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Nitrogen Vacancy diamond nanoparticles (NVNPs) are increasingly integrated with methods for optical detection of magnetic resonance (ODMR), providing new opportunities in magnetic characterization that span the visualization of magnetic fields in microelectronic circuits, environmental sensing and biology. However, only a small number of studies utilize aggregates of NVNPs for surface-wide magnetometry being that spin orientations in aggregate NVNPs are inherently misaligned, precluding their use for proper magnetic field detection compared with expensive monocrystalline diamonds. A postprocessing method for layering NVNPs with aligned NV center orientations can potentially facilitate superior NV magnetometry by allowing sensitive detection combined with simplified probe preparation. We present a novel technology for creating densely stacked monolayers of NVNP with inherent interlayer alignment for sensitive measurement of local magnetic field perturbations in microelectronic traces. We establish spatial characteristics of deposited aggregates and demonstrate their ability to capture magnetic dipoles from conducting microwires via ODMR. Our approach forms a novel accessible protocol that can be used for broad applications in micromagnetometry.

Given a hypergraph $H=(V,E)$, define for every edge $e\in E$ a linear expression with arguments corresponding with the vertices. Next, let the polynomial $p_H$ be the product of such linear expressions for all edges. Our main goal was to find a relationship between the Alon-Tarsi number of $p_H$ and the edge density of $H$. We prove that $AT(p_H)=\lceil ed(H)\rceil+1$ if all the coefficients in $p_H$ are equal to $1$. Our main result is that, no matter what those coefficients are, they can be permuted within the edges so that for the resulting polynomial $p_H^\prime$, $AT(p_H^\prime)\leq 2\lceil ed(H)\rceil+1$ holds. We conjecture that, in fact, permuting the coefficients is not necessary. If this were true, then in particular a significant generalization of the famous 1-2-3 Conjecture would follow.

In \cite[Serra, Vena, Extremal families for the Kruskal-Katona theorem]{sv21}, the authors have shown a characterization of the extremal families for the Kruskal-Katona Theorem. We further develop some of the arguments given in \cite{sv21} and give additional properties of these extremal families. F\"uredi-Griggs/M\"ors theorem from 1986/85 \cite{furgri86,mors85} claims that, for some cardinalities, the initial segment of the colexicographical is the unique extremal family; we extend their result as follows: the number of (non-isomorphic) extremal families strictly grows with the gap between the last two coefficients of the $k$-binomial decomposition. We also show that every family is an induced subfamily of an extremal family, and that, somewhat going in the opposite direction, every extremal family is close to being the inital segment of the colex order; namely, if the family is extremal, then after performing $t$ lower shadows, with $t=O(\log(\log n))$, we obtain the initial segment of the colexicographical order. We also give a ``fast'' algorithm to determine whether, for a given $t$ and $m$, there exists an extremal family of size $m$ for which its $t$-th lower shadow is not yet the initial segment in the colexicographical order. As a byproduct of these arguments, we give yet another characterization of the families of $k$-sets satisfying equality in the Kruskal--Katona theorem. Such characterization is, at first glance, less appealing than the one in \cite{sv21}, since the additional information that it provides is indirect. However, the arguments used to prove such characterization provide additional insight on the structure of the extremal families themselves., Comment: 44 pages, 3 figures, 1 table

We extend the notion of graph homomorphism to cellularly embedded graphs (maps) by designing operations on vertices and edges that respect the surface topology; we thus obtain the first definition of map homomorphism that preserves both the combinatorial structure (as a graph homomorphism) and the topological structure of the surface (in particular, orientability and genus). Notions such as the core of a graph and the homomorphism order on cores are then extended to maps. We also develop a purely combinatorial framework for various topological features of a map such as the contractibility of closed walks, which in particular allows us to characterize map cores. We then show that the poset of map cores ordered by the existence of a homomorphism is connected and, in contrast to graph homomorphisms, does not contain any dense interval (so it is not universal for countable posets). Finally, we give examples of a pair of cores with an infinite number of cores between them, an infinite chain of gaps, and arbitrarily large antichains with a common homomorphic image., Comment: 46 pages, 11 figures

