Miracle-dz/UniFAR-FTUs huggingface dataset:
On the evolution of topology in dynamic clique complexes

Abstract We consider a time varying analogue of the Erdős–Rényi graph and study the topological variations of its associated clique complex. The dynamics of the graph are stationary and are determined by the edges, which evolve independently as continuous-time Markov chains. Our main result is that when the edge inclusion probability is of the form p=n α, where n is the number of vertices and α∈(-1/k, -1/(k + 1)), then the process of the normalised kth Betti number of these dynamic clique complexes converges weakly to the Ornstein–Uhlenbeck process as n→∞.
Cauchy problem and periodic homogenization for nonlocal Hamilton–Jacobi equations with coercive gradient terms

Abstract This paper deals with the periodic homogenization of nonlocal parabolic Hamilton–Jacobi equations with superlinear growth in the gradient terms. We show that the problem presents different features depending on the order of the nonlocal operator, giving rise to three different cell problems and effective operators. To prove the locally uniform convergence to the unique solution of the Cauchy problem for the effective equation we need a new comparison principle among viscosity semi-solutions of integrodifferential equations that can be of independent interest.
Weight functions and log-optimal investment portfolios

Following the paper by Algoet--Cover (1988), we analyse log-optimal portfolios where return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, logarithmic growth rate is a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting; it does not depend on the form of the weight function, although the optimal rate does. The existence of an optimal investment strategy has been established earlier in a great generality by Kramkov--Schachermayer (2003) although our underlying assumptions are different.
Total Quality Management and Performance of Small Medium Scale Enterprises (SMEs) in Nigeria

: SMEs in Nigeria have continued to experience poor quality of products and services despite concerted efforts by governments and the private sector to improve their standards of operations. Empirical research has tried to understand why there is consistent low level of quality products and services offered by SMEs in Nigeria. This study is therefore, an attempt to examine the Effect of TQM dimensions of customer focus, continuous process improvement and executive commitment on the performance of SMEs in Gboko Local Government. The study employed a cross-sectional research design on a population of 198 registered SMEs. Sampling produced a sample size of 132 while only 121 were used for data analysis. Questionnaire was used for data collection with validity and reliability established prior to data collection. Multiple regression analysis revealed that customer focus, continuous process improvement and executive commitment all had a positive significant effect explaining about 44.7 Percent variation in the performance of SMEs in Gboko Local Government. The study recommended that entrepreneurs should focus organizational energies and attention on meeting and exceeding customer expectations as this contributes the greatest in improving the performance of SMEs. SMEs owners should also show commitment and also not neglect to implement continuous process improvements as these have been shown to positively Effect business organizations. Benue shown strategic in understanding the that their of
Improper poisson line process as sirsn in any dimension

Aldous has introduced a notion of scale-invariant random spatial network (SIRSN) as a mathematical formalization of road networks. Intuitively, those are random processes that assign a route between each pair of points in Euclidean space, while being invariant under rotation, translation, and change of scale, and such that the routes are not too long and mainly on "main roads". The only known example was somewhat artificial since invariance had to be added at the end of the construction. We prove that the network of geodesics in the random metric space generated by a Poisson line process marked by speeds according to a power law is a SIRSN, in any dimension. Along the way, we establish bounds comparing Euclidean balls and balls for the random metric space. We also prove that in dimension more than two, the geodesics have "many directions" near each point where they are not straight.
Opportunities and Constraints of Scaling Up Electricity Access in the Gambia

: The availability of adequate, reliable, affordable and sustainable energy is a critical milestone in the socio-economic development of any country. In the Gambia less than half of the population (42%) has access to electricity; over 90% are still dependent on solid biomass for cooking and heating. This has significantly hampered development and intensified poverty. Thus, a top priority for the government today is to scale up electricity access in the country especially in the rural areas. To fulfill this objective, the government has taken a number of policies and strategies all gear towards increasing national electricity access in the country. Implementation of these initiatives in a form of projects through Least Cost Power Development Plan (LCPDP) strategy have yield significant opportunities in the attainment of national energy policy target of 2030 by increasing the number of household and businesses with access to electricity. Notwithstanding, this quest is equally face with constraints in the process.These substantial risk constraints include technical, institutional, policy and financial challenges. Therefore, this article conclude that in order to achieve a reliable and effective supply of the total electricity need within the prevailing condition, the Government should encourage Public Private Arrangement of power supply with indigenize energy entities who can met the generation capacity of 50-100MW.The results further suggest that NAWEC and the Government should sign a performance contractin addition to the already signed service contract. Also, the government should look beyond these short to medium‐term measures and diversify into the long term energy mix measures to include renewal into the grid system.
Education : Teaching and learning at school with artificial intelligence tools – Final report –

