Miracle-dz/UniFAR-FTUs huggingface dataset:
Efficient Clustering Using Alternating Minimization And A Projection-Gradient Method For Dimension Reduction

This paper deals with unsupervised clustering in high dimensional space. The problem is to estimate both labels and a sparse projection matrix of weights. To address this combinatorial non-convex problem maintaining a strict control on the sparsity of the matrix of weights, we propose an alternating minimization of the Frobenius norm criterion. We provide a new efficient algorithm named k-sparse which alternates k-means with projection-gradient minimization. The projection-gradient step is a method of splitting type, with exact projection on the ℓ1 ball to promote sparsity. The convergence of the gradient-projection step is addressed, and a preliminary analysis of the alternating minimization is provided. Experiments on Single Cell RNA sequencing datasets show that our method significantly improves the results of spectral clustering, SIMLR, and Sparcl methods. The complexity of our method is linear with the number of samples (cells), so that the method scales up to large datasets.
K-theory of derivators revisited

We define a $K$-theory for pointed right derivators and show that it agrees with Waldhausen $K$-theory in the case where the derivator arises from a good Waldhausen category. This $K$-theory is not invariant under general equivalences of derivators, but only under a stronger notion of equivalence that is defined by considering a simplicial enrichment of the category of derivators. We show that derivator $K$-theory, as originally defined, is the best approximation to Waldhausen $K$-theory by a functor that is invariant under equivalences of derivators.
Catalytic Esterification of Levulinic Acid into the Biofuel n-Butyl Levulinate over Nanosized TiO2 Particles

Levulinic esters, synthesized by the esterification of biomass-derived levulinic acid with various alcohols, is an important chemical that plays an essential role in the fields of biomass fuel additives, organic synthesis, and high value-added products. In the present work, the catalytic esterification of levulinic acid with n-butyl alcohol was selected as a typical model reaction to investigate the catalytic performance of an inexpensive commercial catalyst, titanium oxide nanoparticles. The influences of reaction time, reaction temperature, and catalyst loading on the conversion of levulinic acid to n-butyl levulinate were systematically examined through single-factor experiments. Additionally, the optimization of the reaction conditions was further investigated by a Box–Behnken design in response to the surface methodology. The desired product, n-butyl levulinate, with a good yield (77.6%) was achieved under the optimal conditions (reaction time of 8 h, reaction temperature of 120 °C, and catalyst dosage of 8.6 wt.%) when using titanium oxide nanoparticles as catalysts. Furthermore, it was found that addition of water to the catalytic system facilitated the reaction process, to some extent. This study reveals that the nanosized TiO2 material, as an efficient solid acid catalyst, had good catalytic performance and stability for the esterification of levulinic acid after six consecutive uses.
Bloch Waves in Bubbly Crystal Near the First Band Gap: A High-Frequency Homogenization Approach

This paper is concerned with the high-frequency homogenization of bubbly phononic crystals. It is a follow-up of the works [H. Ammari et al., Sub-wavelength phononic bandgap opening in bubbly media, J. Diff. Eq., 263 (2017), 5610--5629] which shows the existence of a sub-wavelength band gap. This phenomena can be explained by the periodic inference of cell resonance which is due to the high contrast in both the density and bulk modulus between the bubbles and the surrounding medium. In this paper, we prove that the first Bloch eigenvalue achieves its maximum at the corner of the Brillouin zone. Moreover, by computing the asymptotic of the Bloch eigenfunctions in the periodic structure near that critical frequency, we demonstrate that these eigenfunctions can be decomposed into two parts: one part is slowly varying and satisfies a homogenized equation, while the other is periodic across each elementary crystal cell and is varying. They rigorously justify, in the nondilute case, the observed super-focusing of acoustic waves in bubbly crystals near and below the maximum of the first Bloch eigenvalue and confirm the band gap opening near and above this critical frequency.
Design and Analysis of Heuristic Algorithms for Energy-Constrained Task Scheduling With Device-Edge-Cloud Fusion

