Miracle-dz/UniFAR-FTUs huggingface dataset:
Long Time Existence of IMCF on Metrics Conformal to Warped Product Manifolds

In this paper we study Inverse Mean Curvature Flow (IMCF) on manifolds that are conformal to a warped product manifold. To this end, we show how the gradient conformal vector field in warped product manifolds is related to the conformal vector field on the conformal metric and use this to gain control of the flow in order to show long time existence. Connections are made to recent results of the author on stability of the positive mass theorem (PMT) and the Riemannian Penrose inequality (RPI) where long time existence of IMCF is an important assumption.
Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of central $L$-values

We prove new congruences between special values of Rankin-Selberg $L$-functions for $\mathrm{GL}(n+1)\times\mathrm{GL}(n)$ over arbitrary number fields. This allows us to control the behavior of $p$-adic $L$-functions under Tate twists and to prove the existence of non-abelian $p$-adic $L$-functions for Hida families on $\mathrm{GL}(n+1)\times\mathrm{GL}(n)$. As an application, we prove strong non-vanishing results for central $L$-values: We give sufficient local conditions for twisted central Rankin-Selberg $L$-values to be generically non-zero.
Association of Zn and Cu Levels in Cord Blood and Maternal Milk with Pregnancy Outcomes among the Slovenian Population

Trace elements, including zinc (Zn) and copper (Cu), are known to play important roles in human health. The present study aimed to assess the levels of Zn and Cu in cord blood and maternal milk and to analyze their association with maternal and infant characteristics and pregnancy outcomes in a Slovenian study population of mothers and their neonates recruited within the PHIME prospective cohort study. The study included 324 mothers, but the data on Zn and Cu levels in both cord blood and maternal milk was available for 243 mothers. Questionnaires were used to assess the socio-demographic and health status of the mothers, their lifestyle habits (including detailed nutritional habits), and their residential and occupational histories. Inductively Coupled Plasma Mass Spectrometry (ICP-MS) was used to measure Zn and Cu levels in cord blood and maternal milk. Low Zn levels in cord blood were associated with lower gestational age and birth weight and were correlated with an increased probability of the birth of small for gestational age (SGA) infants. Maternal smoking influenced the Cu levels in both cord blood and maternal milk. Cord blood Cu levels were higher and Cu levels in maternal milk were lower in smoking compared to non-smoking mothers. Most importantly, a decreased Zn/Cu ratio in cord blood was associated with lower gestational age and lower birth weight. This indicates the overall positive effects of Zn and negative effects of Cu on pregnancy outcomes.
A natural probability measure derived from Stern's diatomic sequence

Stern's diatomic sequence with its intrinsic repetition and refinement structure between consecutive powers of $2$ gives rise to a rather natural probability measure on the unit interval. We construct this measure and show that it is purely singular continuous, with a strictly increasing, H\"older continuous distribution function. Moreover, we relate this function with the solution of the dilation equation for Stern's diatomic sequence.
Weighted Pluricomplex energy II

We continue our study of the Complex Monge-Amp\`ere Operator on the Weighted Pluricomplex energy classes. We give more characterizations of the range of the classes $\mathcal E_ \chi$ by the Complex Monge-Amp\`ere Operator. In particular, we prove that a non-negative Borel measure $\mu $ is the Monge-Amp\`ere of a unique function $\varphi \in \mathcal E_\chi$ if and only if $\chi(\mathcal E_\chi ) \subset L^1(d\mu ). $ Then we show that if $\mu = (dd^c \varphi )^n $ for some $\varphi \in \mathcal E_\chi $ then $\mu = (dd^c u )^n $ for some $u \in \mathcal E_\chi (f) $ where $f$ is a given boundary data. If moreover, the non-negative Borel measure$\mu $ is suitably dominated by the Monge-Amp\`ere capacity, we establish a priori estimates on the capacity of sub-level sets of the solutions. As consequence, we give a priori bounds of the solution of the Dirichlet problem in the case when the measure has a density in some Orlicz space.
Developing a Smart and Sustainable Campus in Singapore

