Multivariate dynamic modeling for Bayesian forecasting of business revenue

Forecasting enterprise-wide revenue is critical to many companies and presents several challenges and opportunities for significant business impact. This case study is based on model developments to address these challenges for forecasting in a large-scale retail company. Focused on multivariate revenue forecasting across collections of supermarkets and product categories, hierarchical dynamic models are natural: these are able to couple revenue streams in an integrated forecasting model, while allowing conditional decoupling to enable relevant and sensitive analysis together with scalable computation. Structured models exploit multi-scale modeling to cascade information on price and promotion activities as predictors relevant across categories and groups of stores. With a context-relevant focus on forecasting revenue 12 weeks ahead, the study highlights product categories that benefit from multi-scale information, defines insights into when, how, and why multivariate models improve forecast accuracy, and shows how cross-category dependencies can relate to promotion decisions in one category impacting others. Bayesian modeling developments underlying the case study are accessible in custom code for interested readers.     

Words and Polynomial Invariants of Finite Groups in Non-Commutative Variables

Let V be a complex vector space with basis {x ₁, x ₂, . . . , x _n } and G be a finite subgroup of GL(V). The tensor algebra T(V) over the complex is isomorphic to the polynomials in the non-commutative variables x ₁, x ₂, . . . , x _n with complex coefficients. We want to give a combinatorial interpretation for the decomposition of T(V) into simple G-modules. In particular, we want to study the graded space of invariants in T(V) with respect to the action of G. We give a general method for decomposing the space T(V) into simple modules in terms of words in a Cayley graph of the group G. To apply the method to a particular group, we require a homomorphism from a subalgebra of the group algebra into the character algebra. In the case of G as the symmetric group, we give an example of this homomorphism from the descent algebra. When G is the dihedral group, we have a realization of the character algebra as a subalgebra of the group algebra. In those two cases, we have an interpretation for the graded dimensions and the number of free generators of the algebras of invariants in terms of those words.     

Algorithmic Aspects of Tree Amalgamation

The amalgamation of leaf-labeled trees into a single (super)tree that “displays” each of the input trees is an important problem in classification. We discuss various approaches to this problem and show that a simple and well-known polynomial-time algorithm can be used to solve this problem whenever the input set of trees contains a minimum size subset that uniquely determines the supertree. Our results exploit a recently established combinatorial property concerning the structure of such collections of trees.     

A framework for the automated real-time detection of short tonal sounds from ocean observatories

Acquisition of acoustic data from ocean observatories is expected to play a key role for the long-term monitoring of marine mammals and anthropogenic noise. It typically requires processing of a large volume of acoustic data and it must rely on automated identification of signals. We present an algorithmic framework for the detection of short tonal sounds (e.g. cetacean calls, anthropogenic pings) intended to act as a first stage in a system for the automated real-time detection, classification, and localisation of acoustic sources. The algorithm was validated under a diversity of scenarios expected at ocean observatories. Using simulated signals that emulate a variety of cetacean call-types, perfect identification of signal position was obtained for signal to noise ratios of ?15 to ?5 dB, depending on the signal-type. Separation of real-world data segments with short tonal sounds (mainly cetacean calls) from segments with other sounds or noise resulted in Area Under the ROC Curve values between 0.96 and 0.98. The algorithm can be used to automatically identify cetacean calls and anthropogenic short tonal sounds much faster than in real-time, thereby reducing the burden put on data transmission, storage, or processing by classification and localisation algorithms.     

Thermodynamic Formalism for Contracting Lorenz Flows

We study the expansion properties of the contracting Lorenz flow introduced by Rovella via thermodynamic formalism. Specifically, we prove the existence of an equilibrium state for the natural potential [^( j)]_t(x,y,z):=-tlogJ_(x,y,z)^cu\hat{ \varphi }_{t}(x,y,z):=-t\log J_{(x,y,z)}^{cu} for the contracting Lorenz flow and for t in an interval containing [0,1]. We also analyse the Lyapunov spectrum of the flow in terms of the pressure.     

Generalizing the Cooper-pair instability to doped Mott insulators

Copper oxides become superconductors rapidly upon doping with electron holes, suggesting a fundamental pairing instability. The Cooper mechanism explains normal superconductivity as an instability of a fermi-liquid state, but high-temperature superconductors derive from a Mott-insulator normal state, not a fermi liquid. We show that precocity to pair condensation with doping is a natural property of competing antiferromagnetism and d-wave superconductivity on a singly-occupied lattice, thus generalizing the Cooper instability to doped Mott insulators, with significant implications for the high-temperature superconducting mechanism.     