Mobile edge computing with device-edge-cloud fusion provides a new type of heterogeneous computing environment. We consider task scheduling with device-edge-cloud fusion (without energy concern) and energy-constrained task scheduling with device-edge-cloud fusion as combinatorial optimization problems. The main contributions of the paper are summarized as follows. We design three heuristic algorithms for task scheduling with device-edge-cloud fusion and prove an asymptotic performance bound. We design one heuristic algorithm for energy-constrained task scheduling with device-edge-cloud fusion, which solves the two subproblems of task scheduling and power allocation in an interleaved way. We derive lower bounds for the optimal solutions for both task scheduling with device-edge-cloud fusion and energy-constrained task scheduling with device-edge-cloud fusion, so that the performance of our heuristic algorithms can be compared with that of an optimal algorithm. We experimentally evaluate the performance of our heuristic algorithms and find that the performance of our heuristic algorithms are very close to that of optimal algorithms. To the best of our knowledge, this is the first paper which studies task scheduling with device-edge-cloud fusion and energy-constrained task scheduling with device-edge-cloud fusion as combinatorial optimization problems and conducts analytical performance evaluation.
Therapeutic Ultrasound Halts Progression of Chronic Kidney Disease In Vivo via the Regulation of Markers Associated with Renal Epithelial–Mesenchymal Transition and Senescence

Low-intensity pulsed ultrasound (LIPUS), a therapeutic type of ultrasound, is known to enhance bone fracture repair processes and help some tissues to heal. Here, we investigated the therapeutic potential of LIPUS for the treatment of chronic kidney disease (CKD) in two CKD mouse models. CKD mice were induced using both unilateral renal ischemia/reperfusion injury (IRI) with nephrectomy and adenine administration. The left kidneys of the CKD mice were treated using LIPUS with the parameters of 3 MHz, 100 mW/cm2, and 20 min/day, based on the preliminary experiments. The mice were euthanized 14 days after IRI or 28 days after the end of adenine administration. LIPUS treatment effectively alleviated the decreases in the body weight and albumin/globulin ratio and the increases in the serum renal functional markers, fibroblast growth factor-23, renal pathological changes, and renal fibrosis in the CKD mice. The parameters for epithelial–mesenchymal transition (EMT), senescence-related signal induction, and the inhibition of α-Klotho and endogenous antioxidant enzyme protein expression in the kidneys of the CKD mice were also significantly alleviated by LIPUS. These results suggest that LIPUS treatment reduces CKD progression through the inhibition of EMT and senescence-related signals. The application of LIPUS may be an alternative non-invasive therapeutic intervention for CKD therapy.
Tensor splitting properties of n-inverse pairs of operators

In this paper we study n-inverse pairs of operators on the tensor product of Banach spaces. In particular we show that an n-inverse pair of elementary tensors of operators on the tensor product of two Banach spaces can arise only from l- and m-inverse pairs of operators on the individual spaces. This gives a converse to a result of Duggal and M\"uller, and proves a conjecture of the second named author. Our proof uses techniques from algebraic geometry, which generalize to other relations among operators in a tensor product. We apply this theory to obtain results for n-symmetries in a tensor product as well.
Reduction by symmetries in singular quantum-mechanical problems: General scheme and application to Aharonov-Bohm model

We develop a general technique for finding self-adjoint extensions of a symmetric operator that respects a given set of its symmetries. Problems of this type naturally arise when considering two- and three-dimensional Schrodinger operators with singular potentials. The approach is based on constructing a unitary transformation diagonalizing the symmetries and reducing the initial operator to the direct integral of a suitable family of partial operators. We prove that symmetry preserving self-adjoint extensions of the initial operator are in a one-to-one correspondence with measurable families of self-adjoint extensions of partial operators obtained by reduction. The general scheme is applied to the three-dimensional Aharonov-Bohm Hamiltonian describing the electron in the magnetic field of an infinitely thin solenoid. We construct all self-adjoint extensions of this Hamiltonian, invariant under translations along the solenoid and rotations around it, and explicitly find their eigenfunction expansions.
On the observability inequality of coupled wave equations: the case without boundary

