Research Problems from the BCC21

AbstractA collection of open problems, mostly presented at the problem session of the 21st British Combinatorial Conference

Superpolynomial smoothed complexity of 3-FLIP in Local Max-Cut

We construct a graph with $n$ vertices where the smoothed runtime of the 3-FLIP algorithm for the 3-Opt Local Max-Cut problem can be as large as $2^{\Omega(\sqrt{n})}$. This provides the first example where a local search algorithm for the Max-Cut problem can fail to be efficient in the framework of smoothed analysis. We also give a new construction of graphs where the runtime of the FLIP algorithm for the Local Max-Cut problem is $2^{\Omega(n)}$ for any pivot rule. This graph is much smaller and has a simpler structure than previous constructions.Comment: 18 pages, 3 figure

Hermite interpolation with retractions on manifolds

Interpolation of data on non-Euclidean spaces is an active research area fostered by its numerous applications. This work considers the Hermite interpolation problem: finding a sufficiently smooth manifold curve that interpolates a collection of data points on a Riemannian manifold while matching a prescribed derivative at each point. We propose a novel procedure relying on the general concept of retractions to solve this problem on a large class of manifolds, including those for which computing the Riemannian exponential or logarithmic maps is not straightforward, such as the manifold of fixed-rank matrices. We analyze the well-posedness of the method by introducing and showing the existence of retraction-convex sets, a generalization of geodesically convex sets. We extend to the manifold setting a classical result on the asymptotic interpolation error of Hermite interpolation. We finally illustrate these results and the effectiveness of the method with numerical experiments on the manifold of fixed-rank matrices and the Stiefel manifold of matrices with orthonormal columns

Consumer perception and physicochemical characterization of a new product made from lactic acid fermented orange peels

A new product made from orange peels discarded from juice making has been characterized during the present study. In order to reduce its bitterness, orange peel was fermented during 10 days in two different sugary brines (2% or 5% NaCl content) using a Lactiplantibacillus plantarum strain. The lactic acid fermentation process was characterized by determining pH, sucrose, and the organic acids content. The original peel and the final products were characterized by instrumental texture and color determination, and total flavonoids content. In addition, consumers' expectations and perception of the new products were also studied using an online survey and a consumer study in which acceptance and perceived bitterness were assessed. Results suggested that the 2% NaCl-fermentation process allowed a greater bacteria development (with a higher lactic acid production and larger differences in color parameters with the original peel than the 5% NaCl-fermented samples) although both fermented samples were significantly different from the original peel in their physicochemical characteristics. Total flavonoids content, which has been related to bitterness perception, was significatively lower in the fermented samples than in the raw orange peel (50% reduction). Spanish consumers’ expectations and perception of the new product were similar, and the snack made with the peel fermented in the 2% NaCl-brine was more liked than the same snack made with the original peel, or the 5% NaCl-fermented one. Using a lactic acid fermentation in a sugary brine was useful to decrease the bitterness perception and increase liking of the orange peel, meaning a potential valorization for this orange juice by-product. Implications for gastronomy. The present study includes the physico-chemical characterization and consumers’ perception of a new product developed with one of the main citrus by-products: orange peels. A new ingredient for the Spanish gastronomy is proposed, showing a potential use for one of the main HORECA (HOtels REstaurants Catering sector) and juices industry by-products. A simple lactic-acid fermentation process, inspired in the North-African gastronomy culture, is described, and the consumer perception of the new product, presented as a freeze-dried snack is shown, proposing a new way of decreasing this food waste in Spain. In addition, some ideas about how to decrease bitterness perception on flavonoids-rich materials are shown, contributing to the knowledge on other new foods development

Anomalous dissipation and lack of selection in the Obukhov-Corrsin theory of scalar turbulence