Ultrafast excited state dynamics controlling photochemical isomerization of N-methyl-4-[trans-2-(4-pyridyl)ethenyl]pyridinium coordinated to a {Re I(CO)3(2,2'-bipyridine)} chromophore

Two multifunctional photoactive complexes [Re(Cl)(CO)(3)(MeDpe(+))(2)](2+) and [Re(MeDpe(+))(CO)(3)(bpy)](2+) (MeDpe(+)=N-methyl-4-[trans-2-(4-pyridyl)ethenyl]pyridinium, bpy=2,2'-bipyridine) were synthesized, characterized, and their redox and photonic properties were investigated by cyclic voltammetry; ultraviolet-visible-infrared (UV/Vis/IR) spectroelectrochemistry, stationary UV/Vis and resonance Raman spectroscopy; photolysis; picosecond time-resolved absorption spectroscopy in the visible and infrared regions; and time-resolved resonance Raman spectroscopy. The first reduction step of either complex occurs at about -1.1 V versus Fc/Fc(+) and is localized at MeDpe(+). Reduction alone does not induce a trans-->cis isomerization of MeDpe(+). [Re(Cl)(CO)(3)(MeDpe(+))(2)](2+) is photostable, while [Re(MeDpe(+))(CO)(3)(bpy)](2+) and free MeDpe(+) isomerize under near-UV irradiation. The lowest excited state of [Re(Cl)(CO)(3)(MeDpe(+))(2)](2+) has been identified as the Re(Cl)(CO)(3)-->MeDpe(+ 3)MLCT (MLCT=metal-to-ligand charge transfer), decaying directly to the ground state with lifetimes of approximately 42 (73 %) and approximately 430 ps (27 %). Optical excitation of [Re(MeDpe(+))(CO)(3)(bpy)](2+) leads to population of Re(CO)(3)-->MeDpe(+) and Re(CO)(3)-->bpy (3)MLCT states, from which a MeDpe(+) localized intraligand (3)pipi* excited state ((3)IL) is populated with lifetimes of approximately 0.6 and approximately 10 ps, respectively. The (3)IL state undergoes a approximately 21 ps internal rotation, which eventually produces the cis isomer on a much longer timescale. The different excited-state behavior of the two complexes and the absence of thermodynamically favorable interligand electron transfer in excited [Re(MeDpe(+))(CO)(3)(bpy)](2+) reflect the fine energetic balance between excited states of different orbital origin, which can be tuned by subtle structural variations. The complex [Re(MeDpe(+))(CO)(3)(bpy)](2+) emerges as a prototypical, multifunctional species with complementary redox and photonic behavior.     

A systematic study of carboxylic acids in negative ion mode electrospray ionisation mass spectrometry providing a structural model for ion suppression

We report a systematic investigation of the effects and structural requirements for ion suppression in negative ion mode electrospray ionisation mass spectrometry of a series of carboxylic acids and present a structural model rationalising ion suppression effects.     

Investigating the molecular mechanisms of in-plane mechanochemistry on cantilever arrays

Free-standing cantilevers, which directly translate specific biochemical reactions into micromechanical motion, have recently attracted much attention as label-free biosensors and micro/nano robotic devices. To exploit this mechanochemical sensing technology, it is essential to develop a fundamental understanding of the origins of surface stress. Here we report a detailed study into the molecular basis of stress generation in aqueous environments focusing on the pH titration of model mercaptohexadecanoic acid self-assembled monolayers (SAMs), using in situ reference cantilevers coated with nonionizable hexadecanethiol SAMs. Semiautomated data analysis and a statistical model were developed to quantify cyclic deprotonation/protonation reactions on multiple arrays. In-plane force titrations were found to have the sensitivity to detect ionic hydrogen bond formation between protonated and nonprotonated carboxylic acid groups in the proximity of the surface pK1/2, which generated a mean tensile differential surface stress of +1.2 +/- 0.3 mN/m at pH 6.0, corresponding to 1 pN attractive force between two adjacent MHA molecules. Conversely, the magnitude of compressive differential surface stress was found to increase progressively with pH >/= 7.0, reaching a maximum of -14.5 +/- 0.5 mN/m at pH 9.0, attributed to enhanced electrostatic repulsion between deprotonated carboxylic acid groups. However, striking differences were observed in the micromechanical responses to different ionic strength and ion species present in the aqueous environment, highlighting the critical role of counter- and co-ions on surface stress. Our findings provide fundamental insights into the molecular mechanisms of in-plane mechanochemistry, which may be exploited for biosensing and nanoactuation applications.