Given a family $S$ of $k$--subsets of $[n]$, its lower shadow $\Delta(S)$ is the family of $(k-1)$--subsets which are contained in at least one set in $S$. The celebrated Kruskal--Katona theorem gives the minimum cardinality of $\Delta(S)$ in terms of the cardinality of $S$. F\"uredi and Griggs (and M\"ors) showed that the extremal families for this shadow minimization problem in the Boolean lattice are unique for some cardinalities and asked for a general characterization of these extremal families. In this paper we prove a new combinatorial inequality from which yet another simple proof of the Kruskal--Katona theorem can be derived. The inequality can be used to obtain a characterization of the extremal families for this minimization problem, giving an answer to the question of F\"uredi and Griggs. Some known and new additional properties of extremal families can also be easily derived from the inequality.

As a result of 33 intercontinental Zoom calls, we characterise big Ramsey degrees of the generic partial order. This is an infinitary extension of the well known fact that finite partial orders endowed with linear extensions form a Ramsey class (this result was announced by Ne\v{s}et\v{r}il and R\"odl in 1984 with first published proof by Paoli, Trotter and Walker in 1985). Towards this, we refine earlier upper bounds obtained by Hubi\v{c}ka based on a new connection of big Ramsey degrees to the Carlson-Simpson theorem and we also introduce a new technique of giving lower bounds using an iterated application of the upper-bound theorem., Comment: 30 pages, 7 figures. Minor revision incorporating suggestions of the second anonymous referee

We prove that the ribbon graph polynomial of a graph embedded in an orientable surface is irreducible if and only if the embedded graph is neither the disjoint union nor the join of embedded graphs. This result is analogous to the fact that the Tutte polynomial of a graph is irreducible if and only if the graph is connected and non-separable., Comment: 15 pages - this is the authors accepted manuscript / version of record without journal provided formatting

In 2015, the United Nations adopted 17 Sustainable Development Goals (SDGs) with 169 targets for transformation toward a more sustainable future by 2030. This study seeks to evaluate and analyze SDG target interactions in the Philippines to resolve conflicting targets, and prioritize targets that reinforce others and have no conflicts. To evaluate all 14196 target interactions, two methods are employed. First, experts with over five years of SDG-related experience evaluated interactions using a 7-point scale. Second, a non-parametric Spearman rank correlation is used on official indicator data with resulting coefficients serving as interaction scores. Interaction scores are then coded as synergies (interact positively), trade-offs (negatively) or non-classified (neutrally). Targets are also modelled as nodes and interactions as edges in graphs presented in sdginteractions.herokuapp.com. Results from the two methods were synthesized to formulate recommendations for concerned parties. This includes resolving negative intra-goal target interactions involving targets 3.1 'Reduce maternal mortality', 3.6 'Reduce road injuries and deaths', and 3.7 'Universal access to sexual and reproductive care, family planning, and education'. Ugly targets (at least one negative interaction) including target 3.6, 3.7, and 8.2 'Diversify, innovate, and upgrade for economic productivity' need to be resolved. Targets that reinforce their corresponding SDGs should be prioritized, including 1.1 'Eradicate extreme poverty', 4.2 'Equal access to quality pre-primary education', 6.2 'End open defecation and provide access to sanitation and hygiene', 8.1 'Sustainable economic growth', and 9.4 'Upgrade all industries and infrastructures for sustainability'. Beautiful targets (no negative interactions) should also be prioritized, including target 8.5 and 17.5 'Invest in least developed countries'.

We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recent upper bounds given by Zucker. Using this characterization, we show that the Fra\"iss\'e limit of each such class admits a strong big Ramsey structure, implying that the automorphism group of the Fra\"iss\'e limit has a metrizable universal completion flow., Comment: Revised version; formerly titled "Exact big Ramsey degrees via coding trees."