Presented by Dr. Ulrich Schmid, Dr. Berit Blanc, Michael Toepel (mmb Institut – Gesellschaft für Medienund Kompetenzforschung mbH) Collaborators: Prof. Dr. Niels Pinkwart (German Research Center for Artificial Intelligence) Prof. Dr. Hendrik Drachsler (DIPF | Leibniz Institute for Research and Information in Education) mmb Institut GmbH Folkwangstraße 1 D-45128 Essen Phone: 0201 / 748509-94 Email: schmid@mmb-institut.de Internet: www.mmb-institut.de
Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit

In this work we examine the effect of phase-space noncommutativity on some typically quantum properties such as quantum beating, quantum information, and decoherence. To exemplify these issues we consider the two-dimensional noncommutative quantum harmonic oscillator whose component behavior we monitor in time. This procedure allows us to determine how the noncommutative parameters are related to the missing information quantified by the linear quantum entropy and by the mutual information between the relevant Hilbert space coordinates. Particular questions concerning the thermodynamic limit of some relevant properties are also discussed in order to evidence the effects of noncommutativity. Finally, through an analogy with the Zeeman effect, we identify how some aspects of the axial symmetry of the problem suggest the possibility of decoupling the noncommutative quantum perturbations from unperturbed commutative well-known solutions.
Non-local Impedance Operator for Non-overlapping DDM for the Helmholtz Equation

In the context of time harmonic wave equations, the pioneering work of B. Després [4] has shown that it is mandatory to use impedance type transmission conditions in the coupling of sub‚domains in order to obtain convergence of non‚overlapping domain decomposition methods ̆DDM ̄. In later works [2, 3], it was observed that using non‚local impedance operators leads to geometric convergence, a property which is unattainable with local operators. This result was recently extended to arbitrary geo‚ metric partitions, including conigurations with cross‚points, with provably uniform stability with respect to the discretization parameter [1]. We present a novel strategy to construct suitable non‚local impedance operators that satisfy the theoretical requirements of [1] or [2, 3]. It is based on the solution of elliptic auxiliary problems posed in the vicinity of the transmission interfaces. The deinition of the operators is generic, with simple adaptations to the acoustic or electromagnetic settings, even in the case of heterogeneous media. Besides, no complicated tuning of parameters is required to get eiciency. The implementation in practice is straightforward and applicable to sub‚domains of arbitrary geometry, including ones with rough boundaries generated by automatic graph partitioners.
Time evolution of spin-boson system for different effective spectral density functions

In this paper we firstly obtain two kinds of effective spectral density functions by setting the cut-off frequencies of baths be infinite and finite. Secondly, we investigate the reduced dynamics of open qubits in four kinds of systems constructed with the basic spin-boson model. It is shown that the qubit has different dynamics governed by the two kinds of spectral density functions. In addition, we obtained that a qubit coupled to an intermediate harmonic oscillator has longer decoherence and relaxation times as they are coupled to a common bath than to their respective baths. In solving the dynamics of qubits we use a numerically exact algorithm, iterative tensor multiplication algorithm based on the quasiadiabatic propagator path integral scheme.
On the Asymptotic Behavior of a Dynamic Version of the Neyman Contagious Point Process

We consider a dynamic version of the Neyman contagious point process that can be used for modeling the spacial dynamics of biological populations, including species invasion scenarios. Starting with an arbitrary finite initial configuration of points in with nonnegative weights, at each time step a point is chosen at random from the process according to the distribution with probabilities proportional to the points’ weights. Then a finite random number of new points is added to the process, each displaced from the location of the chosen “mother” point by a random vector and assigned a random weight. Under broad conditions on the sequences of the numbers of newly added points, their weights and displacement vectors (which include a random environments setup), we derive the asymptotic behavior of the locations of the points added to the process at time step n and also that of the scaled mean measure of the point process after time step n → ∞.
Toward Green Residential Systems: Is Cooperation The Way Forward?

Achieving self-sustainability has been one of the key challenges in designing smart grid connected residential systems. Solar enabled and power grid connected, dual-powered residential systems is an attractive solution, but it is not carbon free and cost optimal for the end user. This paper proposes temporal energy cooperation among the dual-powered residences as a potential cost and energy efficient solution. Through this paper, we present a microgrid based, multi-residence cooperative energy transfer mechanism to offset the power grid dependency. The developed analytical framework characterizes the green energy storage as a discrete time Markov model and aims to exploit the temporal residential load variations, towards designing self-sustainable systems at a much lower capital expenditure (CAPEX). Our simulation results capture the variation of optimum residence cluster size as a function of energy sharing price and load skewness to become cost profitable. The results also demonstrate a significant reduction in CAPEX, achieved through the proposed energy cooperative framework, over a non-cooperative residential system.
Void space and scaffold analysis of packed particles: applications in granular biomaterials