In this paper, we study the observability and controllability of wave equations coupled by first or zero order terms on a compact manifold. We adopt the approach in Dehman-Lebeau’s paper [B. Dehman and G. Lebeau, SIAM J. Control Optim. 48 (2009) 521–550. ] to prove that: the weak observability inequality holds for wave equations coupled by first order terms on compact manifold without boundary if and only if a class of ordinary differential equations related to the symbol of the first order terms along the Hamiltonian flow are exactly controllable. We also compute the higher order part of the observability constant and the observation time. By duality, we obtain the controllability of the dual control system in a finite co-dimensional space. This gives the full controllability under the assumption of unique continuation of eigenfunctions. Moreover, these results can be applied to the systems of wave equations coupled by zero order terms of cascade structure after an appropriate change of unknowns and spaces. Finally, we provide some concrete examples as applications where the unique continuation property indeed holds.
Homological Algebra for Superalgebras of Differentiable Functions

This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we extend the classical notion of a dg-algebra to define, in particular, the notion of a differential graded algebra in the world of C-infinity rings. The opposite of the category of differential graded C-infinity algebras contains the category of differential graded manifolds as a full subcategory. More generally, this notion of differential graded algebra makes sense for algebras over any (super) Fermat theory, and hence one also arrives at the definition of a differential graded algebra appropriate for the study of derived real and complex analytic manifolds and other variants. We go on to show that, for any super Fermat theory S which admits integration, a concept we define and show is satisfied by all important examples, the category of differential graded S-algebras supports a Quillen model structure naturally extending the classical one on differential graded algebras, both in the bounded and unbounded case (as well as differential algebras with no grading). Finally, we show that, under the same assumptions, any of these categories of differential graded S-algebras have a simplicial enrichment, compatible in a suitable sense with the model structure.
Scaling limits of energies and correctors

In stochastic homogenization of elliptic equations, the corrector plays a central role. Under a finite range of dependence assumption on the coefficient field, we show that the large-scale spatial averages of the corrector approach those of a variant of the Gaussian free field. In contrast to previous work, the argument does not rely on an underlying product structure of the probability measure. Instead, we rely on the additivity of energy quantities to show central limit theorems for these, and derive the large-scale behavior of the corrector as a consequence.
Dynamics of continued fractions and distribution of modular symbols

We formulate a thermodynamical approach to the study of distribution of modular symbols, motivated by the work of Baladi-Vallee. We introduce the modular partitions of continued fractions and observe that the statistics for modular symbols follow from the behavior of modular partitions. We prove the limit Gaussian distribution and residual equidistribution for modular partitions as a vector-valued random variable on the set of rationals whose denominators are up to a fixed positive integer by studying the spectral properties of transfer operator associated to the underlying dynamics. The approach leads to a few applications. We show an average version of conjectures of Mazur-Rubin on statistics for the period integrals of an elliptic newform. We further observe that the equidistribution of mod $p$ values of modular symbols leads to mod $p$ non-vanishing results for special modular $L$-values twisted by a Dirichlet character.
Property $(TT)$ modulo $T$ and homomorphism superrigidity into mapping class groups

Every homomorphism from finite index subgroups of a universal lattices to mapping class groups of orientable surfaces (possibly with punctures), or to outer automorphism groups of finitely generated nonabelian free groups must have finite image. Here the universal lattice denotes the special linear group G=SL_m(Z[x1,.,xk]) with m at least 3 and k finite. Moreover, the same results hold ture if universal lattices are replaced with symplectic universal lattices Sp_{2m}(Z[x1,.,xk]) with m at least 2. These results can be regarded as a non-arithmetization of the theorems of Farb--Kaimanovich--Masur and Bridson--Wade. A certain measure equivalence analogue is also established. To show the statements above, we introduce a notion of property (TT)/T ("/T" stands for "modulo trivial part"), which is a weakening of property (TT) of N. Monod. Furthermore, symplectic universal lattices Sp_{2m}(Z[x1,.,xk]) with m at least 3 has the fixed point property for L^p-spaces for any p in (1,infinity).
Assessing the Value of Including Unimodality Information in Distributionally Robust Optimization Applied to Optimal Power Flow