The United Nations developed the 17 Sustainable Development Goals (SDGs), with 169 targets, to serve as a plan for solving the world's problems and achieving a more sustainable future. This is modeled as a graph with the targets as nodes, and with the interaction between targets as the edges of the graph. An exhaustive binary comparison is done to analyze the intra- and inter-goal target interactions, entailing over 14000 comparisons. The task is to assign a 'color' to an edge: positive (indivisible), zero (consistent) or negative (cancelling). This is done via a panel of experts who will evaluate the target interactions, through a web application that was developed for coloring the edges. This is an on-going study, and so far, of the 1256 edges colored, only 36 are cancelling (negative), or 2.86%; more than 97% are positive interactions. So far, the "most negative" interactions involve: "Climate Change"; "Life Below Water"; "Peace, Justice and Strong Institutions"; and "Decent Work and Economic Growth". Most useful for planning might be the 'graph of beautiful targets' feature, which shows target with non-negative interactions, and how they connect to each other. These are the targets that may be worked on simultaneously, and currently has more than 130 nodes. This study can help researchers analyze which targets enable or constrain each other, what mitigation can be done to avoid conflicts, and can be configured for sub-national or regional study. Web app at: http://sdg-interactions.herokuapp.com/

Using the Carlson-Simpson theorem, we give a new general condition for a structure in a finite binary relational language to have finite big Ramsey degrees, Comment: 6 pages, extended abstract accepted to EUROCOMB 2021

As a result of 33 intercontinental Zoom calls, we characterise big Ramsey degrees of the generic partial order in a similar way as Devlin characterised big Ramsey degrees of the generic linear order (the order of rationals)., Comment: 6 pages, extended abstract accepted to EUROCOMB 2021

Now that SARS-CoV-2 (COVID-19) vaccines are developed, it is very important to plan its distribution strategy. In this paper, we formulated a multi-objective linear programming model to optimize vaccine distribution and applied it to the agent-based version of our age-stratified and quarantine-modified SEIR with non-linear incidence rates (ASQ-SEIR-NLIR) compartmental model. Simulations were performed using COVID-19 data from Quezon City and results were analyzed under various scenarios: (1) no vaccination, (2) base vaccination (prioritizing essential workers and vulnerable population), (3) prioritizing mobile workforce, (4) prioritizing elderly, and (5) prioritizing mobile workforce and elderly; in terms of (a) reducing infection rates and (b) reducing mortality incidence. After 10 simulations on distributing 500,000 vaccine courses, results show that prioritizing mobile workforce minimizes further infections by 24.14%, which is better than other scenarios. On the other hand, prioritizing the elderly yields the highest protection (439%) for the Quezon City population compared to other scenarios. This could be due to younger people, when contracted the disease, has higher chances of recovery than the elderly. Thus, this leads to reduction of mortality cases.

The Advanced Circulation (ADCIRC) and Simulating Nearshore Waves (SWAN) coupled model is modified to include a stochastic term in the shallow water equations that represents random external forces from debris carried by surge and short-term local scale atmospheric fluctuations. We added $\alpha$-stable noise, uncorrelated in space and time, in the forcing terms of the coupled model. Inputs to the model are unstructured computational mesh derived from topography and bathymetry, land cover classification, tidal potential constituents and atmospheric forcing. The model simulated surge height of around five meters rushing at four meters per second near Tacloban City downtown. Underestimation of simulated surge height is expected with use of bare earth model and absence of fluid sources on the governing equations, while overestimation of simulated peak height also occurs due to presence of concrete barriers that reduced surge height and inundation extent. The stochastic model is sensitive to random external forces during low tide and relatively higher fluid speed. Low tide happens when the fluid speed is maximum and water elevation is lowest, while higher fluid speed is brought by external forces like storm surge. However, the difference of stochastic solutions from the deterministic solution averages to zero and there is no significant improvement of the storm surge model in general when it comes to additive noise. This is an expected result since the noise used has zero mean. As $\alpha$ goes to zero larger jumps occur more frequently so $\sigma$ needs to be as small as $10^{-8}$ for simulation stability.