We have developed a tool for analyzing packed particles in response to the growing popularity of granular biomaterials. Granular hydrogels, including microporous annealed particle (MAP) scaffolds, are a class of material used for therapeutic applications due to their unique properties, including micro-porosity between particles. The microarchitecture of granular materials is challenging to study, which leads many in the field to report the unreliable metric of void volume fraction and/or 2D-slice approximations to ‘pore size’ as the only characterizations of void space. In response, we have created LOVAMAP, a custom software that combines techniques from computational geometry and graph theory to segment the void space into 3-D pores, which are the natural pockets of open space. LOVAMAP’s 44 scaffold features provide the user with a quantitative profile that describes both the interior and entrances of the scaffold. Our visually-rich outputs address topics like void space size, shape, connectivity, paths, isotropy/anisotropy, ligand availability, and infiltration/migration restrictions. Using LOVAMAP, we have studied 60 different types of granular scaffolds, including real MAP scaffolds with corresponding cell data. We use higher dimensional analysis to show that output data from our software can be used to classify types of 3-D pores, as well as characterize entire scaffolds by generating a numeric ‘fingerprint. ’ In conjunction with cell data, LOVAMAP reveals relationships between neurosphere formation and scaffold void space geometry. LOVAMAP is an enabling technology with broad applications for granular biomaterial research and for all fields that study granular material. and the ‘pore size’ is measured as the diameter of the largest enclosed sphere (dusty rose). j, We compare pore size obtained using 2D-analysis vs. 3D-analysis for particle domains comprising 100 µm diameter spheres for three categories of particle stiffness: rigid, semi-soft, and soft (n = 10 each). For each scaffold, 2-D data refers to 2D-subunits from 30 evenly-spaced z-slices across the middle two-thirds of the scaffold, while 3-D data refers to all interior subunits. Results from the two-tailed Mann-Whitney test indicate that 2D-slice vs. LOVAMAP produces statistically different distributions for rigid and semi-soft domains ( p < 0.0001), while the Kolmogorov-Smirnov test shows statistical difference for rigid, semi-soft, and soft domains ( p < 0.0001). k, Showing particles and interior subunits of the following homogeneous domains: 60 spheres results support the notion that collective void space pore orientation follows collective particle orientation.
Variational View to Optimal Stopping Problems for Diffusion Processes and Threshold Strategies

We describe a variational approach to solving optimal stopping problems for diffusion processes, as an alternative to the traditional approach based on the solution of the free-boundary problem. We study smooth pasting conditions from a variational point of view, and give some examples when the solution to free-boundary problem is not the solution to optimal stopping problem. A special attention is paid to threshold strategies which allow reduce optimal stopping problem to more simple one-parametric optimization. Necessary and sufficient conditions for threshold structure of optimal stopping time are derived. We apply these results to both investment timing and optimal abandon models.
A Novel Intelligent Efficient and Dynamic Cluster Based Routing Protocol for IoT Assisted Precision Agriculture

: Day by day population of world is increasing, so there is crucial task in front of farmers to fulfill the basic need of food of individuals. Internet of Things (IoT) plays a crucial role in current agricultural practices for well in time results. An efficient working of IoT network requires intelligent, dynamic and efficient routing protocols which minimizes latency, improves the energy efficiency and increases network lifetime. Such protocols give better contribution in IoT assisted Precision Agriculture (PA) for getting higher yields in stipulated time. There is scope for improvement in the current IoT protocols. Our experimentation and simulation study introduces Novel Intelligent Robust Optimized Dynamic and Efficient Cluster (NIRODEC) based routing protocol for IoT assisted PA. NIRODEC highlights on minimizing latency, improving the energy efficiency and increases network lifetime. The results show that the NIRODEC protocol offers better performance than the protocols mentioned in the state of art. For the experimentation we have considered the case of identifying soil fertility and soil health with consumption of soil nutrients such as nitrogen (N), phosphorus (P), and potassium (K) etc.
Variable Speed Branching Brownian Motion 1. Extremal Processes in the Weak Correlation Regime

We prove the convergence of the extremal processes for variable speed branching Brownian motions where the "speed functions", that describe the time- inhomogeneous variance, lie strictly below their concave hull and satisfy a certain weak regularity condition. These limiting objects are universal in the sense that they only depend on the slope of the speed function at 0 and the nal time t. The proof is based on previous results for two-speed BBM obtained in Bovier and Hartung (2014) and uses Gaussian comparison arguments to extend these to the general case.
Distinct Phenotypic Consequences of Pathogenic C1q e Tumor Necrosis Factor-5 Q3 Mutants Associated with Late-Onset Retinal Degeneration

