A Combinatorial Formula for Macdonald Polynomials

We prove a combinatorial formula for the Macdonald polynomial H_mu(x;q,t) which had been conjectured by the first author. Corollaries to our main theorem include the expansion of H_mu(x;q,t) in terms of LLT polynomials, a new proof of the charge formula of Lascoux and Schutzenberger for Hall-Littlewood polynomials, a new proof of Knop and Sahi's combinatorial formula for Jack polynomials as well as a lifting of their formula to integral form Macdonald polynomials, and a new combinatorial rule for the Kostka-Macdonald coefficients K_{lambda,mu}(q,t) in the case that mu is a partition with parts less than or equal to 2.Comment: 29 page

Effective constructions in plethysms and Weintraub's conjecture

We give a short proof of Weintraub's conjecture by constructing explicit highest weight vectors in the symmetric power of an even exterior power

Emotions in Polybius' Histories

In this dissertation I investigate how emotions work in Polybius’ Histories, his account in Greek of Rome’s rise to supremacy. My argument that moral and rational principles often underlie emotions in the Histories challenges both the Classical dichotomy between emotion and reason and commonplace assumptions that emotions were inherently negative. Moreover, emotion is essential in Polybius’ project of history and for his historiographical theory: Emotions play a crucial role in causation, critically connect moral principle to action in human behavior, and contribute to the educative value of history. Emotion for Polybius is educative for his readership in two ways. Emotions in the historical narrative teach the audience to observe and judge the characters’ reactions to emotions as correct or incorrect. Not only does Polybius present the emotions of his characters, but he also uses history to inculcate a sense of correct, normative emotion in his audience.In Chapter 1, I identify important features of emotion drawn from the modern social sciences, providing a critical vocabulary through which I analyze key passages from the Histories, such as Philip V’s first sack of Thermum. From an analysis of emotional features, it becomes clear that Polybius judges characters above all by the import, appropriateness, direction, and proportionality of their emotion. In Chapter 2, I analyze how Polybius’ emotional vocabulary compares with that of Aristotle’s Rhetoric and David Konstan’s recent analysis in The Emotions of the Ancient Greeks. In Chapter 3, I investigate emotions at work in changes of a state’s governing regime. In Polybius’ theory of the cycle of constitutions, the people’s collective emotional reactions repeatedly spark change from a worse state form to a better one until the end of the cycle. Similarly, in the downfall of Agathocles, the usurping prime minister of Egypt, the people’s emotions both reaffirm positive communal values and (perhaps paradoxically) lead to extreme violence in overthrowing Agathocles’ regime. My analysis in Chapter 4 turns to the prominent role emotions play in causing war between states: how do emotions motivate wars, especially in the paradigm case of the Second Punic War? I look at the justifiability of anger as a cause of war and its implications for Polybius’ theory of history. In the conclusion, after I recap and summarize my findings, I briefly address how the historian tries to inculcate in his readers the appropriate emotional response to certain situations, examining in particular Polybius’ remarks about pity in the Achaean War of 146 BC. For Polybius, emotions play an important role in human decision-making, justifying and prompting individuals’ actions, explaining why states change from worse to better, linking the outbreak of wars to past events, and guiding the readers to develop a correct sense of emotional behavior

Colloidal topological insulators

Topological insulators insulate in the bulk but exhibit robust conducting edge states protected by the topology of the bulk material. Here, we design a colloidal topological insulator and demonstrate experimentally the occurrence of edge states in a classical particle system. Magnetic colloidal particles travel along the edge of two distinct magnetic lattices. We drive the colloids with a uniform external magnetic field that performs a topologically non-trivial modulation loop. The loop induces closed orbits in the bulk of the magnetic lattices. At the edge, where both lattices merge, the colloids perform skipping orbits trajectories and hence edge-transport. We also observe paramagnetic and diamagnetic colloids moving in opposite directions along the edge between two inverted patterns; the analogue of a quantum spin Hall effect in topological insulators. We present a new, robust, and versatile way of transporting colloidal particles, enabling new pathways towards lab on a chip applications

Post-denial Strategies: How to Get from No to Yes

U.S. Citizenship and Immigration Services (USCIS) seems to be denying more petitions than ever these days. Cases that were solid approvals a few years ago now are receiving denials, even though the law and regulations have not changed. But don’t give up hope. Opportunities exist to overcome denials. This practice advisory focuses on post-denial strategies for petitions filed with USCIS, not strategies in immigration court. The article discusses motions to reopen, motions for reconsideration, appeals to the USCIS Administrative Appeals Office (AAO), and litigation. This practice advisory also discusses when filing a new petition may be a better option, and how the beneficiary’s status, including unlawful presence, may affect the options

Post-denial Strategies: How to Get from No to Yes

U.S. Citizenship and Immigration Services (USCIS) seems to be denying more petitions than ever these days. Cases that were solid approvals a few years ago now are receiving denials, even though the law and regulations have not changed. But don’t give up hope. Opportunities exist to overcome denials. This practice advisory focuses on post-denial strategies for petitions filed with USCIS, not strategies in immigration court. The article discusses motions to reopen, motions for reconsideration, appeals to the USCIS Administrative Appeals Office (AAO), and litigation. This practice advisory also discusses when filing a new petition may be a better option, and how the beneficiary’s status, including unlawful presence, may affect the options