Enumeration of Standard Young Tableaux

A survey paper, to appear as a chapter in a forthcoming Handbook on Enumeration.Comment: 65 pages, small correction

Parity Theorems for Combinatorial Statistics

A q-generalization Gn(q) of a combinatorial sequence Gn which reduces to that sequence when q = 1 is obtained by q-counting a statistic defined on a sequence of finite discrete structures enumerated by Gn. In what follows, we evaluate Gn(−1) for statistics on several classes of discrete structures, giving both algebraic and combinatorial proofs. For the latter, we define appropriate sign-reversing involutions on the associated structures. We shall call the actual algebraic result of such an evaluation at q = −1 a parity theorem (for the statistic on the associated class of discrete structures). Among the structures we study are permutations, binary sequences, Laguerre configurations, derangements, Catalan words, and finite set partitions. As a consequence of our results, we obtain bijective proofs of congruences involving Stirling, Catalan, and Bell numbers. In addition, we modify the ideas used to construct the aforementioned sign-reversing involutions to furnish bijective proofs of combinatorial identities involving sums with alternating signs

Representing and decomposing genomic structural variants as balanced integer flows on sequence graphs

The study of genomic variation has provided key insights into the functional role of mutations. Predominantly, studies have focused on single nucleotide variants (SNV), which are relatively easy to detect and can be described with rich mathematical models. However, it has been observed that genomes are highly plastic, and that whole regions can be moved, removed or duplicated in bulk. These structural variants (SV) have been shown to have significant impact on the phenotype, but their study has been held back by the combinatorial complexity of the underlying models. We describe here a general model of structural variation that encompasses both balanced rearrangements and arbitrary copy-numbers variants (CNV). In this model, we show that the space of possible evolutionary histories that explain the structural differences between any two genomes can be sampled ergodically

Dynamic activity patterns and cortico-subcortical interactions in the human brain

openQuesto progetto di tesi si propone di indagare la natura della connettività funzionale dinamica (dFC), con un particolare focus sulle sue basi neurali e sulla sua possibile rilevanza comportamentale. Nello specifico, partendo da uno studio pubblicato nel 2022 da Favaretto e colleghi, valuteremo il ruolo delle comunicazioni cortico-sottocorticali nella modellazione della dFC, nonché l'importanza dei suoi parametri nel predire specifici aspetti demografici e comportamentali.This thesis project aims at broadly investigating the nature of dynamic funtctional connectivity (dFC), with a specific focus on its neural underpinnings and potential behavioral relevance. In particular, leading from a study published in 2022 by Favaretto and collegues, we will assess the role of cortico-subcortical communications in shaping dFC as well as the influence of dFC metrics on demographic traits and individual behavior

The physicality of sound production on acoustic instruments

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University. The thesis is accompanied by 14 compositions which appear in the order specified in the Thesis Introduction.This thesis presents practical research into sound production on instruments, working collaboratively with players, in order to build an understanding of the sounds available. I have explored the way in which instrumental technique can be extended in such a way as to function as the basis for musical material. The function of ‘figuration’ has also be brought into question, by employing seemingly primitive, residual material pushed to such a degree that it is possible to hear what happens underneath a gesture. Research in this area has been conducted by, among others, Helmut Lachenmann and Rebecca Saunders; I am drawn to the way their work highlights the tangible quality of sound. The exploration of the physicality of sound production inevitably encounters the problem that the finished work becomes a catalogue of extended techniques. My research has drawn on the work of these composers and has attempted to resolve this problem by exploring the way in which texture can suggest ‘line’ and the structural implications of sculpting self-referential material through angular and polarized divisions. This facilitates a Braille-like reading of a sound’s progress by foregrounding a non-thematic sound-surface of resonance and decay. This takes a positive and active approach to the problems of musical language, by questioning the functions and expectations put upon music. The possible solutions have been worked through in a series of works for mixed chamber ensembles, in order to investigate the palette possibilities of fusing instruments in intimate settings.The Arts and Humanities Research Counci

Novel approach to observing system simulation experiments improves information gain of surface-atmosphere field measurements

The observing system design of multidisciplinary field measurements involves a variety of considerations on logistics, safety, and science objectives. Typically, this is done based on investigator intuition and designs of prior field measurements. However, there is potential for considerable increases in efficiency, safety, and scientific success by integrating numerical simulations in the design process. Here, we present a novel numerical simulation-environmental response function (NS-ERF) approach to observing system simulation experiments that aids surface-atmosphere synthesis at the interface of mesoscale and microscale meteorology. In a case study we demonstrate application of the NS-ERF approach to optimize the Chequamegon Heterogeneous Ecosystem Energy-balance Study Enabled by a High-density Extensive Array of Detectors 2019 (CHEESEHEAD19). During CHEESEHEAD19 pre-field simulation experiments, we considered the placement of 20 eddy covariance flux towers, operations for 72h of low-altitude flux aircraft measurements, and integration of various remote sensing data products. A 2h high-resolution large eddy simulation created a cloud-free virtual atmosphere for surface and meteorological conditions characteristic of the field campaign domain and period. To explore two specific design hypotheses we super-sampled this virtual atmosphere as observed by 13 different yet simultaneous observing system designs consisting of virtual ground, airborne, and satellite observations. We then analyzed these virtual observations through ERFs to yield an optimal aircraft flight strategy for augmenting a stratified random flux tower network in combination with satellite retrievals. We demonstrate how the novel NS-ERF approach doubled CHEESEHEAD19's potential to explore energy balance closure and spatial patterning science objectives while substantially simplifying logistics. Owing to its modular extensibility, NS-ERF lends itself to optimizing observing system designs also for natural climate solutions, emission inventory validation, urban air quality, industry leak detection, and multi-species applications, among other use cases. © 2021 Stefan Metzger et al