Singapore intends to become a “Smart Nation” through the use of smarter technologies and sustainable means to enhance the quality of life of its inhabitants. Universities are also increasingly seen as places of innovation of new smart and sustainable technologies, provincializing ideas and debates; serving as a testbed for local experimentation. Hence, to determine the status of developing Singapore universities as smart and sustainable campuses, this paper first discusses the role of Singapore’s Smart Nation initiative in relation to the development of smart and sustainable universities in Singapore. In particular, NTU’s development as a smart and sustainable campus. Secondly, a conceptual framework is developed to assess NTU as a smart and sustainable campus by understanding the prevailing dimensions of the smart city discourse. Through a detailed survey and ethnographic field study method conducted on NTU Campus, the study finds that the university has been rapidly deploying smart technologies to enhance students’ learning environment and university residents’ everyday quality of living through technology and sustainability initiatives. This paper contributes meaningfully to the development of smart campuses worldwide and brings an Asian university perspective to the existing research on smart and sustainable campuses.
Multifractal formalism for inverse measures of random weak Gibbs measures

Any Borel probability measure supported on a Cantor set of zero Lebesgue measure on the real line possesses a discrete inverse measure. We study the validity of the multifractal formalism for the inverse measures of random weak Gibbs measures supported on the attractor associated with some $C^1$ random dynamics encoded by a random subshift of finite type, and expanding in the mean. The study requires, in particular, to develop in this context of random dynamics a suitable extension of the results known for heterogeneous ubiquity associated with deterministic Gibbs measures.
On some partially de Rham Galois representations

We study some partially de Rham representations of $\mathrm{Gal}(\bar{L}/L)$ for a finite unramified extension $L$ of $\mathbb{Q}_p$. We study some related subspaces of Galois cohomology and of cohomology of $B$-pairs. As an application, we associate a locally $\mathbb{Q}_p$-analytic representation of $\mathrm{GL}_2(L)$ to a $2$-dimensional trianguline representation of $\mathrm{Gal}(\bar{L}/L)$, by generalizing Breuil's theory in the crystalline case.
The Branching‐Ruin Number and the Critical Parameter of Once‐Reinforced Random Walk on Trees

The motivation for this paper is the study of the phase transition for recurrence/ transience of a class of self‐interacting random walks on trees, which includes the once‐reinforced random walk. For this purpose, we define a quantity, which we call the branching‐ruin number of a tree, which provides (in the spirit of Furstenberg [11] and Lyons [13]) a natural way to measure trees with polynomial growth. We prove that the branching‐ruin number of a tree is equal to the critical parameter for the recurrence/transience of the once‐reinforced random walk. We define a sharp and effective (i.e., computable) criterion characterizing the recurrence/transience of a larger class of self‐interacting walks on trees, providing the complete picture for their phase transition. © 2019 Wiley Periodicals, Inc.
Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets

In many engineered systems, optimization is used for decision making at time scales ranging from real-time operation to long-term planning. This process often involves solving similar optimization problems over and over again with slightly modified input parameters, often under tight latency requirements. We consider the problem of using the information available through this repeated solution process to learn important characteristics of the optimal solution as a function of the input parameters. Our proposed method is based on learning relevant sets of active constraints, from which the optimal solution can be obtained efficiently. Using active sets as features preserves information about the physics of the system, enables interpretable results, accounts for relevant safety constraints, and is easy to represent and encode. However, the total number of active sets is also very large, as it grows exponentially with system size. The key contribution of this paper is a streaming algorithm that learns the relevant active sets from training samples consisting of the input parameters and the corresponding optimal solution, without any restrictions on the problem type, problem structure or probability distribution of the input parameters. The algorithm comes with theoretical performance guarantees and is shown to converge fast for problem instances with a small number of relevant active sets. It can thus be used to establish simultaneously learn the relevant active sets and the practicability of the learning method. Through case studies in optimal power flow, supply chain planning, and shortest path routing, we demonstrate that often only a few active sets are relevant in practice, suggesting that active sets provide an appropriate level of abstraction for a learning algorithm to target.
A step beyond Freiman’s theorem for set addition modulo a prime

Freiman's 2.4-Theorem states that any set $A \subset \mathbb{Z}_p$ satisfying $|2A| \leq 2.4|A| - 3 $ and $|A| < p/35$ can be covered by an arithmetic progression of length at most $|2A| - |A| + 1$. A more general result of Green and Ruzsa implies that this covering property holds for any set satisfying $|2A| \leq 3|A| - 4$ as long as the rather strong density requirement $|A| < p/10^{215}$ is satisfied. We present a version of this statement that allows for sets satisfying $|2A| \leq 2.48|A| - 7$ with the more modest density requirement of $|A| < p/10^{10}$.
The Construction of Image Reference Points and Text Appeals Information Tailoring in Promoting Diners’ Public Environment Maintenance Behavior Intention