The Obukhov-Corrsin theory of scalar turbulence [Obu49, Cor51] advances quantitative predictions on passive-scalar advection in a turbulent regime and can be regarded as the analogue for passive scalars of Kolmogorov's K41 theory of fully developed turbulence [Kol41]. The scaling analysis of Obukhov and Corrsin from 1949-1951 identifies a critical regularity threshold for the advection-diffusion equation and predicts anomalous dissipation in the limit of vanishing diffusivity in the supercritical regime. In this paper we provide a fully rigorous mathematical validation of this prediction by constructing a velocity field such that the unique bounded solution of the advection-diffusion equation is bounded uniformly-in-diffusivity in the full supercritical Obukhov-Corrsin regularity regime and exhibits anomalous dissipation. We also show that for a velocity field in $C^{\alpha}$ of space and time (for an arbitrary $0 \leq {\alpha} < 1$) neither vanishing diffusivity nor regularization by convolution provide a selection criterion for bounded solutions of the advection equation.Comment: 33 pages and 8 figure

Avoiding, pretending, and querying : three combinatorial problems.

A k-term quasi-progression of diameter d is a sequence {Xl,... ,xk} for which there exists a positive integer l such that l \u3c Xi-Xi-1 \u3c l+d, for all i = 2, ... ,k. Quasi-progressions may be thought of as arithmetic progressions with a certain amount of \u27wiggle-room\u27 allowed. Let Q(d, k) be the least positive integer such that every 2-coloring of {1, ... , Q(d, k)} contains a monochromatic k-term quasi-progression of diameter d. We prove a conjecture of Landman for certain values of k and d, provide counterexamples for some other cases, and determine that the conjecture always has the correct order of growth. Let A be the adjacency matrix of a non empty graph. Is there always a nonzero {0, 1}-vector in the row space of A that is not a row of A? Akbari, Cameron, and Khosrovshahi have shown that an affirmative answer to this question would imply bounds on many graph parameters as a function of the rank of the adjacency matrix. We demonstrate the existence of such vectors for certain families of graphs, examine techniques to find and verify the existence of such vectors, and show that if you generalize the problem to allow asymmetry in the matrices then some {0, 1 }-matrices do not have such vectors. In 1981, Andrew Yao asked Should tables be sorted? . When the table has n cells that are filled with entries taken from a key space of m possibilities, he showed that it is possible to decide whether any member of the key space is present in the table by inspecting (querying) only one cell of the table if and only if m \u3c 2n - 2. We make steps toward extending his result to the case where you are permitted two queries by considering several variations of the problem

Row-Hamiltonian Latin squares and Falconer varieties

A \emph{Latin square} is a matrix of symbols such that each symbol occurs exactly once in each row and column. A Latin square $L$ is \emph{row-Hamiltonian} if the permutation induced by each pair of distinct rows of $L$ is a full cycle permutation. Row-Hamiltonian Latin squares are equivalent to perfect $1$-factorisations of complete bipartite graphs. For the first time, we exhibit a family of Latin squares that are row-Hamiltonian and also achieve precisely one of the related properties of being column-Hamiltonian or symbol-Hamiltonian. This family allows us to construct non-trivial, anti-associative, isotopically $L$-closed loop varieties, solving an open problem posed by Falconer in 1970

MEANDERING. Part 1: Turbulent Mixing in Sharp Meander Bends. Part 2: Mathematical Model for Meandering Rivers with Spatial Width Variations