A pathologic feature of late-onset retinal degeneration caused by the S163R mutation in C1q e tumor necrosis factor-5 (C1QTNF5) is the presence of unusually thick deposits between the retinal pigmented epithelium (RPE) and the vascular choroid, considered a hallmark of this disease. We have previously demonstrated that following its speci ﬁ c expression in mouse RPE, the S163R mutant exhibits a reversed polarized distribution relative to the apically secreted wild-type C1QTNF5, and forms widespread, prominent deposits that gradually increase in size with aging. This study shows that S163R deposits expand to a considerable thickness through a progressive increase in the basolateral RPE membrane, substantially raising the total RPE height, and enabling their clear imaging as a distinct hypore ﬂ ective layer by noninvasive optical coherence tomography in advanced aged animals. This phenotype bears a striking similarity to ocular pathology previously documented in patients harboring the S163R mutation. Therefore, we used a similar viral vector-based gene delivery approach to investigate the behavior of two novel pathogenic C1QTNF5 mutants recently reported in patients, P188T and G216C, for which histopathologic data are lacking. We found that both mutants primarily impact the RPE/photoreceptor interface and do not generate basal laminar deposits. The results demonstrate distinct distribution patterns and phenotypic consequences of C1QTNF5 mutants in vivo and suggest that multiple pathobiological mechanisms contribute to RPE dysfunction and vision loss in this disorder. (Am J Pathol 2022, - : 1 e 15;
When Sets Are Not Sum-Dominant

Given a set $A$ of nonnegative integers, define the sum set $$A+A = \{a_i+a_j\mid a_i,a_j\in A\}$$ and the difference set $$A-A = \{a_i-a_j\mid a_i,a_j\in A\}. $$ The set $A$ is said to be sum-dominant if $|A+A|>|A-A|$. In answering a question by Nathanson, Hegarty used a clever algorithm to find that the smallest cardinality of a sum-dominant set is $8$. Since then, Nathanson has been asking for a human-understandable proof of the result. We offer a computer-free proof that a set of cardinality less than $6$ is not sum-dominant. Furthermore, we prove that the introduction of at most two numbers into a set of numbers in an arithmetic progression does not give a sum-dominant set. This theorem eases several of our proofs and may shed light on future work exploring why a set of cardinality $6$ is not sum-dominant. Finally, we prove that if a set contains a certain number of integers from a specific sequence, then adding a few arbitrary numbers into the set does not give a sum-dominant set.
Winning the Internet: A tool for simulating the competitive strategies of satellite-based internet providers

New satellite operators, a changing technological landscape, and increased user demand are poised to remake the current satellite-based internet landscape. Estimation of long-term revenues under various market and competitive assumptions is of interest to operators, customers, and investors. This paper presents an algorithm for simulating the competitive interactions between satellite operators as they compete for a heterogenous, global market. The theoretical underpinnings of the algorithm are presented with reference to economic and aerospace principles. The algorithm’s implementation is then discussed in detail with critical numerical steps and assumptions outlined. A low-order example using representative satellite operators, customers, and contracts is used to illustrate the use of the tool. Results from the low order model agree with prevailing market opinions and show consistent growth for the sector over the upcoming decade. The focus of this paper is on the algorithm and its implementation. A follow-up paper will provide more specific market predictions through enumeration of individual customers and operators.
Two weight commutators for Beurling--Ahlfors operator

We establish the equivalent characterisation of the weighted BMO space on the complex plane $\mathbb{C}$ via the two weight commutator of the Beurling--Ahlfors operator with a BMO function. Our method of proofs relies on the explicit kernel of the Beurling--Ahlfors operator and the properties of Muckenhoupt weight class.
Age evolution in the mean field forest fire model via multitype branching processes

We study the distribution of ages in the mean field forest fire model introduced by Rath and Toth. This model is an evolving random graph whose dynamics combine Erdős-Renyi edge-addition with a Poisson rain of lightning strikes. All edges in a connected component are deleted when any of its vertices is struck by lightning. We consider the asymptotic regime of lightning rates for which the model displays self-organized criticality. The age of a vertex increases at unit rate, but it is reset to zero at each burning time. We show that the empirical age distribution converges as a process to a deterministic solution of an autonomous measure-valued differential equation. The main technique is to observe that, conditioned on the vertex ages, the graph is an inhomogeneous random graph in the sense of Bollobas, Janson and Riordan. We then study the evolution of the ages via the multitype Galton--Watson trees that arise as the limit in law of the component of an identified vertex at any fixed time. These trees are critical from the gelation time onwards.