The environmental maintenance of public dining spaces significantly impacts urban construction’s sustainable and healthy development. This paper studied the influence of image–text information tailoring relationships on behavioral intentions to promote public dining space environment maintenance. We used a two-factor between-subject experimental design, two (image reference points: self vs. others) × two (text appeals: feasibility vs. desirability). We also examined the mediating roles of environmental maintenance attitudes and environmental responsibility perceptions as regards pro-environmental behavioral intentions. The research results showed the following: (1) Among the four image–text information construction methods, the other’s image reference point with the desirability text appeal promotes the diners’ pro-environmental behavioral intention with optimal effectiveness; and (2) Environmental maintenance attitudes and environmental responsibility perceptions play mediating roles in promoting diners’ intention to maintain environmental behavior in the image–text combined information presentation. Environmental responsibility perceptions cannot be mediated alone and must be progressively mediated with environmental maintenance attitudes.
Multi-objective non-linear solid transportation problem with fixed charge, budget constraints under uncertain environments

ABSTRACT Transportation-based models are widely used to solve real-life problems such as supply chain problems, inventory level problems, business models, management problems, etc. The parameters of these problems have been conventionally measured as deterministic. However, these parameters have vagueness due to the uncertainty in the data sets. Such uncertainty of the parameters is generally measured using randomness (probability theory) or fuzziness (fuzzy theory), with certain assumptions and limitations. Closed intervals interpretation is another concept to deal with the uncertainties of real-world issues in recent decades, avoiding the limitations in probability theory and fuzzy set theory. This study formulates a fixed-charged multi-objective non-linear solid transportation with parameters such as availability of items, conveyance capacity, transportation cost, requirement, and budget for destinations in the form of closed intervals, where objectives are minimization of total transportation cost and action of time under the restriction over budget. An efficient solution procedure is developed with the help of interval analysis based on the parametric perception of intervals. Initially, the objective functions are converted into a crisp function using multiple integrations, and as a result, the problem is converted into a deterministic multi-objective non-linear programming problem. In addition, a real-world numerical problem is considered for testing the developed solution process for greater comprehension and clarity.
Quasi-equilibrium problems with generalized monotonicity

In this work, we propose a new existence result for quasi-equilibrium problems using generalized monotonicity in an infinite dimensional space. Also, we show that the notions of generalized monotonicity can be characterized in terms of solution sets of equilibrium problems and convex feasibility problems. Moreover, we show that the concept of pseudomonotonicity and upper sign property are related under suitable assumptions.
Nodal portraits of quantum billiards: Domains, lines, and statistics

We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and chaotic classical dynamics but also between different geometric shapes of the billiard system itself. We discuss, in particular, how a random superposition of plane waves can model chaotic eigenfunctions and highlight the connections of the complex morphology of the nodal lines thereof to percolation theory and Schramm-Loewner evolution. Various approaches to counting the nodal domains---using trace formulae, graph theory, and difference equations---are also illustrated with examples. The nodal patterns addressed pertain to waves on vibrating plates and membranes, acoustic and electromagnetic modes, wavefunctions of a "particle in a box'" as well as to percolating clusters, and domains in ferromagnets, thus underlining the diversity---and far-reaching implications---of the problem.
Recognizing the flat torus among $RCD^*(0,N)$ spaces via the study of the first cohomology group

We prove that if the dimension of the first cohomology group of a $RCD^*(0,N)$ space is $N$, then the space is a flat torus. This generalizes a classical result due to Bochner to the non-smooth setting and also provides a first example where the study of the cohomology groups in such synthetic framework leads to geometric consequences.
Stability conditions on Kuznetsov components

We introduce a general method to induce Bridgeland stability conditions on semiorthogonal decompositions. In particular, we prove the existence of Bridgeland stability conditions on the Kuznetsov component of the derived category of many Fano threefolds (including all but one deformation type of Picard rank one), and of cubic fourfolds. As an application, in the appendix, written jointly with Xiaolei Zhao, we give a variant of the proof of the Torelli theorem for cubic fourfolds by Huybrechts and Rennemo.
Multi-temporal orthophoto and digital surface model registration produced from UAV imagery over an agricultural field

Abstract Correcting the three-dimensional geometric error is essential to effectively use the multi-temporal unmanned aerial vehicle (UAV) orthophoto and digital surface model (DSM) acquired from the agricultural field. Although ground control points (GCPs) obtained through field surveys are usually used to calibrate geometrical errors establishing/maintaining GCPs and surveying them in the field are time-consuming and inefficient. Therefore, we propose a simple and efficient methodology to improve the geometric registration of multi-temporal orthophotos and DSMs without GCPs. In the proposed method, coarse to fine image registration is performed first, which corrects severe to slight errors by sequential feature and area-based matching methods. Subsequently, we extract height-invariant regions in multi-temporal DSM pairs, called elevation invariant feature (EIF), using the EIFs to register DSMs by estimating a linear regression model. Various experiments were conducted to analyze the absolute and relative accuracies using ten multi-temporal orthophotos and DSMs, and the robustness of the proposed method was evaluated using data obtained from another site. The experimental results demonstrate that the geometric quality of registered orthophotos and DSMs was significantly improved.
Functional Integration on Constrained Function Spaces II: Applications