Influences of reaction zone thickening and local extinctions on the burning rate of extremely turbulent hydrogen-enriched methane-air flames are investigated using simultaneous planar laser-induced fluorescence of formaldehyde molecule and hydroxyl radical as well as separate stereoscopic particle image velocimetry techniques. Karlovitz numbers upto 76 are examined. It is shown that, by increasing the turbulence intensity, the preheat and reaction zone thicknesses can increase to values that are, respectively, 6.3 and 4.9 of the corresponding laminar flames. Broadening of these zones for intensely turbulent hydrogen-enriched methane-air flames is shown experimentally for the first time. Broadening of the reaction zone suggests that the flamelet assumption used for development of the burning rate formulations may not hold. Thus, a new formulation, which does not utilize the flamelet assumption, is developed and used to calculate the burning rate of the tested flames. It is shown that, at small turbulence intensities, the burning rate values follow those of the local consumption speed, which is developed in the literature based on the flamelet assumption. However, at large turbulence intensities, the estimated burning rate features large values, and the ratio of this parameter to the local consumption speed is consistent with the ratio of the global and local consumption speeds reported in the literature. It is shown that the ratio of the normalized burning rate to the normalized local consumption speed is correlated with the broadening of reaction zone, suggesting that the disparity between the values of the burning rate and local consumption speed is linked to the reaction zone thickening. It is shown, although the flame thickening increase the burning rate, local extinctions decrease this parameter leading to the bending behavior reported in the literature.

We prove that the universal homogeneous 3-uniform hypergraph has finite big Ramsey degrees. This is the first case where big Ramsey degrees are known to be finite for structures in a non-binary language. Our proof is based on the vector (or product) form of Milliken's Tree Theorem and demonstrates a general method to carry existing results on structures in binary relational languages to higher arities., Comment: 10 pages, 2 figures. Minor corrections and presentation improvements suggested by the referees

Semi-functional linear regression models postulate a linear relationship between a scalar response and a functional covariate, and also include a non-parametric component involving a univariate explanatory variable. It is of practical importance to obtain estimators for these models that are robust against high-leverage outliers, which are generally difficult to identify and may cause serious damage to least squares and Huber-type $M$-estimators. For that reason, robust estimators for semi-functional linear regression models are constructed combining $B$-splines to approximate both the functional regression parameter and the nonparametric component with robust regression estimators based on a bounded loss function and a preliminary residual scale estimator. Consistency and rates of convergence for the proposed estimators are derived under mild regularity conditions. The reported numerical experiments show the advantage of the proposed methodology over the classical least squares and Huber-type $M$-estimators for finite samples. The analysis of real examples illustrate that the robust estimators provide better predictions for non-outlying points than the classical ones, and that when potential outliers are removed from the training and test sets both methods behave very similarly., Comment: In press

The fractional and circular chromatic numbers are the two most studied non-integral refinements of the chromatic number of a graph. Starting from the definition of a coloring base of a graph, which originated in work related to ergodic theory, we formalize the notion of a gyrocoloring of a graph: the vertices are colored by translates of a single Borel set in the circle group, and neighbouring vertices receive disjoint translates. The corresponding gyrochromatic number of a graph always lies between the fractional chromatic number and the circular chromatic number. We investigate basic properties of gyrocolorings. In particular, we construct examples of graphs whose gyrochromatic number is strictly between the fractional chromatic number and the circular chromatic number. We also establish several equivalent definitions of the gyrochromatic number, including a version involving all finite abelian groups.

Given a countably infinite hypergraph $\mathcal R$ and a finite hypergraph $\mathcal A$, the big Ramsey degree of $\mathcal A$ in $\mathcal R$ is the least number $L$ such that, for every finite $k$ and every $k$-colouring of the embeddings of $\mathcal A$ to $\mathcal R$, there exists an embedding $f$ from $\mathcal R$ to $\mathcal R$ such that all the embeddings of $\mathcal A$ to the image $f(\mathcal R)$ have at most $L$ different colours. We describe the big Ramsey degrees of the random countably infinite 3-uniform hypergraph, thereby solving a question of Sauer. We also give a new presentation of the results of Devlin and Sauer on, respectively, big Ramsey degrees of the order of the rationals and the countably infinite random graph. Our techniques generalise (in a natural way) to relational structures and give new examples of Ramsey structures (a concept recently introduced by Zucker with applications to topological dynamics)., Comment: 8 pages, 3 figures, extended abstract for Eurocomb 2019