Uncertainties, such as renewable generation and load consumption, has been a major source of risk in power system planning. To safely incorporate these uncertainties, we need to ensure all physical constraints affected are satisfied at high probability level. To manage the uncertainties, different stochastic optimal power flow formulations have been proposed. Conventional approaches either provide over-conservative results or rely on accurate estimates on uncertainty distributions. Recently, an alternative distributionally robust optimal power flow formulations with only data-driven moment information are shown to provide better trade-offs between objective and reliability. In this paper, we further consider a distributionally robust optimal power flow problems with both moment and unimodality information, based on the facts that most practical uncertainties are unimodal. We formulate the problem using chance constraint and provide various reformulations and approximations with efficient solving techniques. We evaluate the proposed approaches on the modified IEEE 118/300-bus system with high penetrated renewable generation and demonstrate the values of including the unimodality information and benefits against the conventional approaches.
Numerical Simulations of Drainage Grooves in Response to Extensional Fracturing: Testing the Phobos Groove Formation Model

The long, shallow, parallel grooves that cut across the surface of the Martian moon Phobos remain enigmatic, with distinct implications for understanding the evolution of loose airless soils and the origin of Mars and its satellites. Phobos orbits deep inside the fluid Roche limit and is gradually spiraling in, creating global tidal strain, which leads to a model in which orbital decay is driving the formation of surface grooves on Phobos. Here we test this model by simulating the extension of a mildly cohesive regolith shell, driven by Phobos’s tidal strain imposed by orbital migration. Modeling Phobos as a rubble-pile interior overlaid by a cohesive layer, we find that the tidal strain could create parallel fissures with regular spacing, depending on the latitude and longitude. Fracture opening triggers drainage of upper loose material into these deep-seated valleys, which we show could lead naturally to the formation of groove-like structures. We map the prominent linear depressions on Phobos and find that some at midlatitudes correlate with the model-predicted groove orientations. Our analysis supports a layered heterogeneous structure for Phobos with possible underlying failure-induced fractures, as the precursor of the eventual demise of the de-orbiting satellite. However, we do observe significant areas showing absences and anomalies that are not consistent with the tidal fracturing model. The in situ observations on Phobos by the Mars Moons eXploration mission will conclusively determine the origin of its enigmatic striations.
Uniform Yomdin–Gromov parametrizations and
points of bounded height in valued fields

We prove a uniform version of non-Archimedean Yomdin-Gromov parametrizations in a definable context with algebraic Skolem functions in the residue field. The parametrization result allows us to bound the number of F_q[t]-points of bounded degrees of algebraic varieties, uniformly in the cardinality q of the finite field F_q and the degree, generalizing work by Sedunova for fixed q. We also deduce a uniform non-Archimedean Pila-Wilkie theorem, generalizing work by Cluckers-Comte-Loeser.
Higher-order linking forms for knots

We construct examples of knots that have isomorphic $n$th-order Alexander modules, but non-isomorphic $n$th-order linking forms, showing that the linking forms provide more information than the modules alone. This generalizes work of Trotter [T], who found examples of knots that have isomorphic classical Alexander modules, but non-isomorphic classical Blanchfield linking forms.
Earthworm invasion in Chayu River valley of Tibet under climate change