This thesis concerns the investigation of the meandering phenomena, focusing on the hydrodynamic (Part I) and on the morphodynamic (Part II) of meandering rivers. In the first part of this work, sharp curved single-bend open channel flow with a flat bed, representative of the early phase of bed erosion, is investigated by the use of Large Eddy Simulation (LES). The three-dimensional (3D) numerical simulation can provide flow field information that are difficult to obtain in the laboratory or in a real river. The focus is to provide insight into the physics of sharp meandering bends, highlighting the main flow and secondary flow characteristics and the role of turbulence. The latter plays an important role in many processes that are key in natural rivers, such as the phenomena of spreading and mixing of suspended matter, of sediment transport and scour processes. Turbulence affects the strength of the curvature-induced secondary flow in the core of the flow domain, a typical feature of curved open-channel flow. It rules the intensity of the bed shear stresses and the friction losses along the bend. It is especially important in the flow regions near the banks, affecting the stability of the channel banks. At the inner bank, the model predicts, rather accurately, the boundary layer detachment and the formation of an internal shear layer. Furthermore, the model adequately reproduces the outer-bank cell of secondary flow and the local increase of turbulent kinetic energy. In this work, two curved channels are investigated with the intent to underline the influence of the water depth on the flow features. Finally, the effects of the super-elevation of the free surface on the meandering hydrodynamics are analyzed using a Detached Eddy Simulation (DES) model available in the free software OpenFOAM. In the second part of this work, a mathematical model for meandering rivers with spatial width variations is developed. The mathematical modeling of the long-term evolution of meandering rivers needs an efficient computation of the flow field. Therefore, the development of a mathematical model based on the complete response of a meandering river to spatially varying channel axis curvature and width is necessary. For this purpose, we elaborate a morphodynamic model able to predict the spatial distribution of the flow field and the equilibrium bed configuration of an alluvial river characterized by arbitrary distributions of both the channel axis curvature and the channel width. Owing to analytical character of the model, it provides a computationally efficient tool that can be easily incorporated in long-term river planform evolution models. Furthermore, it can be used to rapidly evaluate the morphological tendencies of an alluvial river in response to variations in planform geometry or hydrodynamic forcing. The model is tested by comparison with the bed topography observed in a typical reach of the Po River, showing that in presence of wide, mildly curved and long bend and weak width variations, the river topography is described with a good accuracy

The relationship between activity level and the movement pattern of supine to standing

Call number: LD2668 .T4 PELS 1989 G74Master of ScienceKinesiolog

Human-in-the-Loop Simulation Evaluating the Collocation of the User Request Evaluation Tool, Traffic Management Advisor, and Controller-Pilot Data Link Communications: Experiment 1 - Toll Combination

The Federal Aviation Administration (FAA) Free Flight Program successfully deployed the User Request Evaluation Tool (URET), Traffic Management Advisor (TMA), and Controller-Pilot Data Link Communications (CPDLC) to a limited number of Air Route Traffic Control Centers (ARTCCs). As deployment expands nationwide, several facilities may eventually receive all three tools. Before this occurs, it is important to identify any potential human factors issues that may arise due to the collocation of these tools at the controller\u2019s workstation. In this report, we present the first of three high fidelity human-in-the-loop simulation experiments we conducted to evaluate the impact of URET, TMA, and CPDLC collocation on controller workload, situational awareness, and teamwork. We examined collocation issues with a \u201cstovepipe\u201d independent configuration where none of the tools were integrated or directly communicated with each other. In this first experiment, twelve Air Traffic Control Specialists (ATCSs) participated as Rside/ D-side controller teams operating a high altitude generic sector using all combinations of the three tools. The most important collocation issue identified was that controllers had difficulty accessing important information on the D-side display when URET and CPDLC were both operational (i.e., display clutter). Although neither tool alone caused display clutter, both tools in combination made it difficult for D-side controllers to find the information they needed quickly. This was especially true for accessing CPDLC windows, which became covered when controllers used URET. Another collocation issue was that D-side controllers had to access TMA delay time information from the R-side display. Controllers thought it was important to have TMA information available on the D-side display where it could be easily accessed by D-side controllers. However, controllers were concerned that simply showing the TMA List on the D-side might add to the D-side display clutter. Good human factors design principles prescribe that users must have immediate access to important information and that critical information should never be covered. A \u201cstovepipe\u201d independent deployment of these tools will result in impaired access to timely information. The results of this study indicated that better efforts should be made towards integrating the information from URET, TMA, and CPDLC on the D-side monitor prior to deployment