit discrimination based on sexual orientation. Ultimately, this article attempts to propose a unified theory under which discrimination based on sexual orientation would be included under Title VII’s prohibition against discrimination “because of sex.

Yukawa Textures and Anomaly Mediated Supersymmetry Breaking

We present a detailed analysis of how a mixed-anomaly-free U(1) symmetry can be used to both resolve the slepton mass problem associated with Anomaly Mediated Supersymmetry Breaking and generate the fermion mass hierarchy via the Froggatt-Nielsen mechanism. Flavour changing neutral currents problems are evaded by a specific form of the Yukawa textures.Comment: 33 pages, TeX, Uses Harvmac (big) and epsf. Added references and minor changes and corrections. Improved texture discussio

Quantifying Equivocation for Finite Blocklength Wiretap Codes

This paper presents a new technique for providing the analysis and comparison of wiretap codes in the small blocklength regime over the binary erasure wiretap channel. A major result is the development of Monte Carlo strategies for quantifying a code's equivocation, which mirrors techniques used to analyze normal error correcting codes. For this paper, we limit our analysis to coset-based wiretap codes, and make several comparisons of different code families at small and medium blocklengths. Our results indicate that there are security advantages to using specific codes when using small to medium blocklengths.Comment: Submitted to ICC 201