Climate change affects biological invasion. To understand the invasion pattern of alien species of earthworm in Gongrigabu river watershed of Chayu river in Tibet under climate change, the participate rural appraise (PRA) was applied to investigate and analyze the peasant’s perception of the appearance time and harm of alien species of earthworm in 13 villages. The results showed that the local climate was warming and drying, and climate warming was the main reason for the invasion of alien species of earthworms. Since the appearance of alien species of earthworm at an altitude of 1528 m in 2008, they had invaded the upstream area at a climbing speed of 71.43 m·a-1 and had been outbreaking in areas below 2028 m. For the climate change adaptation measures, the local peasants should change the crop layout.
3D gravity inversion based on deep learning

Gravity inversion is a typical geophysical inversion method that obtains the underground density distribution by analyzing the gravity anomaly. Normally, it can be divided into geophysics-based and deep learning based inversion. The 3D geophysics-based inversion is a time- and memory-consuming method, so 3D inversion is not routinely implemented in practical data interpretation. Here, we propose a deep learning method to transfer the 3D inversion problem to a multiple layers 2D mapping problem by decomposing the 3D target into four 2D images, including the horizontal location, vertical center, thickness and density distribution. This method is denoted as “decomposition network”. By implementing synthetic experiments with regular and complex models, and comparing with the 3D U-Net inversion, the proposed network has proved can reconstruct underground targets with high accuracy and high efficiency.
Floer theory for Hamiltonian PDE using model theory

Under natural restrictions it is known that a nonlinear Schr\"odinger equation is a Hamiltonian PDE which defines a symplectic flow on a symplectic Hilbert space preserving the Hilbert norm. When the potential is one-periodic in time and after passing to the projectivization, it makes sense to ask whether the natural analogue of the Arnold conjecture holds. After employing methods from non-standard model theory, we show how Hamiltonian Floer theory can be used to prove the existence of infinitely many fixed points of the time-one flow of nonlinear Schr\"odinger equations of convolution type.
Rank two vector bundles on polarised Halphen surfaces and the Gauss-Wahl map for du Val curves

A genus-g du Val curve is a degree-3g plane curve having 8 points of multiplicity g, one point of multiplicity g-1, and no other singularity. We prove that the corank of the Gauss-Wahl map of a general du Val curve of odd genus (>11) is equal to one. This, together with the results of [1], shows that the characterisation of Brill-Noether-Petri curves with non-surjective Gauss-Wahl map as hyperplane sections of K3 surfaces and limits thereof, obtained in [3], is optimal.
Greedy Adaptive Compression in Signal-Plus-Noise Models

The purpose of this article is to examine the greedy adaptive measurement policy in the context of a linear Guassian measurement model with an optimization criterion based on information gain. In the special case of sequential scalar measurements, we provide sufficient conditions under which the greedy policy actually is optimal in the sense of maximizing the net information gain. In the general setting, we also discuss cases where the greedy policy is not optimal.
Modeling post-holiday surge in COVID-19 cases in Pennsylvania counties

COVID-19 arrived in the United States in early 2020, with cases quickly being reported in many states including Pennsylvania. Many statistical models have been proposed to understand the trends of the COVID-19 pandemic and factors associated with increasing cases. While Poisson regression is a natural choice to model case counts, this approach fails to account for correlation due to spatial locations. Being a contagious disease and often spreading through community infections, the number of COVID-19 cases are inevitably spatially correlated as locations neighboring counties with a high COVID-19 case count are more likely to have a high case count. In this analysis, we combine generalized estimating equations for Poisson regression, a popular method for analyzing correlated data, with a semivariogram, to model daily COVID-19 case counts in 67 Pennsylvania counties between March 20, 2020 to January 23, 2021 in order to study infection dynamics during the beginning of the pandemic. We use a semivariogram that describes the spatial correlation as a function of the distance between two counties as the working correlation. We further incorporate a zero-inflated model in our spatial GEE to accommodate excess zeros in reported cases due to logistical challenges associated with disease monitoring. By modeling time-varying holiday covariates, we estimated the effect of holiday timing on case count. Our analysis showed that the incidence rate ratio was significantly greater than one, 6-8 days after a holiday suggesting a surge in COVID-19 cases approximately one week after a holiday.