Some well-known examples of constrained quantum systems commonly quantized via Feynman path integrals are re-examined using the notion of conditional integrators introduced in [1]. The examples yield some new perspectives on old results. As an interesting new application, the formalism is used to construct a physical model of average prime counting functions modeled as a constrained gamma process.
Does tax aggressiveness and cost of debt affect firm performance? The moderating role of political connections

Abstract Firms in emerging economies continue to suffer as a consequence of tax evasion, high cost of financing, political interference, weak governance systems, and bureaucratic institutions. In order to understand how these challenges complicate commercial activities, this study examines how tax aggressiveness, cost of debt, and political connections affect firm performance in Pakistan. Unlike previous research, we also explore if political connections moderate the association between (i) tax aggressiveness and firm performance and (ii) cost of debt and firm performance. Our robust empirical analysis reveals that tax aggressive firms have weaker performance while politically connected firms have better performance, ceteris paribus. Further, we find that tax aggressive firms having politically connected board members have better performance as compared to their non-connected counterparts. Similarly, firms with a high cost of debt and politically connected board members have better performance as compared to non-connected firms. Thus, we argue that political connections help connected firms in overcoming the adverse consequences of tax aggressiveness and the high cost of debt through their influence in procuring government projects, subsidies, and other benefits. Therefore, policymakers are advised to restrict politically connected board members from extending favors and concessions to connected firms. We also encourage shareholders to exercise their voting power and monitoring capabilities for mitigating agency problems inherent in politically connected firms.
Sudoku Rectangle Completion

Over the last decade, Sudoku, a combinatorial number-placement puzzle, has become a favorite pastimes of many all around the world. In this puzzle, the task is to complete a partially filled $9 \times 9$ square with numbers 1 through 9, subject to the constraint that each number must appear once in each row, each column, and each of the nine $3 \times 3$ blocks. Sudoku squares can be considered a subclass of the well-studied class of Latin squares. In this paper, we study natural extensions of a classical result on Latin square completion to Sudoku squares. Furthermore, we use the procedure developed in the proof to obtain asymptotic bounds on the number of Sudoku squares of order $n$.
Nanosensor Location Estimation in the Human Circulatory System Using Machine Learning

The human body can be considered a complex natural network due to the variety of interconnections between the different body regions. One example is the network of blood vessels, where artificial communication channels can be rendered using nanosensors that travel in the bloodstream as collectors and carriers of information. Further advancing this vision, in this work we investigate the detection and localization capabilities of flowing nanosensors in the blood flow to report abnormalities in the human body. Specifically, we target the detection quorum sensing molecules and provide a methodology to evaluate its performance. The methodology consists of modeling the traveling path of nanosensors along the vessels through a Markov chain, and the use of machine learning (ML) models to compute their transition probabilities. We illustrate the resulting distribution of nanosensors in the body, which evidences a close match to expected results. We also evaluate their detection and localization capabilities in different body regions revealing their effectiveness to determine the presence of abnormalities in the human vessels.
Banach limits and traces on $\mathcal L_{1,\infty}$

We introduce a new approach to traces on the principal ideal $\mathcal L_{1,\infty}$ generated by any positive compact operator whose singular value sequence is the harmonic sequence. Distinct from the well-known construction of J.~Dixmier, the new approach provides the explicit construction of every trace of every operator in $\mathcal L_{1,\infty}$ in terms of translation invariant functionals applied to a sequence of restricted sums of eigenvalues. The approach is based on a remarkable bijection between the set of all traces on $\mathcal L_{1,\infty}$ and the set of all translation invariant functionals on $l_\infty$. This bijection allows us to identify all known and commonly used subsets of traces (Dixmier traces, Connes-Dixmier traces, etc.) in terms of invariance properties of linear functionals on $l_\infty$, and definitively classify the measurability of operators in $\mathcal L_{1,\infty}$ in terms of qualified convergence of sums of eigenvalues. This classification has led us to a resolution of several open problems (for the class $\mathcal L_{1,\infty}$) from~\cite{CS}. As an application we extend Connes' classical trace theorem to positive normalised traces.